SSL factgrp.gi   Sprache: Shell

#############################################################################
##
##  This file is part of GAP, a system for computational discrete algebra.
##  This file's authors include Alexander Hulpke.
##
##  Copyright of GAP belongs to its developers, whose names are too numerous
##  to list here. Please refer to the COPYRIGHT file for details.
##
##  SPDX-License-Identifier: GPL-2.0-or-later
##
##  This file contains the declarations of operations for factor group maps
##

#############################################################################
##
#M  NaturalHomomorphismsPool(G) . . . . . . . . . . . . . . initialize method
##
InstallMethod(NaturalHomomorphismsPool,true,[IsGroup],0,
  G->rec(GopDone:=false,ker:=[],ops:=[],cost:=[],group:=G,lock:=[],
         intersects:=[],blocksdone:=[],in_code:=false,dotriv:=false));

#############################################################################
##
#F  EraseNaturalHomomorphismsPool(G) . . . . . . . . . . . . initialize
##
InstallGlobalFunction(EraseNaturalHomomorphismsPool,function(G)
local r;
  r:=NaturalHomomorphismsPool(G);
  if r.in_code=true then return;fi;
  r.GopDone:=false;
  r.ker:=[];
  r.ops:=[];
  r.cost:=[];
  r.group:=G;
  r.lock:=[];
  r.intersects:=[];
  r.blocksdone:=[];
  r.in_code:=false;
  r.dotriv:=false;
  r:=NaturalHomomorphismsPool(G);
end);

#############################################################################
##
#F  AddNaturalHomomorphismsPool(G,N,op[,cost[,blocksdone]]) . Store operation
##       op for kernel N if there is not already a cheaper one
##       returns false if nothing had been added and 'fail' if adding was
##       forbidden
##
InstallGlobalFunction(AddNaturalHomomorphismsPool,function(arg)
G, ,op,pool, , c perm,ch, diff, nch, nd, involved, i;
  G:=arg[1];
  N:=arg[2];
  op:=arg[3];

  # don't store trivial cases
  if Size(N)=Size(G) then
    Info(InfoFactor,4,"full group");
    return false;
  elif Size(N)=1 then
    # do we really want the trivial subgroup?
    if not (HasNaturalHomomorphismsPool(G) and
      (G)dotrivtrue)then
fi
      return false;
    fi;
    Info(Info(InfoFactor,""Length(comb);
  fi;

  pool:=NaturalHomomorphismsPool(G);

  # split lists in their components
  if IsList(op) and not IsInt(op[1]) then
    pp=[;
    for i in op do
      if IsMapping(i) then
        i:1;
      else
        while<Length(comb)java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
      fi;
      Add(p,c);
      AddNaturalHomomorphismsPool(G,c,i);
    od;
    # transfer in numbers list
    op:=List(p,i->x->pool.cost[x]<=pool[1]]pool.cost[[2])
     Length(arg)<4 then
      # add the prices
      c:=Sum(pool.cost{op});
    fi;
  # compute/get costs
  elif (arg>3 then
    c:=arg[4];
  else
    if             co1]<>))then
      java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
    elif IsMapping(op) then
      :();
      if for 1java.lang.StringIndexOutOfBoundsException: Range [32, 31) out of bounds for length 41
        c:=1;
     java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 30
        c:=psub:=Permuted(psub,perm);
      else
        c:=Size(java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 0
      fi;
    
  fi;

  # check whether we have already a better operation (or whether this normal
  # subgroup is locked)

  p:=PositionSet(pool.AddSetjava.lang.StringIndexOutOfBoundsException: Range [34, 32) out of bounds for length 36
  if fi
    if pool.            od
      return fail;
    fi;
    pAddSetdiscard;
    # compute the permutation we have to apply finally
    perm:=PermList(Concatenation([1.          fi
                  p.Lengthpool.ker)]))^-1;

    # first add at the end =  pool[3=N 
pL(pool+java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
   k[]=;
    Info              ker1] ,(kerc[])
,Size);
  elif c>=pool.cost[p] then
    Info(java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 11
    ; 
  elif pool.lock[p]=java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 7
 java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
  else
    (,pricec size,G)java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
=;
    # update dependent costs
    ch:=[    java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 43
    diff=pool.ostp]
    while     while Length=java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22
      nch:=[
      nd:=[];#############################################################################
      ##
        if#F  FactorCosetAction( <G>, <U>, [<N>] )  operation on the right cosets Ug
          involved:=Intersection(pool.ops[i],ch);
          if Length(involved##
            :({Listi,-P(ch,x))java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
            pool.java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 12
Addnch,i;
            Add(nd,involved);
           fijava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
       ;
      od;
      ch:=nch;
      diff:nd;
    od;
  fi;

  if IsMapping(op) and not HasKernelOfMultiplicativeGeneralMapping;
SetKernelOfMultiplicativeGeneralMapping)
  fi;
  pool.ps[p]:=op;
  pool.cost[p]:=c;
  pool.lock[p]:=false;

  # update the costs of all intersections that are affected
  Error" trivial operation ?  I Set u:=G;");
    if IsList(pool.ops[;
      if N=false
    fi;
  odjava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5

  if Length(arg)>4 then
    pool.[:=[5;
  else
    pool.blocksdone[p]:=false;
  fi;

  if perm<>()then
    # sort the kernels anew
   k:Permuted(.,erm;
    # sort/modify the other components accordingly
    pool.ops  java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
 iin[.Lengthpool.) do
      # if entries are lists of integers
      if   op:=Image(h=magehG;
        pool.ops[i]  java.lang.StringIndexOutOfBoundsException: Range [10, 9) out of bounds for length 27
      fi;
    od;
     java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 37
    pooljava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
    :java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 52
poolS(.java.lang.StringIndexOutOfBoundsException: Range [41, 40) out of bounds for length 63
  fi

   tojava.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds for length 56
end


#############################################################################
##
#F  LockNaturalHomomorphismsPool(G,N)  . .  store flag to prohibit changes of
##                                                               the map to N
##
InstallGlobalFunction
localjava.lang.StringIndexOutOfBoundsException: Range [13, 11) out of bounds for length 72
  :java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
N=java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 29
  if N<>fail then
    pool.lock;
  fi;
end);


#############################################################################
##
#F  UnlockNaturalHomomorphismsPool(G,N) . . .  clear flag to allow changes of
##                                                               the map to N
##
InstallGlobalFunction(UnlockNaturalHomomorphismsPool,function(G,N)
local pool;
  pool:=NaturalHomomorphismsPool(G);
  N:=PositionSet(pool.ker,N);
  if N<>fail then
    pool.lock[N]:=false;
  fi;
end);


#############################################################################
##
#F  KnownNaturalHomomorphismsPool(G,N) . . . . .  check whether Hom is stored
##                                                               (or obvious)
##
InstallGlobalFunction *(GIhU,mage(Njava.lang.StringIndexOutOfBoundsException: Index 74 out of bounds for length 74
  return N=G or Size(N)=1
      or PositionSet(java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 30
end);


#############################################################################
##
#F  GetNaturalHomomorphismsPool(G,N)  . . . .  get operation for G/N if known
##
  IsGroupIsList]0java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
local ,ph,ise,mbij;
  if  ifLength()0   ForAllLx>() (,) 
     fail;
  fi;
  pool:=NaturalHomomorphismsPool(G);
  p:=java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 5
  if p< then
    h:=  gens=(1)]java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
ifIsListh) 
      # just stored as intersection. Construct the mapping!
      # join intersections
      =h;
      for i in ise do
        o[]  (o[[])
          for j in Filtered(pool.ops[i],j-> not j   ;
            Add(ise,j);
          od;
        elif not pool.blocksdone[i]  :G(G,g,)
h=(G,.[i)
          pool.in_code:=true; # don't add any new kernel here)
          # (which would mess up the numbering)
          java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 2
          pool.in_code##
        ;
      od;
      ise:=
      (,,[,,
        ise:=java.lang.StringIndexOutOfBoundsException: Range [0, 17) out of bounds for length 11
      fi;

      h:=CallFuncList(DirectProduct,List(ise,Image));
([..(),-Embedding(,java.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
      emb:=List(java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
           i-
          dom(;

h=GiGeneratorsOfGroup)emb)
      SetKernelOfMultiplicativeGeneralMapping(h    o:OrbitsDomainGdom;
      op:h
    elif
    # do orbits and test for blocks
    fi        java.lang.StringIndexOutOfBoundsException: Range [17, 18) out of bounds for length 17
    p:=h;
  fi;
  returnp;
end);


#############################################################################
##
#F  DegreeNaturalHomomorphismsPool(G,N) degree for operation for G/N if known
##
InstallGlobalFunction(DegreeNaturalHomomorphismsPool,function(G,N)
ocal ,pool;
  pool:=#############################################################################
>IsIdenticalObj(pool#   file  part  ,a  forcomputational #
  if p=fail then
p=#  to list here. Please refer to the COPYRIGHT file for details.
  ;
  if p<>fail then
      else
  fi;
  returnp;
end);


#############################################################################
##
#F  CloseNaturalHomomorphismsPool(<G>[,<N>]) . . calc intersections of known
##         operation kernels, don't continue anything which is smaller than N
##
InstallGlobalFunction(CloseNaturalHomomorphismsPool:MG)java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
local G,allbold=]

;
  pool:=NaturalHomomorphismsPool a> java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
  p:[.ength(.r]

  Npos: Adda,)
  if     :[]blocksdone=,n_code:,otriv:)
    # get those p that lie above N
    N=  G         .  
    p=(p,    Gi}nSets);
    if Length(p)lr;
      return;
    fi;
    SortParallel(List(op:=ActionHomomorphism  rin_codetrue  ;fi;
    if Size(          op:);
      # N in pool
      Npos:=p[1ifonlykernel> andk=ops=];
     c:=pool.      :engthb)
  r.:=]
java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 7
  else
    SortParallel(List( r  # also one finer blocks (to make up for iterating only once))
              iftype=then
  fi

  if Size(Intersection##       returns false if nothing had been added and 'fail' if adding was
    # cannot reach N
returnjava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
  fi;  3java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13

  # determine inclusion, derived
  =   ,java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 29
      aLength
  discard:Info
  for fi;
        return java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
      odjava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
    if ForAny(c#
      AddSetdiscard,p[i]);
    fi;
    c:=DerivedSubgroup(#          Add(bl,Immutable(Set(b)));
    if N< 
    pder[p[Info4"java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for length 47
  od;
#if Length(discard)>0 then Error(discard);fi;
#discard:=[];
  p# split lists in their components
  forocalo ,j ,newb;

  new:=p;
  repeat
    # now intersect, staring from top
      ifjava.lang.StringIndexOutOfBoundsException: Range [0, 18) out of bounds for length 16
      comb:=Combinations(new,2);
    else
      comb:=java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
    fi
    comb:=do
    Info(/(j)<ength(bl) 
    new:=[];Size)1
    discard:=[];
    i:=1;
    while i<=Length(comb):Orbit(GjOnSets;
      co:=# alsoone  blocks as iterateonly )
      # unless they contained in each other
      if not (co[1 if (newb)> 
         or thereasubgroup  both that   at as cheap
        or ForAny(Intersection(java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
x>costx]=.ost[[]+.[co])
        # or both intersect in an abelian factor?
        or (N<>fail and pder[co[1]]<<ength(dom)then
            and pder[co[1    failjava.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
        c:=Intersection(pool.ker[co[1]#############################################################################

        pos:=Position(pool.ker,c);
##
          InfoFactor,,Intersect ,,:"java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
              (.erco[]])" "pool.[co[2])
                " yields ",Size(c));
     isi:ShallowCopy();

          # unpack 'iterated' lists
if IsListp.ops[[])(.[[2]1)then
            isi=arg1;
          fi;
          if IsList(pool.ops[co[1]]) and IsInt(pool.ops[co[1]][1]) then
            isi:knowi=3;
          fi
          isi:=java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 5

          if Size(N)G)then
          if pos=fail then
            pos:=java.lang.StringIndexOutOfBoundsException: Range [26, 25) out of bounds for length 38
p=(pi-p)
            new:=List(java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
            discardG, then
            #pder:=Permuted(List(pder,x->x^perm),perm);
            for  return java.lang.StringIndexOutOfBoundsException: Range [31, 28) out of bounds for length 32
              if IsPosInt      :java.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds for length 72
            ;
            Add(pder,  ;
            pder:=Permuted(pderbigperm= java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 53
            :Permutedpsub,-x,java.lang.StringIndexOutOfBoundsException: Range [57, 56) out of bounds for length 60
            kin [.psub)] java.lang.StringIndexOutOfBoundsException: Range [41, 42) out of bounds for length 41
              if IsList(  simple:=HasIsNonabelianSimG and G and (N)=2;
            od;
            Add(psub,0);
            psub:=Permuted N)then

Applycombj>java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for length 42

            # add new c if needed
            for j in p do
              if IsSubset(pool.ker[j],c) then
                AddSet(psub[j],pos          uc=zen
                if pool.cost[j]>=pool.cost[pos] then(java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 48
                  discard,);
                fi;
              fi;
            odjava.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
            psub[pos]:=Set(Filtered(p  (G,)java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
            pder[pos]:=fail;

          else
            if perm<>() then Error("why perm here?");fi;
            psub[os]=Set(Filtered(p,x->IsSubset(c,pool.ker[x])));

          fi;
          AddSet(new,pos);
          (psub],>cx<pool.ost[)then
            AddSetfi;
          fi;
          pder[pos]:=fail;
          if c=N   # (We might always add random java.lang.StringIndexOutOfBoundsException: Range [56, 55) out of bounds for length 73
            ; 
          fi;

        else
          Info(InfoFactor #else
              Size(#fi;
                 " yields"Size(c)java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
        fi;

      fi;
      i:=i+1;
    od;
#discard:=[];
    for i in discard do psub[i if fthen
    :D(nionpnew),);
    new:=    hard:=10000
    SortParallel((pool.{}Size)p)
    java.lang.StringIndexOutOfBoundsException: Range [0, 16) out of bounds for length 14
  until Length(new)=0;

end);


#############################################################################
##
#F  FactorCosetAction( <G>, <U>, [<N>] )  operation on the right cosets Ug
##                                        with possibility to indicate kernel
##
InstallGlobalFunction("DoFactorCosetAction",function(arg)
localG,,h,;
  G:=arg[1];
  u:=arg[2];
  if Length(arg)>2 then
    N:=arg[3];
  else
    N            :Subgroup([andom())java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
  fi;
  if IsList(u) and Length(u)=0 then
    u:=G;
    Error("only trivial operation ?            :=Group(Concatenation(GeneratorsOfGroup(u)[      else
  fi;
 if falsethen
    N:(,         fijava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
     AddNaturalHomomorphismsPoolG,,;
  rt=RightTransversal(G,  rt:=RightTransversal(G,u cost big stabilizer chain calculation -- just
  if not IsRightTransversalRep( op=            
    # the right transversal has no special `PositionCanonical' method.
    rt          
  fi;
   h=ctionHomomorphismG,OnRight"surjective);
  op:=Image(h,G);
  SetSize(op,IndexNC(G,N)java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 13

  # and note our knowledge
  KnownNaturalHomomorphismsPool,java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
  and 5*totalcntIndexNC,),nowi1000) 
  return h;
end);

InstallMethod(FactorCosetAction,java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
  IsIdenticalObj,[IsGroup,IsGroup],0,
function(G,U)
  return DoFactorCosetAction(G,U);
end);

InstallOtherMethod(FactorCosetAction,
  "by right transversal operation, given kernel",IsFamFamFam,
  [IsGroup,IsGroup, c=Sum(.ostop});
unction(,,)
  return DoFactorCosetAction(G,U,N  
end);        # k"onnen)

(InstallMethod(FactorCosetActionelse
  IsIdenticalObj,[IsGroup        # der Index ist nicht so klein, da"s wir keine Chance haben
java.lang.StringIndexOutOfBoundsException: Range [12, 8) out of bounds for length 13
local hom;
  hom:=notjava.lang.StringIndexOutOfBoundsException: Range [21, 20) out of bounds for length 59
  return
end);

InstallOtherMethod(FactorCosetAction,
  "by right transversal operation, given kernel, Niceo",IsFamFamFam,
  
function(,U)
local hom;
  hom:RestrictedNiceMonomorphismNiceMonomorphism(G),G#java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
return java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 74
end);

# action on lists of subgroups
(FactorCosetAction
  "On cosets list       
  [IsGroup,IsList],        :CoreG,;
      else
ocal ,gens,;
  if Length(L)=0 or
    )
  fi;
q:(,x-FactorCosetAction
  gens:=MappingGeneratorsImages(java.lang.StringIndexOutOfBoundsException: Range [6, 1) out of bounds for length 33
  imgs:=List(zzz=java.lang.StringIndexOutOfBoundsException: Range [41, 38) out of bounds for length 61
  d:=imgs[1];
  for i in [2..Length(imgs)] do
    d:=SubdirectDiagonalPerms(d      fijava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
  od;
  imgs:=Group
q=java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for length 48
  q;
end);


#############################################################################
##
#M  DoCheapActionImages(G) . . . . . . . . . . All cheap operations for G
##
InstallMethod(java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 12

        max:=x>G,)IsSubset(x,);
function(G)
local pool, dom, o, java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
  found,          java.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds for length 60

  onlykernel:=ValueOption("onlykernel");
  =(;
  pool:=NaturalHomomorphismsPool(G);
falsethen

    dom:=MovedPoints(zzz:java.lang.StringIndexOutOfBoundsException: Range [42, 41) out of bounds for length 47
    # orbits
    o:=OrbitsDomain(G,dom);
    o:=Set(o,Set);

    # do orbits and test for blocks
    foriin o do
      if Length(java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
        # only works if domain are the first n points
        not (1Info+java.lang.StringIndexOutOfBoundsException: Range [34, 33) out of bounds for length 36
        opjava.lang.StringIndexOutOfBoundsException: Range [13, 9) out of bounds for length 14
        Range N;# all new
        java.lang.StringIndexOutOfBoundsException: Range [37, 35) out of bounds for length 63
                            op,  (,"vs "badi;
        type:=1;
      else
        op:=############################################################################
        type:=2;
      fi;

      Go:=Image(op,G);
      # all minimal and maximal blocks
      mov:MovedPoints(Go)java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
      allb:=Go,java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
      allbold:=[];
      b,;
      Info(InfoFactor,1,"Smaller degree for order ",Size(G),", deg: ",NrMovedPoints(G));
        j:= java.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for length 30
        Add(allbold,j);
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
        # >1.
        Length(/(j<ound 
          b:=List(Orbit(G,i{    :;

          #Add(bl,Immutable(Set(b)));
          op:=ActionHomomorphism(G,Set(b),OnSets,"surjective    s)<GeneratorsOfGroupG)
          onlyimage;`'same
          k:=KernelOfMultiplicativeGeneralMapping:=Group()java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
          if       SetSizeHSize))java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
                  :=Length()
          fi;
          AddNaturalHomomorphismsPool(G,k,op);

           finerblocks t  upfor 
           java.lang.StringIndexOutOfBoundsException: Range [18, 17) out of bounds for length 24
            newbif("java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 41
          else
            newb:=Blocks(Go,Blocks(Go,mov,j),OnSets);
java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 13

          if ()1
            :Unionnewb1);
            if (newbinallbor newb  java.lang.StringIndexOutOfBoundsException: Range [57, 58) out of bounds for length 57
              Add(      k:=Group(erg);Se:erg;java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 39
              SortBy(allb,Length);
            fi;
          fi;

        fi;

      od;

      #if Length(i)<500 and Size(Go)>10*Length(i) then
      #else
#        # one block system
#        b:=Blocks(G,i);
#        if Length(b)>1 then
#          Add(bl,Immutable(Set(b)));
#        fi;
#      fi;
    od;

    pool.GopDone:=true;
  fi;

end);

BindGlobal:]
function(G,mustfaithful)
local dom, o,      gut:=[;

  dom:=s:k,oi,;
  # orbits
  o:=OrbitsDomain(G,dom);
  o:=Set(o,Set);


  # all good blocks
  :dom
  allb:=java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 11
java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 18
     Length(o:=java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
      Size((java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for length 66
      then
        b:java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
        bl:=b;
        java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
        newb:=Blocks(G,b     iin[.Length()] do
        if Length(newb)>1 then
          newb:=Union(newb[1]);
           java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 34
            (,newb;
          fi;
        fi;
    fi;
  od;
  if Length      =java.lang.StringIndexOutOfBoundsException: Range [20, 19) out of bounds for length 37
    ;
  else
    return fail;
  fi;

end);


#############################################################################
##
#F  GenericFindActionKernel  random search for subgroup with faithful core
##
 too  
BindGlobal:b
G N , java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 0
 u nu,cor bigpermermm,java.lang.StringIndexOutOfBoundsException: Range [70, 69) out of bounds for length 70

  G:=arg[1od;
  N:=arg[2];
   
    knowi:=arg[3] sS(G;
  else
    knowi:=IndexNC(G,N);
  fi;

  # special treatment for solvable groups. This will never be triggered for
  # perm groups or nice groups
  if Size(N)>1 and java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
    perm:=java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for length 70
    perm:=perm#
    return perm;
  fi;

  # special treatment for abelian factor
  ifH:java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 61
    if IsPermGroup(G)       SetSizeH,SizeG);
java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for length 32
    else
      perm:=java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 6
    fi;
    return perm;
  fi;

  bigperm:=IsPermGroup:true

  # what is a good degree:
  goodi:=Minimum(Intjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

simple=java.lang.StringIndexOutOfBoundsException: Range [37, 36) out of bounds for length 85
  uc:=TrivialSubgroup(=java.lang.StringIndexOutOfBoundsException: Range [18, 17) out of bounds for length 18
  # look if it is worth to look at action on N
elian  replace abelian  
  if IsAbelian(N) and (      bl:=Blocks(H,MovedPoi(H);
      <50000then
    zen:=Centralizer(      ImagesSource(onlyimage) #`onlyimage' forces same generators
    ifzen)Size()
      cnt:=0;
      repeat
        cnt:=cnt+1;
        zen:=Centralizer(G,Random(N));
         (orSize(G))SizeN)and
            IndexNC(G,zen)<IndexNC        H:Image(map);
          uc:=zen;
        fi;
      # until enough searched or just one orbit
      until cnt=9 or (IndexNC(G,zen)1=N)java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
      AddNaturalHomomorphismsPool(G,N,uc,IndexNC(G,ucjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
    else
      (nfoFactor,3"centralizer too big");
    fi;
  fi;

  pool:=NaturalHomomorphismsPool(G);
  pool.dotriv:=true;    DoCheapActionImages(H::=(H));
  CloseNaturalHomomorphismsPool(G,    (H);
  pool.dotriv:fi;
  ise:=Filtered(pool.ker,x->IsSubset(x,N));
  if Length(isejava.lang.StringIndexOutOfBoundsException: Range [54, 31) out of bounds for length 54
    ise:=G;
  else
    ise:=Intersection(ise);
  fi;

  # try a random extension step
  # (We might always first add a random element and get something bigger)
  v:Njava.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7

  #if Length(arg)=3 then
    ## in one example 512->90, ca. 40 tries

  #else
#cnt:=25;
  #fi;

  =[];
  badi;
  hard:=ValueOption("hard");
  if hard= nch:=[java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
    hard   hom;
  elif hard=true then
    hard:=10000;
  fi;
  totalcnt:=0;
  interrupt:=false;
  cnt:=20;
  repeat
    u:=v;
    repeat
      repeat
        if Length(arg)<4 or Random(1,2)=1 then
          if IsCyclic(u) and Random(1,4)=1 then
            # avoid being stuck with a bad first element
            u:=Subgroup(G,[Random(G)]);
          fi;
          if Length(GeneratorsOfGroup(u))<2 then
            # closing might cost a big stabilizer chain calculation -- just
            # recreate
            nu:=Group(Concatenation(GeneratorsOfGroup(u),[Random(G)]));
          else
            end;
          fi;
        else
          if Length(GeneratorsOfGroup(u)java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 0
            # closing might cost a big stabilizer chain calculation -- just#F  ImproveActionDegreeByBlocks( <G>, <N> , hom )
            # recreate
            nu:=Group(Concatenation(GeneratorsOfGroupgimgimg,dom,bi,p,,k,estdeg,op,cbjava.lang.StringIndexOutOfBoundsException: Range [68, 67) out of bounds for length 73
          else
            :ClosureGroupuarg4])java.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
          ;
        fi;
        (,G
        totalcnt:=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
        if KnownNaturalHomomorphismsPool(G,N)            :Sum{x>,)};
         IndexNC,v,hard
             and 5*            (,i)
          # interrupt if we're already quite good
          :java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
        fi.=;
        if ForAny(badcores,x->IsSubset(nu,x)) then
          nu:=u;
        fi;
        # Abbruchkriterium: Bis kein Normalteiler, es sei denn, es ist N selber
        # (das brauchen wir, um in einigen trivialen F"allen abbrechen zu
        # k"onnen)
#Print("nu=",Length(GeneratorsOfGroup(nu))," : ",Size(nu),"\n");
      until

        # der Index ist nicht so klein, da"s wir keine Chance haben
        ((not .locksdone[]=true;
        Length(Orbit(nu,java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 0
        IndexNC(,nu)>50 or Factorial(IndexNC(G,nu))>=java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 20
        not IsNormal(G,nu))       gimg;

      Info(InfoFactor,4,"Index ",IndexNC(G,nu));
      java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

    until totalcntSetKernelOfMultiplicativeGeneralMapping(op,)java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
      # und die Gruppe ist nicht zuviel schlechter als der
      # beste bekannte Index. Daf"ur brauchen wir aber wom"oglich mehrfache
      # Erweiterungen.
        ((a)for in[.Length(.)] do

    if IndexNC(G,u)<knowi then

      #Print("Index:",IndexNC(G,u),"\n");

      <>G then
        cor:=TrivialSubgroup(G);
      else
        cor:=Core(G,u);
      fi;
ifSize(N and IsSubsetcor) injava.lang.StringIndexOutOfBoundsException: Range [71, 70) out of bounds for length 75
        Add(badcores,cor);
      fi;
      # store known information(we do't act, just store the subgroup).
      # Thus this is fairly cheap
      pool.dotriv:=true;
      zzz:=AddNaturalHomomorphismsPool(InfoFactor,2" allseeds";

      if IsPerm(zzz) and zzz<>() then# all blocks
        CloseNaturalHomomorphismsPool);
      fi;
      pool.dotriv:=false;

      zzz:=DegreeNaturalHomomorphismsPoolbestdeg:Length()java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31

      Info(InfoFactor,3,"  ext ",

      if cnt<10 and Size(cor)>Size
        ValueOption("inmax")=fail thenbb:=Blocksimg,,dom1],suboi])java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
        if IsSubset(SolvableRadical(N)<Size((u)) java.lang.StringIndexOutOfBoundsException: Range [83, 83) out of bounds for length 66
             onesare needed will needed, rest will have wrong kernel
sTF,":,;
      else
     =java.lang.StringIndexOutOfBoundsException: Range [45, 42) out of bounds for length 58
        fi;
        max:=Filtered(=Permuted              f<then
        for # if en        java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 57
          cor:=Core(G,i);
          AddNaturalHomomorphismsPool,,java.lang.StringIndexOutOfBoundsException: Range [0, 53) out of bounds for length 49
        
        (G,java.lang.StringIndexOutOfBoundsException: Range [49, 50) out of bounds for length 49
        Info(InfoFactor,3,"  Maxes:  sto.limit=gimg)java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
      fi;
    else
      zzz:=DegreeNaturalHomomorphismsPool(G,N);
    ;
    if IsInt(zzz) then
      knowi:=zzz;
    fi;

    #                    List(gimgbas,i->PositionProperty(bb,j->i in j)));

    if cnt=0 and zzz>badi then
      badi:=Int(java.lang.StringIndexOutOfBoundsException: Range [43, 20) out of bounds for length 43
      Info(InfoWarning+InfoFactor,2,
        index java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 53
                                                    opLength(b);
      totalcnt:=0;
      ;
      v:=N; # all new
    fi;
  until interrupt or cnt<=0                :=java.lang.StringIndexOutOfBoundsException: Range [58, 55) out of bounds for length 60
;

  return GetNaturalHomomorphismsPool(G,N);

end );

#############################################################################
##
#F  SmallerDegreePermutationRepresentation( <G> )
##
InstallGlobalFunction pool fi
localojava.lang.StringIndexOutOfBoundsException: Range [46, 1) out of bounds for length 46


  change:=false;
  oInfoFactor:true;
  cheap:=bestdeg:engthbb;
  if cheap=":bb
    java.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for length 30
  fi;

  cheap:=cheap=true;

  if Length(GeneratorsOfGroup(G))>7 then
    s:=SmallGeneratingSet(G);
    if Length(s)=0 then s:=[One(G)];fi;
    if Length(s            fi;
      Info(            i:=ii:=i+;
      H=();
      change:=true;
      SetSize(H,Size(G));
      return SmallerDegreePermutationRepresentation(H);
    fi;



  # deal with large abelian components first (which could be direct)if <failb,i-U(bdomi)
  if cheap<pop:=(gimgbOnSetss";
    hom:MaximalAbelianQuotient(G);
    i:=IndependentGeneratorsOfAbelianGroup(Image(hom));
o=iOrder;
    if ValueOption("norecurse")<>true and
      Product(o)           stolimit=()java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
      Info(InfoFactor,2,"append abelian rep");
      s:=AbelianGroup(IsPermGroup,o);
      ihom:=GroupHomomorphismByImagesNC(Image(hom),#            if gimgbas<>false then
      erg:=SubdirectDiagonalPerms(
            List(GeneratorsOfGroup(G),x->Image(ihom,#            fi;
            GeneratorsOfGroup(G));
      k:=Group(erg);SetSize(k,Size(G));              =java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for length 39
      hom:=roupHomomorphismByImagesNC(,k,GeneratorsOfGroup(G)erg)
      return hom*SmallerDegreePermutationRepresentation(AddNaturalHomomorphismsPool(java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
    fi;
  fi;

  # known simple?
  if HasIsSimpleGroup(G) and IsSimpleGroup
      and NrMovedPoints(G)>=SufficientlySmallDegreeSimpleGroupOrder(Size(G))
        then return k:=KernelOfMultiplicativeGe()java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
  fi;

  if not IsTransitive(G,MovedPoints(G)) then
    o:=ShallowCopy(OrbitsDomain(GSetKernelOfMultiplicativeGeneralMapping,PreImage,k);
    SortBy(o, Length);

            (G
      s:java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      ##                                                               the map to Nb);
      k:=G;
      gut:=[];
      for i in             :true;
        sbestop;
        if Size(s)<Size(k) then
          k:=s;
          Add(gut,i  =NaturalHomomorphismsPool(G)then
        fi;
      od
      # reduce each orbit separately
      o:=o{gut};
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      o,(a,)eturn )Length();nd);
    od;

    SortBy(,Length)

    InstallGlobalFunction(UnlockNaturalHomomorphismsPool,functionG,
    k:=G;
    for i in [1..Length(  java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
      Info(InfoFactor,1,"Try to shorten orbit ",i," Length ",Length(o[i]));
     java.lang.StringIndexOutOfBoundsException: Range [8, 7) out of bounds for length 58
      k2:#############################################################################
      k#############################################################################
      H:=Range(s);

      # is there an action that is good enough for improving the overall
      # kernel, even if it is not faithful? If so use the best of them.InstallMethod(,generic   java.lang.StringIndexOutOfBoundsException: Range [58, 57) out of bounds for length 74
      b:=java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 0
      if b<>fail then
        ,2,Blocksfor kernelreduce "L();
      :=ctionHomomorphism(H,b,,surjective";
        s:=s*b;
      fi;

      s=s*s))java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
      Info(InfoFactor,1,"Shortened (""fjava.lang.StringIndexOutOfBoundsException: Range [41, 40) out of bounds for length 52
      erg:=SubdirectDiagonalPerms  if java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 62
    od;:n);
    if NrMovedPoints(erg)<NrMovedPoints(G) then
      s:=Grouperg()  # `erg' arose from `SubdirectDiagonalPerms'
      SetSize(s,Size(G));
      s:=ClosureGroup(DerivedSubgroup(g),n);
      SetIsBijective(s,true);
      return s;
    fi;
    return (G)java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
  fi;# intransitive treatment



  # if the original group has no stabchain we probably do not want to keepf(alev)
  # it (or a homomorphisms pool) there -- make a copy for working
  # intermediately with it.
  if not HasStabChainMutable:[a;
    H:= GroupWithGenerators( GeneratorsOfGroup( G ),One(G
    change:=true;
    if       wait:=[;
      SetSize(H,Size(G));
    fi;
    f java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 29
      SetBaseOfGroup(       iinm do
    fi;
  else
    H:=G;
  fi;
  hom:=IdentityMapping(H);
  b:=NaturalHomomorphismsPool(H);
  bdotriv:true;
  AddNaturalHomomorphismsPool(H,TrivialSubgroup(          :TryMaximalSubgroupClassReps(:inmax,infactorpermrep,);
  b.otriv:false;

  # cheap initial block reduction?
  if IsTransitive(H,MovedPoints(H)) then
    improve:=true;
    while improve and (cheap or NrMovedPoints(H)*5>Size(H)) do
      improve:=false;
      bl:=Blocks(H,MovedPoints(H));
               IsSubset(j, then
      ImagesSource(              use:=ClosureGroup(n,DerivedSubgroup())
      bl:=KernelOfMultiplicativeGeneralMapping(map);
      G,bl,ap;
      if Size(bl)=1 then
        hom:=hom*map;
        H=(map;
        change:=true;
        Info(InfoFactor,2," quickblocks Add,)java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
      fifi;
    od;
  fi;

  b:=NaturalHomomorphismsPool(H);
  b.dotriv:           else
  if change then
    DoCheapActionImages(H:onlykernel:=TrivialSubgroupfi;
  else
    DoCheapActionImages(H);
  fi;
  CloseNaturalHomomorphismsPooljava.lang.StringIndexOutOfBoundsException: Range [42, 41) out of bounds for length 63
  b.dotriv:=false;
  :java.lang.StringIndexOutOfBoundsException: Range [35, 34) out of bounds for length 57
  if map<>fail and Image(map)<>H 
    Info(InfoFactor,,cheap   to degree",NrMovedPoints())
    hom:=hom*map;
    H:=Image();
  fi;

  o:=      fi;
  if    not java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
    sGjava.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds for length 70
     # just stored as intersection. Construct the mapping!
      hom:=hom*s;
    fi;
  java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5

  return hom;
end);

#############################################################################
##
#F  ImproveActionDegreeByBlocks( <G>, <N> , hom )
##  extension of <U> in <G> such that   \bigcap U^g=N remains valid
##
        wait:=Filtered)
omb,improvebp,bbi,,,,op,bc,bestblock,bdom,
      bestop,sto,subomax;
  (java.lang.StringIndexOutOfBoundsException: Range [18, 17) out of bounds for length 49

  # remember that we computed the blocksjava.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds for length 55
      

  # special case to use it for improving a permutation representation
  if Size(N)=1 then
    Info(InfoFactor,1,;
    b.ker:=[N];
    bops:=;
    b.cost:=[Length(MovedPointsInfoFactor,,pop ,(Listisex-I())java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
    b.lock:=[false];
    ocksdone:[false]];
    subomax:=;
  else
    subomax:=500;


  i:=PositionSet(b.ker,N);
  if b.blocksdone[i] then

  fi)
  b.blocksdone[i]:=true;

  #############################################################################
    return 1;
  fi;

gimg:Imageoh,)java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
  java.lang.StringIndexOutOfBoundsException: Range [6, 4) out of bounds for length 51
:(img;
  bdom:=fail;

  if IsTransitive(img,dom) then
    # one orbit: Blocks
    repeat
      b:=Blocks(img,dom);badcomb, idxactk,;
      improve:=false;
      if b>1then
        if Length    
          subo=(dom[1];
          subo:java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
        else
          subo:=fail;
        fi;
        bc h=G,,N;# will implicitly store
         <faildomhiefSeriesThroughG,o,)
          fi
          # if the degree is not too big or if we are desperate then go for
          # all blocks
          # greedy approach: take always locally best one (otherwise there
          # might be too much work to do)
          bestdeg=(dom;
          bp:=[]; #Blocks pool
          i #and HasElementaryAbelianFactorGroup(dom[i-1],dom[j+1])##
          i=engthsubo) [+)2000
            if subo[i] in bc then
              bb:=b;
            
              =v:=RightTransversal[i1dom];
            fi;
            if Length(bb)>1 and not (bb[1] in bp or        oo:=rbitsDomain(G,v,,vfunction(rep,)
              (InfoFactor,,found   "Length()java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
              # new nontriv. system found
              AddSet(bp,bb[1]);
              # store action
              op:=1;# remove old homomorphism to free memory
              if            :StabilizerGk]functiong)
                bb:bb,i-I(b{i});
              fi;

              op:=bbOnSets,sjava.lang.StringIndexOutOfBoundsException: Range [64, 63) out of bounds for length 66
              HasSize(img  not ()then
                sto:=                G,u,,IndexNC,);
                sto.limit:=Size(gimg);
                # try only with random (will exclude some chances, but is
                .  sizeis aproofjava.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
                .:
#                if gimgbas<>false then
#                  SetBaseOfGroup(Range(op),
#                    List(gimgbas,i->PositionProperty(bb,j->i in j)));
#                fi;
         ifSize())=Size() then
                  sto.random:=1000;
                  :=TrivialSubgroup(gimg)
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
                   dom=ker)java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 27
                  AddNaturalHomomorphismsPoolp,->pool.[i,));
                      KernelOfMultiplicativeGeneralMapping(op),
                                              op,Length(bb));
                else
                  k:=[]; # do not trigger improvement
                fijava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
              else
                k:=Info(InfoFactor,2,"Try reductionorbits";
                SetSize(Range(op),IndexNC(gimg,k));
                -ClosureGroup,);
                SetKernelOfMultiplicativeGeneralMapping(op,PreImage(oh,k));
                AddNaturalHomomorphismsPool(G,
            op),
                                            op,Length(bb));

      fi;
              # and note whether we got better
              #improve:=improve or (Size(k)=1);
              if Size
                java.lang.StringIndexOutOfBoundsException: Range [29, 23) out of bounds for length 30
            bestdeg:Lengthbb;
                bestblock:=bb;
                bestop:=op;
              ol.ker    ifLength()1 java.lang.StringIndexOutOfBoundsException: Range [23, 24) out of bounds for length 23
                        fi(iOnPoints,s";
            # break the test loop if we found a fairly small block system
            # (iterate greedily immediately)
                     =Filtered(ppool.c;
java.lang.StringIndexOutOfBoundsException: Range [43, 29) out of bounds for length 29
            fi;
             greeNaturalHomomorphismsPoolmjava.lang.StringIndexOutOfBoundsException: Range [51, 47) out of bounds for length 56
          ;
        else
          (InfoFactor,t only  )java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
          op:=1;# remove old homomorphism to free memory
          if bdom<>fail then
            :Set((b,->Immutable(Union(bdom{});
          fi;
          op:=ActionHomomorphism(gimg,b,OnSets,"surjective");
           gimg)  HasStabChainMutable() then
            sto:=StabChainOptions(Range(op));
            sto
            # try only with random (will exclude some chances, but is
            # quicker. If the size is OK we have a proof anyhow).
            sto.random:    =);
#            if gimgbas<>false then
#              SetBaseOfGroup(Range(op),
#                 List(gimgbas,i->PositionProperty(b,j->i in j)));
#            fi;
            if Size(Range(op))=Size(gimg)cnt:=OrbitsDomain,)i-Length()>1)java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
              sto.random:=1000;
              k:=TrivialSubgroup(gimg);
              op:=oh*op;
              SetKernelOfMultiplicativeGeneralMapping(op,PreImage(oh,k)u:Core((G,);
              AddNaturalHomomorphismsPool(G,
                  java.lang.StringIndexOutOfBoundsException: Range [55, 54) out of bounds for length 59
                                          op,Length(b));AddNaturalHomomorphismsPool(u,,java.lang.StringIndexOutOfBoundsException: Range [52, 51) out of bounds for length 58
      java.lang.StringIndexOutOfBoundsException: Range [36, 35) out of bounds for length 41
              k:=[; # do not trigger improvement
            fi;
          else
            k:=KernelOfMultiplicativeGeneralMapping(op);
            SetSize(Range(op),IndexNC(gimg,k));
            # keep action knowledge
            op:opjava.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22
            SetKernelOfMultiplicativeGeneralMapping(op,PreImage(oh,k));
            AddNaturalHomomorphismsPool(G,
                KernelOfMultiplicativeGeneralMapping(op),
                                          ;
          ;

ifSize()1fi
            :tjava.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
            
            bestop:=op;
    # whether anything stabilizing can be of use
        fi;
         java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
          mapping
          =;
          img:=Image    s:=;
          :MovedPoints(mg;
        fi
      fi;
    until InfoInfoFactor,,stabilizer index "IndexNC(G,s))
  fi;
  Info(InfoFactor,1,"end of blocks search")j   if  (badnormals,java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
  (GN)java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
end);

#############################################################################
##
#M  FindActionKernel(<G>)  . . . . . . . . . . . . . . . . . . . . generic
##
" for finite groups,sIdenticalObj
  [      =(,)java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28

RedispatchOnCondition(FindActionKernel,IsIdenticalObj,[IsGroup,IsGroup],
  [IsGroup     N<failjava.lang.StringIndexOutOfBoundsException: Range [20, 19) out of bounds for length 44

InstallMethod(FindActionKernel#=];
  fori in find   notany part of m

BindGlobal("FactPermRepMaxDesc",function(g,n,maxlev)
local limdegall,,recurse,start;
  if ValueOption("infactorpermrep")=true then return false;fi;
  deg    # now intersect, staring from top
  deg1java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
:[
=Info,"",cnt;
    Info(InfoFactor2": ",           java.lang.StringIndexOutOfBoundsException: Range [35, 34) out of bounds for length 57
  c:    :[;
  Info(InfoFactor,1,"Try maximals for limit ",lim            notjava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 9

:functiona,
  local m,ma,nm,i,j#              o:(u;
    InfoInfoFactor,idx/Size(ojava.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
    m:=[a];
    while Length(# the permimage won't be sufficiently large
     :=]
      ma:=[];
      for i in m do
ifForAll(all,y->RepresentativeActiong,iy)fail)then
          Add(all,i);
         (2,Maximals"I(gi))java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63
          nm:=(inmax,cheap);
          (nm,->IndexNC(x<lim  java.lang.StringIndexOutOfBoundsException: Range [60, 59) out of bounds for length 72
          java.lang.StringIndexOutOfBoundsException: Range [20, 18) out of bounds for length 25
          for j in
             IsSubsetj)then
              (n,java.lang.StringIndexOutOfBoundsException: Range [50, 49) out of bounds for length 54
               not(,cthen
                j:=use;
                use:=true;
              else
                Add(wait,j);
                use:=                  :0java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
              fi;
            else
              use:=true;
            fi
            if fi
              co:=Core(g,   x->poolx<oolcost[[+poolo2]
                  if (not blocksdone) and<00  <ndexNC(,N) then
              c:=Intersection(co,c);
              Add(ma,j);
            fi;
          odjava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13

          Info("yields ",Size(c));
        ;
      od;
      if Length(ma)>0     =G,N)or
        CloseNaturalHomomorphismsPool(,);
        i:=DegreeNaturalHomomorphismsPool(g,n);
        if i<       GenericFindActionKernelG,s<> java.lang.StringIndexOutOfBoundsException: Range [58, 59) out of bounds for length 58
          deg:=i;
          Info(InfoFactor,1,"Itmax       Info(InfoFactor,1,"  Random search foInfoFactor,"  Random   ,bestdeg;
          if lev>1 or deg<lim then return 
        fi;
        m:=ma;
        SortBy(m,x->-Size(x));
      elif lev<maxlev then
        # no improvement. Go down
        wait:" java.lang.StringIndexOutOfBoundsException: Range [43, 42) out of bounds for length 60
          indo
          if recurse(i,lev+1) then return true;fi;
        od;
        m:=[];
      else
        m:=[];
      fi;
    od;
    if Size(c)>Size(n) 
      Info(InfoFactor,#M  FindActionKernel(<G>)  . . . . . . . . . . . . . .#
    else
   Ijava.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 49
    fi;
    falsejava.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
   end;

java.lang.StringIndexOutOfBoundsException: Range [16, 8) out of bounds for length 26

java.lang.StringIndexOutOfBoundsException: Range [4, 3) out of bounds for length 20


#############################################################################
##
#M  FindActionKernel(<G>)  . . . . . . . . . . . . . . . . . . . . permgrp
##
InstallMethodF,""
  [IsPermGroupIsPermGroup]],java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
function(G,N)
local pool, dom, bestdeg##                             this function returns an epimorphism from G
      badcomb, idx, i, comb,act,k,j;

  if IndexNC(G,N)<50 then
    # small index, anything is OK
    return GenericFindActionKernel(G,   java.lang.StringIndexOutOfBoundsException: Range [21, 20) out of bounds for length 49
  else
    # get the known ones, including blocks &c. which might be of use
    DoCheapActionImagesG);

    # find smallish layer actions
    oo:=ClosureGroup(SolvableRadical(G), h, )java.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
    dom:=java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 0
    dom:=Filtered(dom,  if (HasSize(N) and Size((  (N=)or N)and

    i:=2;
    while i<=Length(dom) do
      j:=i;
      while j<Length(dom)
        #and HasElementaryAbelianFactorGroup(dom[i-1],dom[j+1])
        and dom[1]dom[        and IndexNC(dom[i-1],dom[j+1
        j:=j+1;
     od
if(domi]j)=2000then
            
        oo:=psubjava.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 25
          return v[:=GetNaturalHomomorphismsPoolGN;
          end);
        for k in oo do
          if (k> then
            :=Gk[1,x)
              return v[PositionCanonical(v,x^gproj:=ProjectionGproj)java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
            end);
            repeat
              if G,)then
                AddNaturalHomomorphismsPool(G,Core(G    java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
              fi;
              m:=u;
              u:=java.lang.StringIndexOutOfBoundsException: Range [31, 29) out of bounds for length 52
            until m=u;
      
        od
      fi;
      i:=j+1;
    od;

    pool:=NaturalHomomorphismsPool(G);
    dom:=MovedPoints(G);

    # store regular to have one anyway
     not G IsFinite(G)
    AddNaturalHomomorphismsPool(G,N,N,bestdeg);

    # check if there are multiple orbits
    oh:G,);
    s    ifh>then
    if not ForAny(s,i->IsSubset(N,i)) then
      Info toorbits");
      s:=List(s,i->ClosureGroup(i Length(ovedPointsRange, found);
      if Intersection(s)=N then
        Info(java.lang.StringIndexOutOfBoundsException: Range [24, 23) out of bounds for length 57
        List(s,i->
      fi;
    fi

    CloseNaturalHomomorphismsPool(G,N);

    # action in orbit image -- sometimes helps;
    if Length(o)>1 then
      for i in o do

=ActionHomomorphism(G,i,OnPoints,"surjective");
        k:=KernelOfMultiplicativeGeneralMapping(act)
        :=(k,N) # pre-image of (image of normal subgroup under act) of ( of  subgroupunder )
=(act)
       :=(Image(ct,u)

        o:=java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 13
ifIsInt()hen otherwise  do
          (Gk,*o;
        fi;
      od; ;
     (G,)
    fi;

    bestdeg:=DegreeNaturalHomomorphismsPool(G,N            

    (InfoFactor1"andknown          Info(InfoFactor,5,"Intersect ",co,": ",

    =java.lang.StringIndexOutOfBoundsException: Range [21, 14) out of bounds for length 22
    # use subgroup that fixes a base of N
    # get orbits of a suitable stabilizer.
    o:=    for i in disca;
    snew:
badnormalsF KnownNaturalHomomorphismsPool() java.lang.StringIndexOutOfBoundsException: Range [44, 45) out of bounds for length 44
    if ()1and     if A<50 or (IsInt(A) and<()(G)))
   cnt:(OrbitsDomains,dom)i-Length()>;
      for i in do
        v:=ClosureGroup(N,        Info(InfoFactor,2,"use(nfoFactor,,use  )
############################################################################
          and not ForAny(badnormals,j->IsSubset(v,j)java.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 7
u=G,v);
            u:=arg[2];:arg[;
            Add(badnormals,u);
          fi;
          AddNaturalHomomorphismsPool    :a[3;
        
      java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9

      
aturalHomomorphismsPoolN;

      java.lang.StringIndexOutOfBoundsException: Range [39, 13) out of bounds for length 51

      Info(InfoFactor,1,"Base Stabilizerandjava.lang.StringIndexOutOfBoundsException: Range [0, 50) out of bounds for length 5

      if
        # should be better...
        bestdeg:=ImproveActionDegreeByBlocks  ;
          java.lang.StringIndexOutOfBoundsException: Range [40, 37) out of bounds for length 44
        =true;
        
      java.lang.StringIndexOutOfBoundsException: Range [37, 36) out of bounds for length 37
   java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

    java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 whetherjava.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 48
   :,)-ength([])
    by right   filter := IsPermGroupGeneralMappingByImages a
    oo:=OrbitsDomainjava.lang.StringIndexOutOfBoundsException: Range [9, 8) out of bounds for length 15
    s:=G;
    for i in oo   return hom*DoFac (NiceObject(),hU,Image            andjava.lang.StringIndexOutOfBoundsException: Range [38, 39) out of bounds for length 38
      s:=StabilizerOfBlockNC(s,i[1]);
    od;
InfoInfoFactor,2"  [[IsGroup,java.lang.StringIndexOutOfBoundsException: Range [20, 17) out of bounds for length 21

    if not (,->sSubsets,j) 
 wethiswayjava.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
ifSizee(FamilyObj( G ) ),
        badnormals,y>java.lang.StringIndexOutOfBoundsException: Range [52, 51) out of bounds for length 59
 fi
      java.lang.StringIndexOutOfBoundsException: Range [35, 32) out of bounds for length 48
    java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      m:=G; # guaranteed fail
    fi

    if ""java.lang.StringIndexOutOfBoundsException: Range [1, 0) out of bounds for length 0
      =(Gs)
      blocksdone:=false;
      Info(InfoFactor#############################################################################
    elif Size(m)>Size(N) =    o:=OrbitsDomain( < java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
     # no hard work for trivial cases
        ,k
# try to find a subgroup, which does not contain any part of m
#java.lang.StringIndexOutOfBoundsException: Range [20, 13) out of bounds for length 75
        Gjava.lang.StringIndexOutOfBoundsException: Range [0, 48) out of bounds for length 45
(,FilteredGeneratorsOfGroupG- )java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
        

        cnt:=1;
        badcomb:=[];
        repeat
java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
          for comb in [.#
#rint(>c,njava.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
             notForAnybadcombj>j)then
              :SubgroupNC(G
              o:=ClosureGroup(N,u);
              idx:#        :(hom;
              < Factorialjava.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
                 java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 59
                badcombImmutable()Info(2"subgroup index ",(,u)
    v:PreImage(u)
              if idx<bestdeg and Size(G)>Size(o)
              and not ForAny(java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 29
                m:=(o)java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
                if Size(m)java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      (InfoFactor,3" ,
                  
                  if not m java.lang.StringIndexOutOfBoundsException: Range [10, 29) out of bounds for length 13
                    Addm;
                  fi;
                fi
                if idx,             Addallb,;
                  (3," ,omb,")
                  java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 0
                  (>1then
                  fjava.lang.StringIndexOutOfBoundsException: Range [36, 35) out of bounds for length 36
                  0;
                ;
              java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
            fi;# all good blocks
    od,dub)
          cnt=k=k)
        SizeCjava.lang.StringIndexOutOfBoundsException: Range [39, 28) out of bounds for length 66
      fi:=;
fjava.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7

    Info(,,Stabilizer           
    force
    if    ;
      #######################################################################;
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
        GetNaturalHomomorphismsPool(G,N));
      blocksdone:=java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 2
      Info(InfoFactor,2,"[  and    
    fi;

    =IndexNC)
      B , arg
      if GenericFindActionKernel(local G, N, knowi, goodi, simple, ,zen,cntjava.lang.StringIndexOutOfBoundsException: Range [5, 3) out of bounds for length 25
        blocksdone:=true;
      fi;
bestdeg(,java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
   I"Random "bestdeg);
    fi;

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      cnt# perm groups or nice groups
actPermRepMaxDescN,)
          =GRightCosets(,N,java.lang.StringIndexOutOfBoundsException: Range [56, 55) out of bounds for length 70
      if bestdeg<cnt then blocksdone:=falsereturn;
      Info(InfoFactor,        # special treatment for abelian factor(N then
    fi;

    if not blocksdone then
      ImproveActionDegreeByBlocksG,GGGN)O"";
    fi;

    Info  :andNrMovedPointsG>0000
    return GetNaturalHomomorphismsPool(G,N)  =java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 59
    o;
  fi;

java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5

#############################################################################
##
#M  FindActionKernel(<G>)  . . . . . . . . . . . . . . . . . . . . generic
##
F,",java.lang.StringIndexOutOfBoundsException: Range [54, 53) out of bounds for length 54
[sGroup java.lang.StringIndexOutOfBoundsException: Range [43, 42) out of bounds for length 54
function(G,N)
local hom,hom2;
  dotriv=java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
  :G),Image(hom,);
   hom2 then
    return hom*hom2;
  else
    return hom extension
  fi;
end);

java.lang.StringIndexOutOfBoundsException: Range [40, 10) out of bounds for length 40

#############################################################################
##
#M  NaturalHomomorphismByNormalSubgroup( <G>, <N> )  . .  mapping G ->> G/N
##                             this function returns an epimorphism from G
##  with kernel N. The range of this mapping is a suitable (isomorphic)
##  permutation group (with which we can compute much easier).
InstallMethod(NaturalHomomorphismByNormalSubgroupOp,
lObj,sGroup,,,
function(G,N)
local proj,h,pool;

  # catch the trivial case N=G
  G,N  GN= then
    h:=FACTGRP_TRIV;  # a new group is created:Group(Concatenation),[([]])
    ( G, h GeneratorsOfGroup(G ,
           List( GeneratorsOfGroup G ,i ( );  # a new group is created
    SetKernelOfMultiplicativeGeneralMapping( h, G );
hjava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
       ;

  # catch trivial case N=1 (IsTrivial might not be set)
  if (HasSize(N) and Size(N)=1) or (HasGeneratorsOfGroup(N) and
    ForAll(GeneratorsOfGroup(N),IsOne)) then
    return IdentityMapping(G);
  fi;

  
  pool:=NaturalHomomorphismsPool(G)
  h:=PositionSet(pool.ker,N);
  if h<>fail java.lang.StringIndexOutOfBoundsException: Range [0, 16) out of bounds for length 0
    
  fi;

java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 75
  if # store known informationwe do't,just store the ubgroup)
    h      dotriv:=true
  ;

  if HasDirectProductInfo(,);
    for proj in [1..Length(DirectProductInfo(G)      ;
            =java.lang.StringIndexOutOfBoundsException: Range [42, 41) out of bounds for length 47
      h:=NaturalHomomorphismByNormalSubgroup
      AddNaturalHomomorphismsPool(G,
        if IsSubset(SolvableRadical(u),N) and Size(N)<Size(SolvableRadical(u)) then
    od max=DoMaxesTF(u,"":c)
  fi;
   fi;

  h:=          in do
   h>fail and RootInt(2)IndexNC(,N then
    :GetNaturalHomomorphismsPoolN);
  else
    h:=fail;
  fi;

  if h=fail then
    # now we try to find a suitable operation

    # redispatch upon finiteness test, as following will fail in infinite case
     HasIsFinite(G) and IsFinite(G) then
      GN;
    fi;

    if = and zzzbadi then
    if h<>fail then
      Info(InfoFactor,1,"Action Info(nfoWarningInfoFactor,2,
        Length(MovedPoints(Range(h)))," found");
    else
      Error("I       totalcnt=0;
      # nothing had been found, Desperately one could try again, but that=N;# all new
      # would create a possible infinite loop.
      h:  ,N )java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
    fi;
  fi;
  # return the map
  h
end);

java.lang.StringIndexOutOfBoundsException: Range [64, 63) out of bounds for length 79
  [IsGroup,IsGroup],[IsGroup and IsFinite,IsGroup],0);

patchOnCondition(,java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
  [][  ,)

RedispatchOnCondition(FactorGroupNC,IsIdenticalObj,
  IsGroup,[IsGroup ,0;

#############################################################################
##
#M  NaturalHomomorphismByNormalSubgroup( <G>, <N> ) . .  for solvable factors
##
NH_TRYPCGS_LIMIT:=if cheap<then
InstallMethodhom=java.lang.StringIndexOutOfBoundsException: Range [32, 31) out of bounds for length 35
if java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 41
  (InfoFactor,append )
function G N 
local   map,  pcgs, A, filter;

  if KnownNaturalHomomorphismsPool),x->Imageihomhom,)),
A=G)
    if < or(A) AGN)IndexNC(,),2)^2 
      :java.lang.StringIndexOutOfBoundsException: Range [40, 38) out of bounds for length 44
      if map<>java.lang.StringIndexOutOfBoundsException: Range [2, 1) out of bounds for length 17
        Info(InfoFactor,2,"use stored map");
        return map;
      fi;
    fi
  java.lang.StringIndexOutOfBoundsException: Range [0, 4) out of bounds for length 0

  if IndexNC(      :;
    or Minimum:Stabilizerk,[]OnTuples);
    TryNextMethod((s<(
  fi

  # Make  a pcgs   based on  an  elementary   abelian series (good  for  ag={;
  # routines).
  pcgs :
  ifjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      TryNextMethod();
  java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5

  # Construct or look up the pcp group <A>.
  A:=CreateIsomorphicPcGroup

  b:DoActionBlocksForKernel

  # Construct the epimorphism from <G> onto <A>.
  map := rec();
      :*java.lang.StringIndexOutOfBoundsException: Range [50, 49) out of bounds for length 60
            IsToPcGroupGeneralMappingByImages java.lang.StringIndexOutOfBoundsException: Range [0, 49) out of bounds for length 47
            IsGroupGeneralMappingByPcgs 
            IsMapping and IsSurjectiveGjava.lang.StringIndexOutOfBoundsException: Range [37, 36) out of bounds for length 67
HasSource and
             return s
            return IdentityMapping(G

  map.sourcePcgs group hasno weprobablydonot   
  map# intermediately with it.

   java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
  NewType( GeneralMappingsFamily
           ElementsFamily FamilyObj(   ),
            ElementsFamily( SetBaseOfGroup(H,BaseOfGroup(Gjava.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
            Source,G,
            Range,A,

            ImagesSource,A,
            KernelOfMultiplicativeGeneralMapping(H) 
            );

  return improve
end );

#############################################################################
##
#F  PullBackNaturalHomomorphismsPool( <hom> )
##
 InfoFactor2, "NrMovedPointsH);
local s,r,nat,k;
   b:H
  r:=Range(hom);
  java.lang.StringIndexOutOfBoundsException: Range [4, 1) out of bounds for length 58
    nat:=hom.=java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
    AddNaturalHomomorphismsPool(s,PreImage(homInfoInfoFactor,, actionsimproved  degree "NrMovedPoints(H);
od;
end);

#############################################################################
##
#F  TryQuotientsFromFactorSubgroups(<hom>,<ker>,<bound>)
##
InstallGlobalFunction(TryQuotientsFromFactorSubgroups,function(hom
local s,pjava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
  sjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  p:=Image(hom);
  k:=KernelOfMultiplicativeGeneralMapping##  extension of <U> in <G> such that   \bigcap U^g=N remains valid
  it:=DescSubgroupIterator(p:skip:=4);
  repeat
    u:=NextIterator(,mprove,,bb,kbestdeg,opbcbestblock,dom
    Info(InfoExtReps,2,"Factor subgroup index "      bestop,,subomax;
    v:=PreImage(hom,u);
    d:=DerivedSubgroup(v);
    ifnot (d,k)then
      d:=ClosureGroup(ker,d);
      if not IsSubset(d,k) then
       :NaturalHomomorphismByNormalSubgroup(v,d);
        mak:=Image(ma,k);
        lev:=0;
    ops=oh]java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
        b.blocksdone:[java.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds for length 26
          lev:=lev+1;
          low:=ShallowCopy(LowLayerSubgroups(Range(ma .[i]=true;
          SortBy(low,x->-Size(x));
          sub:=First(low,x->not IsSubset(x,mak));

        :PreImagema,;
        Info(InfoExtReps,2,"Found factor permrep ",IndexNC(s,sub));
        d:=Core(s,sub);
        java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 0
        tersection(d;
        if if IsTransitivedom)then
      fi;
    fi;
  IndexNCu>bound
end);

#############################################################################
##
#M  UseFactorRelation( <num>, <den>, <fac> )  . . . .  for perm group factors
##
InstallMethod( UseFactorRelationbc:F(,>1 ini;
   [ IsGroup and HasSize, IsObject, IsPermGroup ], subo<>ail ((subo<subomax) then
   function( num, den, fac )
   local limit;
   if not HasSize(fac) 
          # might be too much work to do)
       (,Size(num) / Size( );
     else
 Size  ;
        IsBound( ()limit ) then
         limit := Minimum( limit, StabChainOptions(fac).limit );
       fi;
       bb=(mg,om,dom[]si])java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
     ;
   fi;
  TryNextMethod(;
   end );