Quelle  perf6.grp   Sprache: Shell

##########################
#
#[b^,b^
##  This file's 5,c^2*d*c^2*d^-1,c^2*d-,c2**^2*^-
##
##  c^-1*d^-1*e*d*e*d^-1*e*d*e^-1,
##  to list here. Please refer to the COPYRIGHT file for details.
##
##  SPDX-License-Identifier: GPL-2.0-or-later
##
##  This file contains the perfect groups of sizes 43200-87480
##  All data is based on Holt/Plesken: Perfect Groups, OUP 1989
##

  PERFGRP[81]:=[# 43200.1
  [[1,"abcde",
  function(a,b,c,d,e)
  a-d-*ada^1e-**,
  [[a^2,b^3,(ab-1*d^-1*b*db^-e-1**]java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
 ^,**^*^c^2**c^2*e^-1,
  c^-1*d^-1b^1*^1**,-^be],
  a^-1*d^-1*a*d,a^-1*e^-1*a*e,
  b^-1*d^-1*b*d,b^-1*e^-1*b*e],
  [,*a*^-*,,],ab,edc^d]]];
  end,
  [5,80]],
  A5x A62^"[33,1,1],2,
  [1,3],[5,80]],
  [24,]
  [  " ^1 x A6",[33,1,2]2,
  function(a,b,c,d,e)
  
  [[a^4,["abcde",
  ^,(d*-)5java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
  c^-1*d^-1*e*d*e*d^-1*e*d*e^-1,
  -*d^1**,^1*^1ae
  b^-1*d^-1*b*d,b^-1*e^-1*b*e],
  [a*bde,a,,c,d]]
  end,
  [24,6]a-1e^-1*a*,b^*-bd
  "A5 21x "33,12,2java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
  [13,24,],
  # 43200.3
  [[1,"abcde",
  function(a,b,c,d,e)
  return
  [[a^4,b^3,(a*b)^5,c^2*a^2,d^3,e^3,(d*e)^4*c[,3,]
  ^-1)^5,^-1*d^-1ede-e*java.lang.StringIndexOutOfBoundsException: Range [33, 34) out of bounds for length 33
  *e*^-*za-1ya*^-java.lang.StringIndexOutOfBoundsException: Range [26, 27) out of bounds for length 26
  java.lang.StringIndexOutOfBoundsException: Range [4, 3) out of bounds for length 30
  b^-1*e^-1*b*e],[[a*bend,
  end,
  [960]],
  "( A5 x A6 ) 2^1",[33,1,3],2,
  [1,3],960]
  java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 4
  ]=#43320.
  [[1,"abyz",
  function(a,b,y,z)
  [[1"abdyz"java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
  y^19,z,^1
  *z^-1*y*z,a^-1*y*a*z^-1,
  ^1z*a*y,
  b^-1*y*b*(y^(-1*6)*z^(-1*9))^-1,
  b^-1*z*b*(y^(-1*5)*z^5)^-1],[[a,b]]];
  ,
  [361],[0,0,2,2b1*y**y^-*6*^-*))^1
  A521 192"5,21],1,
  1,endjava.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
   .2(therpres.
  [[1,"abdyz[[,abuvwxyz",
  function(a,b,d,y,z)
  return
  [[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b,
  y^19,z^[[a2,^3(*)^5,^3v^3w,x^3,^3z^,u^1v
  a^-1*y*java.lang.StringIndexOutOfBoundsException: Range [2, 1) out of bounds for length 30
  ^1yb(y^-1*6)z(1*9)-java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
  b^-1*z*b*(y^(-1,^-*x**v-**yy^1)-1java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
  ,^-1*za*(^-1*v^-x-*y)
  361,[0,022,,2
  ];
  PERFGRP[83]:=[# 43740.1
  [1"abuvwxyz"java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
  function(a,b,u,v,w,x,y,z)
  return
  [[a^2,b^3,(a*b)^5,u^3,v^3,w^3,x^3,y^3,z^3,u^-1*v
  ^-1*u*v,u  ^-1*u*v,ujava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 7
  java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
  u^-1*z^-1*u*z,
  a^-1*u*a*(u^-1*v*a^1*b^1***c*-cb*^1d^,
  z)-java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
  a-1***(^-1*w**y-1*z-)^-
  ,a^-1*x*a*(e^1*t^1ete-*^-*e*,
  ae^1v-**v,^,^,^,^,
  ,a^-1*z*a*(u^-1*v^-1*x^-1*y*z)
  ^-1,b^-1*u*b*(u*w^-1*y)^-1  s^1*^-s*t,^1^1***e^java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
  ^-**b*(*^-*)-,
  b^-1*w*b*(w*y)^-1,b^-1*x*b*(x*z)^-1,
  b^-1*y*ba^-1u**s^1,-1**at^-1,
  [ab,ab*b-*a*,];
  end,
  [8]java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
  "A5 3^-1*sc*(t**u)^1,c^-*t**^-1,
  1,18]
  ];
  ERFGRP[4]:[ 460801
  [,abcdstuve"
function(,,c,,,t,u,v,)
  return
  [[a^2*d^-1,b,80],
  a-b^1c*cb-1**-,^2,
  d^-1*b^-1*d*b,d^-1*c^-1*d*c,
  d^-1*e^-1*d*e,e^4,e^-1*s^-1*e*s,
  e^-1*t^-1*e*t,e^-1*u^-1*e*u,
  e^-1*v^;
  sPERFGRP85:=[# 48000.
  s1v1s,^1*^-*java.lang.StringIndexOutOfBoundsException: Range [15, 16) out of bounds for length 15
  t^-1*v^-  [c^18*^2cb^37"22,-2,
*u-a-**aa*^1
  a^-1*u*a*  ]java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
  -**b(t**e^-1,
  b^-1*t*b*(s*t*u*v)^-1,
  b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1,
  c^-return
  c^-1*u*java.lang.StringIndexOutOfBoundsException: Range [2, 1) out of bounds for length 46
  c^-1*v*c*(s*t*u*v*e^2)^-1],
  [[b,c],[c*b*a*d,b,s,e]]];
  end,
  [64,80]],
  "A6 2^1 x ( 2^4 E 2^1 A ) C 2^1",[13,7,1],8,
  3,[64,80]]
  ];
  PERFGRP[85]:=[# 48000.1
  [[4,1920,3,3000,2,120,3,1],
  "A5 # 2^5 5^2 [1]",6,1,
  1,[16,24,25]],
  # 48000.2
  [[4,1920,4,3000,2,120,4,1],
  "A5 # 2^5 5^2 [2]",6,1,
  1,[80,25]],
  # 48000.3
  [[4,1920,5,3000,2,120,5,1],
  "A5 # 2^5 5^2 [3]",6,1,
  1,[10,24,25]]
  ];
  PERFGRP[86]:=[# 50616.1
  [[1,"abc",
  function(a,b,c)
  return
  [[c^18*a^2,c*b^4*c^-1*b^-1,b^37,a^4,a^2*b^(-1
  *1)*a^2*b,a^2*c^-1*a^2*c,
  c*a*c*a^-1,(b*a)^3,
  c^(-1*2)*b*c^2*b^3*a*b^2*a*c*b^2*a],[[b,c^4]]]
  ;
  end,
  [152]],
  "L2(37) 2^1 = SL(2,37)",22,-2,
  21,152]
  ];
  PERFGRP[87]:=[# 51840.1
  [[1,"abd",
  function(a,b,d)
  return
  [[a^2,b^5,(a*b)^9,(a^-1*b^-1*a*b)^3,(b*a*b*a
  *b^-1*a*b^-1*a)^2*d^-1,d^2,
  a^-1*d*a*d^-1,b^-1*d*b*d^-1],
  [[b^-1*a*b*a*(b^3*a)^2*b*a*b^3*a*b^-1,
  a*b^3*a*b*a*b^2*a*b*a*b^3*(a*b^-1)^2*d]
  ]];
  end,
  [80]],
  "U4(2) 2^1",28,-2,
  22,80]
  ];
  PERFGRP[88]:=[# 51888.1
  [[1,"abc",
  function(a,b,c)
  return
  [[c^23,c*b^(-1*22)*c^-1*b^-1,b^47,a^2,c*a*c*a
  ^-1,(b*a)^3],[[b,c]]];
  end,
  [48],[0,2,2]],
  "L2(47)",22,-1,
  27,48]
  ];
  PERFGRP[89]:=[# 56448.1
  [[2,168,1,336,1],
  "( L3(2) x L3(2) ) 2^1 [1]",[34,1,1],2,
  [2,2],[7,16]],
  # 56448.2
  [[3,336,1,336,1,"d1","d2"],
  "( L3(2) x L3(2) ) 2^1 [2]",[34,1,2],2,
  [2,2],128]
  ];
  PERFGRP[90]:=[# 57600.1
  [[2,960,1,60,1],
  "A5 x A5 # 2^4 [1]",[29,4,1],1,
  [1,1],[16,5]],
  # 57600.2
  [[2,960,2,60,1],
  "A5 x A5 # 2^4 [2]",[29,4,2],1,
  [1,1],[10,5]]
  ];
  PERFGRP[91]:=[# 57624.1
  [[1,"abxyz",
  function(a,b,x,y,z)
  return
  [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,x^7,y^7,
  z^7,x^-1*y^-1*x*y,x^-1*z^-1*x*z,
  y^-1*z^-1*y*z,a^-1*x*a*z^-1,
  a^-1*y*a*y,a^-1*z*a*x^-1,
  b^-1*x*b*z^-1,
  b^-1*y*b*(y^-1*z^-1)^-1,
  b^-1*z*b*(x*y^2*z)^-1],
  [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,y]]];
  end,
  [56]],
  "L3(2) 7^3",[10,3,1],1,
  2,56],
  # 57624.2
  [[1,"abxyz",
  function(a,b,x,y,z)
  return
  [[a^2,b^3,(a*b)^7*z^-1,(a^-1*b^-1*a*b)^4,
  x^7,y^7,z^7,x^-1*y^-1*x*y,
  x^-1*z^-1*x*z,y^-1*z^-1*y*z,
  a^-1*x*a*z^-1,a^-1*y*a*y,
  a^-1*z*a*x^-1,b^-1*x*b*z^-1,
  b^-1*y*b*(y^-1*z^-1)^-1,
  b^-1*z*b*(x*y^2*z)^-1],
  [[a*b*x^2,b*a*b^-1*a*b^-1*a*b*a*b^-1,y
  ]]];
  end,
  [56]],
  "L3(2) N 7^3",[10,3,2],1,
  2,56]
  ];
  PERFGRP[92]:=[# 58240.1
  [[1,"abd",
  function(a,b,d)
  return
  [[a^2,b^4,(a*b)^5,(a^-1*b^-1*a*b)^7*d,(a*b^2)
  ^13,
  a*b^-1*a*b^2*a*b^2*(a*b^-1*a*b*a*b^2)^2
  *a*b^2*a*b*(a*b^2)^4,d^2,
  a^-1*d*a*d^-1,b^-1*d*b*d^-1],
  [[a*b^2,(a*b*a*b^2)^2*a*b^2*a*b^-1
  *(a*b^2*a*b*a*b^2)^2]]];
  end,
  [1120]],
  "Sz(8) 2^1",28,-2,
  23,1120]
  ];
  PERFGRP[93]:=[# 58320.1
  [[1,"abcwxyz",
  function(a,b,c,w,x,y,z)
  return
  [[a^4,b^3,c^3,(b*c)^4*a^2,(b*c^-1)^5,a^2*b*a^2
  *b^-1,a^2*c*a^2*c^-1,
  a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,w^3,
  x^3,y^3,z^3,w^-1*x^-1*w*x,
  w^-1*y^-1*w*y,w^-1*z^-1*w*z,
  x^-1*y^-1*x*y,x^-1*z^-1*x*z,
  y^-1*z^-1*y*z,a^-1*w*a*z^-1,
  a^-1*x*a*x^-1,
  a^-1*y*a*(w^-1*x^-1*y^-1*z^-1)
  ^-1,a^-1*z*a*w^-1,
  b^-1*w*b*x^-1,b^-1*x*b*y^-1,
  b^-1*y*b*w^-1,b^-1*z*b*z^-1,
  c^-1*w*c*(w^-1*x*y^-1*z^-1)^-1,
  c^-1*x*c*(x^-1*z)^-1,
  c^-)^-,
  c^-1*z*c*x],
  [[c*b*a^-1,b,w],[b,c*a*b*c,z]]];
  end,
  [80,30]],
  "A6 2^1 x 3^4'",[14,4,1],2,
  3,[80,30]],
  # 58320.2
  [[1,"abcstuv",
  function(a,b,c,s,t,u,v)
  return
  [[a^4,b^3,c^3,(b*c)^4*a^(-1*2),(b*c^-1)^5,a^-1
  *b^-1*c*b*c^-*c*^-,
  a^(-1*2)*b^-1*a^2*bb-*zb(z^1Z^1b-**Z
  s^3,t^3,u^3,v^3,s^-1*t^-1*s*t,
  s^-1*u^-1*s*u,s^-1*v^-1*s*v,
  t125]]
  u^-1*v^-1*u*v,a^-1  " 215^ E 52"[3,,],
  a^-1*t*a*v^-1,a^-1*u*a*s,
  a^-1*v*a*t,b^-1*s*b*(s*v^-1)^-1,
  b^-1*t*b*(t*u^-1*v)^-1,
  b^-1*u*b*u^-1,b^-1*v*b*v^-1,
  c^-1*s*c*(s^-1*t*u^-1*v)^-1,
  c^-1*t*c*(s*t*u*v)^-1,
  c^-1*u*c*(s^-1*v^-1)^-1,
  c^-1*v*c*(t^-1*u^-1*v)^-1],
  [[a,b,c]]];
  end,
  [81]],
  "A6 2^1 3^4",[14,4,2],1,
  3,81],
  # 58320.3 (otherpres.)
  [[1,"abcdstuv",
  function(a,b,c,d,s,t,u,v)
  return
  [[a^2*d^-1,b^3,c^3,(b*c)^4*d^-1,(b*c^-1)^5,
  a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,d^2,
  d^-1*b^-1*d*b,d^-1*c^-1*d*c,s^3,
  t^3,u^3,v^3,s^-1*t^-1*s*t,
  s^-1*u^-1*s*u,s^-1*v^-1*s*v,
  t^-1*u^-1*t*u,t^-1*v^-1*t*v,
  u^-1*v^-1*u*v,a^-1*s*a*u^-1,
  a^-1*t*a*v^-1,a^-1*u*a*s,
  a^-1*v*a*t,b^-1*s*b*(s*v^-1)^-1,
  b^-1*t*b*(t*u^-1*v)^-1,
  b^-1*u*b*u^-1,b^-1*v*b*v^-1,
  c^-1*s*c*(s^-1*t*u^-1*v)^-1,
  c^-1*t*c*(s*t*u*v)^-1,
  c^-1*u*c*(s^-1*v^-1)^-1,
  c^-1*v*c*(t^-1*u^-1*v)^-1],
  [[a,b,c]]];
  end,
  [81]]]
  ];
  PERFGRP[94]:=[# 58800.1
  [[1,"abc",
  function(a,b,c)
  return
  [[c^24,b^7,c^(-1*8)*b^2*c^8*b^-1,c*b^3*c*b^2*c
  ^(-1*2)*b^(-1*3),a^2,c*a*c*a^-1,(b*a)^3,
  ]
  *b^-1*a],[[b,c]]];
  end,
  [50]],
  "java.lang.StringIndexOutOfBoundsException: Range [2, 1) out of bounds for length 23
  8]
  ];
  PERFGRP[]=#60480java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
  [[1,"abd",
  function(a,b,d)
  return
  [^2,^4,(ab^*^,a-*^1a)5java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
  (a*b^2)^5,(a*b*a*b*a*b^3)^5,
  ("A5  2^3^ 4],,,
  a^-1*d*a*d^-1,b^-1*d*b*d^1060]
  [[a*b*a,b^2*a*b^-1*a  PERFGRP[106]=[ .java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
  endjava.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
  []],
  "L3(4) 3^1",[27,0,1],-3,
  20,63],
  # 60480.2
  [[2,120,1,504,1],
  " ^ xL2()"[35,,]2java.lang.StringIndexOutOfBoundsException: Range [30, 31) out of bounds for length 30
  [1,4],[24,9]],
  # 60480.3
  [[2,168,1,360,[312011320,,d1,""]
  L(2 x ,3701,1java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
  [2,3]]
  ];
:=fail;
  PERFGRP[97]:=[# 62400.1
  [[1,"ab",
  function(a,b)
  return
  [[a^2,b^3,(a*b)^15,(a^-1*b^-1*a*b)^5,(a*b*a*b*a
  *b*a*b^-1*a*b^-1*a*b^-1)^3,
  (a*b^-1*a*b*a*b*a*b*a*b*a*b)^4],
  [[(a*b)^5*a,b*a*b^-1*(a*b)^6]]];
  end,
  [65]],
  "34"28-,
  29,65]
  ];
  PERFGRP[98]:=[# 64512.1
  [[1,"abcuvwxyzd",
  function(a,b,c,u,v,w,x,y,z,d)
  return
  [[a^2,b^3,(a*b)^7,b^-1*(a*b)^3*c^-1,c*b^-1
  *c*b*a^-1*b^-1*c^-1*b
  *c^-1*a,u^2,v^2,w^2,x^2,y^2,z^2,d^2,
  u^-1*v^-1*u*v,u^-1*w^-1*u*w,
  u^-1*x^-1*u*x,u^-1*y^-1*u*y,
  u^-1*z^-1*u*z,u^-1*d^-1*u*d,
  v^-1*w^-1*v*w,v^-1*x^-1*v*x,
  v^-1*y^-1*v*y,v^-1*z^-1*v*z,
  v^-1*d^-1*v*d,w^-1*x^-1*w*x,
  w^-1*y^-1*w*y,w^-1*z^-1*w*z  [88][0,,2],
  java.lang.StringIndexOutOfBoundsException: Range [2, 1) out of bounds for length 32
  x^-1*z^-1*java.lang.StringIndexOutOfBoundsException: Range [2, 1) out of bounds for length 8
  y^-1*z^-1*y*z,y^-1*d^-1*y*d,
  z^-1*d^-1*z*d,a^-1*u*a*(u*x)^-1,
  a^-1*v*a*(v*y)^-1,a^-1*w*a*(w*z)^-1,
  a^-1*x*a*x^-1,a^-1*y*a*y^-1,
  a^-1*z*a*z^-1,a^-1*d*a*d^-1,
  b-**b**
  b^-1*v*b*(y*z)^-1,
  b^-1*w*b*(x*y*z)^-1,
  b^-1*x*b*(v*w*x)^-1,
  b^-1*y*b*(u*v*w*y)^-1,
  java.lang.StringIndexOutOfBoundsException: Range [4, 3) out of bounds for length 13
 *(d)^c^1**(w)-,
  c^-1*w*c*(u*v)^-1,
  -**c*(**^1c^-*y**^-,
  c^-1*z*c*y^-1,c^-1*d*c*d^-1],
  [[b^-1*c,u*d]]];
  end,
  1],
  "L2(8) 2^6 E 2^1",[16,7,1],2,
  4,112],
  # 64512.2
  [[1,"abcuvwxyzf",
  function(a,b,c,u,v,w,xv^1*x1v*x^-y-*vy,
  return
  [[a^2*f,bv^1*^1*zw^-1*x^-1*w*x,
  *^-**^-*-*c
  *b^-1*c*b*a*(y*z)^-1,f^2,u^2,vx-y^1x*y^-*^1**java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
  w^,x^2y^2,z,^-1v-*u*v,
  u^-1*w^-1*u*w,u^-1*x^-1*u*x,
  u^-1*y^-1*u*y,u^-1*z^-1*u*z,
  u^-1*f^-1*u*f,v^-1*w^-1*v*w,
  v^-1*x^-1*v*x,v^-1*y^-1*v*y,
  v^-1*z^-1*v*z,v^-1*f^-1*v*f,
  w^-1*x^-1*w*x,w^-1*y^-1*w*y,
  w^-1*z-1wz,-*^1wfjava.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
  x^-1*y^-1*x*y,x^-1*z^-1*x*z,
  x^b-*y*b*(u^1*w**z)^1,
  y^-1*f^-1*y*f,z  b-1z**w*^1^-][[2ab,u];
  -*ua*ux)-1a^-*a(*)-,
  a^-1*w*a*(w*z)^-1,a
  a^-1*y*a*y^-"5^136"[,62]1java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
  a^-1*f*a*f^-1,
  b^-1*u*b*(x*y*f^-1)^-1,
  b^-1*v*b*(y*z)^-1,
  b^1w**(*y*z^1,
  b^-1*x*b*(v*w*x)^-1,
  b^-1*y*b*(u*v*w*y)^-1,
  b^-1*z*b*(u*w*z*f^-1)^-1,
  -*f**^1,
  c^-1*u*c*(v*f^-1)^-1,
  ^1v**w*f^1)-,
  c^-1*w*c*(u*v*f)^-1,
  ^1x**x**)-
  c^-1*y*c*(x*f)^-1,
  c^e-*b-1e*b,e^-1*s^-1*e*s,
  c^-1*f*c*f^-1],[[b^-1*c,u*f]]];
  end,
  [112]],
  "L2(8) N 2^6 E 2^1 I",[16,7,2],2,
  4,112],
  # 64512.3
  [[1,"abcuvwxyzd",
  function(a,b,c,u,v,w,x,y,z,d)
  return
  [[a^2,b^3,(a*b)^7,b^-1*(a*b)^3*c^-1,b^-1*c
  ^-1*b*c^-1* d^1e-1d*e,s3t^,^,^3
  *c*b*a*(y*z*d)^-1,s^-*^1**,s^-1u^1su
  y^2,z^2,u^-1*v^-1*u*v,u^-1*w^-1*u*w
  ,u^-1*x^-1*u*x,u^-1*y^-1*u*y,
  u^-1*z^-1*u*z,u^-1*d^-1*u*d,
  v^-1*w^-1*v*w,v^-1*x^-1*v*x,
  v^-1*y^-1*v*y,v^-1*z^-1*v*z,
  v^-1*d^-1*v*d,w^-1*x^-1*w*x,
  w^-1*y^-1*w*y,w^-1*z^-1*w*z,
  w^-1*d^-1*w*d,x^-1*y^-1*x*y,
  x^-1*z^-1*x*z,x^-1*d^-1*x*d,
  y^-1*z^-1*y*z,y^-1*d^-1*y*d,
  z^-1*d^-1*z*d,a^-1*u*a*(u*x)^-1,
  a^-1*v*a*(v*y)^-1,a^-1*w*a*(w*z)^-1,
  a^-1*x*a*x^-1,a^-1*y*a*y^-1,
  a^-1*z*a*z^-1,a^-1*d*a*d^-1,
  b^-1*u*b*(x*y)^-1,b^-1*v*b*(y*z)^-1,
  b^-1*w*b*(x*y*z*d)^-1,
  ^1*xb(**)1,
  b^-1*y*b*(u*v*w*y*d)^-1,
  b^-1*z*b*(u*w*z)^-1,b^-1*d*b*d^-1,
  c^-1*u*c*(v*d)^-1,c^-1*v*c*(w*d)^-1,
  c^-1*w*c*(u*v)^-1,
  c^-1*x*c  b^-1*s*b*(s*v^1*d-)-1,
  c^-1*y*c*(x*d)^-1,c^-1*z*c*y^-1,
  ^-*c^-1,[b^1c*,ud]]
  end,
  112,
  "L2(8) N 2^6 E 2^1 II",[16,7,3],java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 21
  4,112]"5 213^ C  3^1 x 3^1 )",2639java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
  # 64512.4
  [[1,"abcuvwxyzd",
  function(a,b,c,u,v,w,x,y,z,d)
  return
  [[a^2*d,b^3,(a*b)^7,b^-1*(a*b)^3*c^-1,b^-1
  *c^-1*b*c^-1*a^-1*c
  *b^-1*c*b*a*(y*z*d)^-1,d^2,u^2,
  w^2,x^2,y^2,z^2,u^-1*v^-1*u*v,
  u^-1*w^-1*u*w,u^-1*x^-1*u*x,
  u^-1*y^-1*u*y,u^-1*z^-1*u*z,
  u^-1*d^-1*u*d,v^-1*w^-1*v*w,
  v^1x-*vx,v-*^1*v,
  v^-1*z^-1*v*z,v^-1*d^-1*v*d,
  w^-1*x^-1*w*x,w^-1*y^-1*w*y,
  w^-1*z^-1*w*z,w^-1*d^-1*w*d,
  x^-1*y^-1*x*y,x^-1*z^-1*x*z,
  x^-1*d^-1*x*d,y^-1*z^-1*y*z,
  y^-1*d^-1*y*d,z^-1*d^-1*z*d,
  a^-1*u*a*(u*x)^-1,a^-1*v*a*(v*y)^-1,
  a^-1*w*a*(w*z)^-1,a^-1*x*a*x^-1,
  a^-1*y*a*y^-1,a^-1*z*a*z^-1,
  a^-1*d*a*d^-1,b^-1*u*b*(x*y*d)^-1,
  b^-1*v*b*(y*z)^-1,
  b^-1*w*b*(x*y*z*d)^-1,
  b^-1*x*b*(v*w*x)^-1,
  b^-1*y*b*(u*v*w*y*d)^-1,
  b^-1*z*b*(u*w*z*d)^-1,b^-1*d*b*d^-1
  ,c^-1*u*c*v^-1,c^-1*v*c*w^-1,
  c^-1*w*c*(u*v*d)^-1,
  c^-1*x*c*(x*z)^-1,c^-1*y*c*x^-1,
  c^-1*z*c*(y*d)^-1,c^-1*d*c*d^-1],
  [[b^-1*c*d,java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
  end,
java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 9
  L2)N21III,16,7]2,
  4,112]
]
  PERFGRP[99]:=[# 64800.1
  [[2,60,1,1080,1],
  be*e^1,
  [1,3],[5,18]]
  ];
  PERFGRP[100]:=[# 65520.1
  [[2,60,1,1092,1],
  "A5 x L2(13)",40,1,
  [1,6],[5,14]]
  ];
  PERFGRP[]=[#688801
  [[1,"abc",
  unctionabc
  return
  [[c^20*a^2,c*b^8*c^-1*b^-1,b^41,a^4,a^2*b^(-1
  *1)*a^2*b,a^2*c^-1*a^2*c,
  c*a*c*a^-1,(b[108]
  [[b,"A6 34 E31 "[,54]3
  end,
  [336]],
  "L2(41) 2^1 = SL(2,41)",22,-2,
  25,336]
  ];
  PERFGRP[102][ .java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
  [[4,23040r
  "A6 3^1 x ( 2^4 E 2^[a^*d^-1b3c^(*)4,(*c^-)^5a^1
  3,[64,18]],
  # 69120.2
  [423040,,10802,,,1,
  "A6 3^1 x ( 2^4 E 2^1 A ) C N 2^1",[13,6,2],12,
  3,[384,18]],
  # 69120.3
  [,23040,,1080,36031,
  "A6 3^1 x 2^1 x ( 2^4 E 2^1 )",[13,6,3],12,
  3,[12,80,18]],
  # 69120.4
  [[1,"abcuvwxyz",
  function(a,b,c,u,v,w,x,y,z)
  return
  [[a^6,b^3,c^3,(b*c)^4,(b*c^-1)^5,ax^1*-**dy^-d-**,
  *b*c*b^-1*c*b*c^-1,u^2,v^2,w^2,
  x^2,y^2,z^2,u^-1*v^-1*u*v,
  u^-1*w^-1*u*w,u^-1*x^-1*u*x,
  u^-1*y^-1*u*y,u^-1*z^-1*u*z,
  v^-1*w^-1*v*w,v^-1*x^-1*v*x,
  v^-1*y^-1*v*y,v^-1*z^-1*v*z,
  w^-1*x^-1*w*x,w^-1*y^-1*w*y,
  w^-1*z^-1*w*z,x^-1*y^-1*x*y,
  x^-1*z^-1*x*z,y^-1*z^-1*^1,
  a^-1*u*a*(v*x)^-1,
  a^-1*v*a*(u*v*w*x)^-1,a^-1*w*a*x^-1
  ,a^-1*x*a*(w*x)^-1,
  a^-1*y*a*(x*z)^-1,
  a^-1*z*a*(w*x*y*z)^-1,b^-1*u*b*u^-1
  ,b^-1*v*b*v^-1,b^-1*w*b*(u*x)^-1,
  b^-1*x*b*(v*w*x)^-1,
  b^-1*y*b*(u*y*z)^-1,
  b^-1*z*b*(v*y)^-1,c^-1*u*c*w^-1,
  c^-1*v*c*x^-1,c^-1*w*c*(y*z)^-1,
  c^-1*x*c*y^-1,c^-1*y*
  c^-1*z*c*(u*v)^-1],[[b,c]]];
  end,
  [64]],
  "A6 3^1 # 2^6 [4]",[13,6,4],1,
  3,64]
  ];
  PERFGRP[103]:=[# 74412.1
  [[1,"abc",
  function(a,b,c)
  return
  [[c^26,c*b^4*c^-1*b^-1,b^53,a^2,c*a*c*a^-1,
  ba)^3,(1*)b***2ab^2*a*cb*]java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46
  [[b,c]]];
  end,
  [54]],
  "L2(53)",22,-1,
  30,54]
  ];
  PERFGRP[104]:=[# 75000.1
  [1,abxyzd"
  function(a,b,x,y,z,d)
  return
  [[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-1,end,
  x^-1*y^-1*x*y,x^-1  "6 ^ x3^4",14,5,5]3java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
  y^-1*z^-1*y*z,x^-1*d^-1*x*d,
  y^-1*d^-1*y*d,z^-1*d^-1*z*d,
  a^-1*d^-1*a*d,b^-1*d^-1*b*d,
  a^-1*x*a*z^-1*d,a^-1*y*a*y*d^-1,
  a^-1*z*a*x^-1*d^-1,
  b^-1*x*b*z^-1,
  b^-1*y*b*(y^-1*z)^-1,
  b^-1*z*b*(x*y^(-1*2)*z)^-1],
  [[a*b,x],[b,a*b*a*b^-1*a,x]]];
  end,
  [24,25]],
  "A5 2^1 x 5^3 E 5^1",[3,4,1],10,
  1,[24,25]],
  # 75000.2
  [[1,"abwxyz",
  function(a,b,w,x,y,z)
  return
  [[w^5,x^5,y^5,z^5,w^-1*x^-1*w*x,w^-1*y^(-1
  *1)*w*y,w^-1*z^-1*w*z,
  x^-1*y^-1*x*y,x^-1*z^-1*x*z,
  y^-1*z^-1*y*z,a^-1*w*a*z^-1,
  a^-1*x*a*y,a^-1*y*a*x^-1,
  a^-1*z*a*w,b^-1*w*b*z,
  b^-1*x*b*(y*z^-1)^-1,
  b^-1*y*b*(x^-1*y^2*z^-1)^-1,
  b^-1*z*b*(w*x^2*y^(-1*2)*z^-1)^-1,a^4,
  b^3,(a*b)^5,a^2*b^-1*a^2*b],
  [[a*b,b*a*b*a*b^-1*a*b^-1,x]]];
  end,
  [30]],
  "A5 2^1 5^4",[3,4,2],1,
  1,30],
  # 75000.3
  [[1,"abyzYZ",
  function(a,b,y,z,Y,Z)
  return
  [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,y^5,z^5,Y^5,Z^5,
  y^-1*z^-1*y*z,y^-1*Y^-1*y*Y,
  y^-1*Z^-1*y*Z,z^-1*Y^-1*z*Y,
  z^-1*Z^-1*z*Z,Y^-1*Z^-1*Y*Z,
  a^-1*y*a*z^-1,a^-1*z*a*y,
  a^-1*Y*a*Z^-1,a^-1*Z*a*Y,
  b^-1*y*b*z,b^-1*z*b*(y*z^-1)^-1,
  b^-1*Y*b*Z,b^-1*Z*b*(Y*Z^-1)^-1],
  [[a,b,y],[a,b,Y]]];
  end,
  [25,25]],
  "A5 2^1 5^2 x 5^2",[3,4,3],1,
  1,[25,25]],
  # 75000.4
  [[1,"abyzYZ",
  function(a,b,y,z,Y,Z)
  return
  [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,y^5,z^5,Y^5,Z^5,
  y^-1*z^-1*y*z,y^-1*Y^-1*y*Y,
  y^-1*Z^-1*y*Z,z^-1*Y^-1*z*Y,
  z^-1*Z^-1*z*Z,Y^-1*Z^-1*Y*Z,
  a^-1*y*a*(z*Y^-1)^-1,
  a^-1*z*a*(y^-1*Z)^-1,
  a^-1*Y*a*Z^-1,a^-1*Z*a*Y,
  b^-1*y*b*(z^-1*Y^-1*Z)^-1,
  b^-1*z*b*(y*z^-1*Z)^-1,b^-1*Y*b*Z,
  b^-1*Z*b*(Y*Z^-1)^-1],
  [[b,a*b*a*b^-1*a,y*Y^-1*Z^-1]]];
  end,
  [125]],
  "A5 2^1 5^2 E 5^2",[3,4,4],1,
  1,125]
  ];
  PERFGRP[105]:=[# 77760.1
  [[4,960,1,4860,1,60],
  "A5 # 2^4 3^4 [1]",6,1,
  1,[16,15]],
  # 77760.2
  [[4,960,2,4860,1,60],
  "A5 # 2^4 3^4 [2]",6,1,
  1,[10,15]],
  # 77760.3
  [[4,960,1,4860,2,60],
  "A5 # 2^4 3^4 [3]",6,1,
  1,[16,60]],
  # 77760.4
  [[4,960,2,4860,2,60],
  "A5 # 2^4 3^4 [4]",6,1,
  1,[10,60]]
  ];
  PERFGRP[106]:=[# 79200.1
  [[2,120,1,660,1],
  "( A5 x L2(11) ) 2^1 [1]",[36,1,1],2,
  [1,5],[24,11]],
  # 79200.2
  [[2,60,1,1320,1],
  "( A5 x L2(11) ) 2^1 [2]",[36,1,2],2,
  [1,5],[5,24]],
  # 79200.3
  [[3,120,1,1320,1,"d1","d2"],
  "( A5 x L2(11) ) 2^1 [3]",[36,1,3],2,
  [1,5],288]
  ];
  PERFGRP[107]:=[# 79464.1
  [[1,"abc",
  function(a,b,c)
  return
  [[c^21*a^2,c*b^9*c^-1*b^-1,b^43,a^4,a^2*b^(-1
  *1)*a^2*b,a^2*c^-1*a^2*c,
  c*a*c*a^-1,(b*a)^3],[[b,c^2]]];
  end,
  [88],[0,0,2]],
  "L2(43) 2^1 = SL(2,43)",22,-2,
  26,88]
  ];
  PERFGRP[108]:=[# 79860.1
  [[1,"abxyz",
  function(a,b,x,y,z)
  return
  [[a^2,b^3,(a*b)^5,x^11,y^11,z^11,x^-1*y^-1*x*y,
  x^-1*z^-1*x*z,y^-1*z^-1*y*z,
  a^-1*x*a*z^-1,a^-1*y*a*y,
  a^-1*z*a*x^-1,
  b^-1*x*b*(x*y^(-1*5)*z^(-1*2))^-1,
  b^-1*y*b*(x^(-1*4)*y^-1)^-1,
  b^-1*z*b*x^(-1*5)],
  [[a*b,b*a*b*a*b^-1*a*b^-1,y*z^5]]];
  end,
  [66]],
  "A5 11^3",[5,3,1],1,
  1,66]
  ];
  PERFGRP[109]:=[# 80640.1
  [[1,"abdwxyz",
  function(a,b,d,w,x,y,z)
  return
  [[a^2*d^-1,b^4*d^-1,(a*b)^7,(a*b)^2*a*b^2*(
  a*b*a*b^-1)^2*(a*b)^2
  *(a*b^-1)^2*a*b*a*b^-1,d^2,
  d^-1*a^-1*d*a,d^-1*b^-1*d*b,w^2,
  x^2,y^2,z^2,w*x*w*x,w*y*w*y,w*z*w*z,x*y*x*y,
  x*z*x*z,y*z*y*z,a^-1*w*a*y^-1,
  a^-1*x*a*z^-1,a^-1*y*a*w^-1,
  a^-1*z*a*x^-1,b^-1*w*b*(w*x*y*z)^-1
  ,b^-1*x*b*y^-1,b^-1*y*b*(w*x)^-1,
  b^-1*z*b*(w*z)^-1],
  [[a,b],[a*b,b*a*b*a*b^2*a*b^-1*a*b*a*b^-1
  *a*b*a*b^2*d,w]]];
  end,
  [16,240]],
  "A7 2^1 x 2^4",[23,5,1],2,
  8,[16,240]],
  # 80640.2
  [[1,"abef",
  function(a,b,e,f)
  return
  [[a^2,b^4,(a*b)^7*e,(a*b^2)^5*(e*f)^-1,(a^-1*b
  ^-1*a*b)^5,(a*b*a*b*a*b^3)^5*f,
  (a*b*a*b*a*b^2*a*b^-1)^5,e^2,f^2,
  e^-1*f^-1*e*f,a^-1*e*a*e^-1,
  a^-1*f*a*f^-1,b^-1*e*b*e^-1,
  b^-1*f*b*f^-1],
  [[a*e,b*a*b*a*b^-1*a*b^2*f^-1]]];
  end,
  [224]],
  "L3(4) 2^1 x 2^1",[27,2,1],-4,
  20,224],
  # 80640.3
  [[1,"abf",
  function(a,b,f)
  return
  [[a^2,b^4*f^(-1*2),(a*b)^7,(a*b^2)^5*f^-1,(a^-1
  *b^-1*a*b)^5*f^(-1*2),(a*b*a*b*a*b^3)^5
  *f,(a*b*a*b*a*b^2*a*b^-1)^5,f^4,
  a^-1*f*a*f^-1,b^-1*f*b*f^-1],
  [[a,b*a*b*a*b^-1*a*b^2*f^-1]]];
  end,
  [224]],
  "L3(4) 2^1 A 2^1 I",[27,2,2],-4,
  20,224],
  # 80640.4
  [[1,"abe",
  function(a,b,e)
  return
  [[a^2,b^4*e^(-1*2),(a*b)^7*e,(a*b^2)^5*e^-1,(a^(-1
  *1)*b^-1*a*b)^5*e^(-1*2),
  (a*b*a*b*a*b^3)^5*e^(-1*2),
  (a*b*a*b*a*b^2*a*b^-1)^5,
  a^-1*e*a*e^-1,b^-1*e*b*e^-1],
  [[a*e^2,b^-1*a*b^-1*a*b*a*b^2]]];
  end,
  [224]],
  "L3(4) 2^1 A 2^1 II",[27,2,3],-4,
  20,224],
  # 80640.5
  [[2,60,1,1344,1],
  "( A5 x L3(2) ) # 2^3 [1]",[31,3,1],1,
  [1,2],[5,8]],
  # 80640.6
  [[2,60,1,1344,2],
  "( A5 x L3(2) ) # 2^3 [2]",[31,3,2],1,
  [1,2],[5,14]]
  ];
  PERFGRP[110]:=[# 84672.1
  [[2,168,1,504,1],
  "L3(2) x L2(8)",[38,0,1],1,
  [2,4],[7,9]]
  ];
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  PERFGRP[112]:=[# 86400.1
  [[2,120,1,720,1],
  "( A5 x A6 ) 2^2",[33,2,1],4,
  [1,3],[24,80]]
  ];
  PERFGRP[113]:=[# 87480.1
  [[1,"abuvwxyz",
  function(a,b,u,v,w,x,y,z)
  return
  [[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-1,u^3,v^3,w^3,x^3,
  y^3,z^3,u^-1*v^-1*u*v,u^-1*w^-1*u*w
  ,u^-1*x^-1*u*x,u^-1*y^-1*u*y,
  u^-1*z^-1*u*z,
  a^-1*u*a*(u^-1*v*w^-1*x^-1*y)^-1
  ,a^-1*v*a*(u*v*w^-1*z)^-1,
  a^-1*w*a*(u^-1*w*x*y^-1*z^-1)^-1
  ,a^-1*x*a*(v^-1*w*y^-1)^-1,
  a^-1*y*a*(u*v^-1*w^-1*y^-1*z)^-1
  ,a^-1*z*a*(u^-1*v^-1*x^-1*y*z)
  ^-1,b^-1*u*b*(u*w^-1*y)^-1,
  b^-1*v*b*(v*x^-1*z)^-1,
  b^-1*w*b*(w*y)^-1,b^-1*x*b*(x*z)^-1,
  b^-1*y*b*y^-1,b^-1*z*b*z^-1],
  [[a*b,u,v],[a*b,b*a*b*a*b^-1*a*b^-1,z]]];
  end,
  [24,18]],
  "A5 2^1 x 3^6",[2,6,1],2,
  1,[24,18]],
  # 87480.2
  [[1,"abuvwxyz",
  function(a,b,u,v,w,x,y,z)
  return
  [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,u^3,v^3,w^3,x^3,
  y^3,z^3,u^-1*v^-1*u*v,u^-1*w^-1*u*w
  ,u^-1*x^-1*u*x,u^-1*y^-1*u*y,
  u^-1*z^-1*u*z,v^-1*w^-1*v*w,
  v^-1*x^-1*v*x,v^-1*y^-1*v*y,
  v^-1*z^-1*v*z,w^-1*x^-1*w*x,
  w^-1*y^-1*w*y,w^-1*z^-1*w*z,
  x^-1*y^-1*x*y,x^-1*z^-1*x*z,
  y^-1*z^-1*y*z,a^-1*u*a*v^-1,
  a^-1*v*a*u,a^-1*w*a*(u^-1*x)^-1,
  a^-1*x*a*(v*w^-1)^-1,
  a^-1*y*a*(u*w^-1*x^-1*y^-1*z^-1)
  ^-1,a^-1*z*a*(w^-1*y^-1*z)^-1,
  b^-1*u*b*(u^-1*v^-1*w)^-1,
  b^-1*v*b*(u^-1*v*w)^-1,
  b^-1*w*b*u^-1,b^-1*x*b*(w*y)^-1,
  b^-1*y*b*(u^-1*w*x*y*z)^-1,
  b^-1*z*b*(w*y*z^-1)^-1],[[a^2,a*b,u]]];
  end,
  [36]],
  "A5 2^1 3^6'",[2,6,2],1,
  1,36],
  # 87480.3
  [[1,"abstuvde",
  function(a,b,s,t,u,v,d,e)
  return
  [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,d^3,d^-1*a
  ^-1*d*a,d^-1*b^-1*d*b,
  d^-1*s^-1*d*s,e^3,e^-1*a^-1*e*a,
  e^-1*b^-1*e*b,e^-1*s^-1*e*s,
  d^-1*e^-1*d*e,s^3,t^3,u^3,v^3,
  s^-1*t^-1*s*t,s^-1*u^-1*s*u
  *d^-1,s^-1*v^-1*s*v*e^-1,
  t^-1*u^-1*t*u*e^-1,
  t^-1*v^-1*t*v*(d*e^-1)^-1,
  u^-1*v^-1*u*v,
  a^-1*s*a*(u*e^-1)^-1,
  a^-1*t*a*(v*e)^-1,
  a^-1*u*a*(s^-1*d)^-1,
  a^-1*v*a*(t^-1*d)^-1,
  b^-1*s*b*(s*v^-1*d^-1)^-1,
  b^-1*t*b*(t*u^-1*v*d*e^-1)^-1,
  b^-1*u*b*u^-1,b^-1*v*b*v^-1],
  [[a,b,d],[a,b,e]]];
  end,
  [243,243]],
  "A5 2^1 3^4 C ( 3^1 x 3^1 )",[2,6,3],9,
  1,[243,243]],
  # 87480.4
  [[1,"abcdwxyz",
  function(a,b,c,d,w,x,y,z)
  return
  [[a^2*d^-1,b^3,c^3*(w*x*y^-1)^-1,(b*c)^4,
  (b*c^-1)^5,a^-1*b^-1*c*b*c*b^-1*c*b
  *c^-1,d^3,w^3,x^3,y^3,z^3,d^-1*w^-1*d
  *w,d^-1*x^-1*d*x,d^-1*y^-1*d*y,
  d^-1*z^-1*d*z,w^-1*x^-1*w*x,
  w^-1*y^-1*w*y,w^-1*z^-1*w*z,
  x^-1*y^-1*x*y,x^-1*z^-1*x*z,
  y^-1*z^-1*y*z,a^-1*d*a*d^-1,
  a^-1*w*a*z^-1,a^-1*x*a*x^-1,
  a^-1*y*a*(w^-1*x^-1*y^-1*z^-1)
  ^-1,a^-1*z*a*w^-1,
  b^-1*d*b*(d*w*y^-1*z)^-1,
  b^-1*w*b*x^-1,b^-1*x*b*y^-1,
  b^-1*y*b*w^-1,b^-1*z*b*z^-1,
  c^-1*d*c*(d*x^-1*z^-1)^-1,
  c^-1*w*c*(w^-1*x*y^-1*z^-1)^-1,
  c^-1*x*c*(x^-1*z)^-1,
  c^-1*y*c*(w*x^-1)^-1,c^-1*z*c*x],
  [[b,c*a*b*c,d*y^-1*z]]];
  end,
  [30]],
  "A6 3^1 E 3^4' I",[14,5,1],1,
  3,30],
  # 87480.5
  [[1,"abcdwxyz",
  function(a,b,c,d,w,x,y,z)
  return
  [[a^2*d^-1,b^3*(w*x*y*z^-1)^-1,c^3*(w*y
  ^-1*z^-1)^-1,(b*c)^4,(b*c^-1)^5,
  a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,d^3,
  w^3,x^3,y^3,z^3,d^-1*w^-1*d*w,
  d^-1*x^-1*d*x,d^-1*y^-1*d*y,
  d^-1*z^-1*d*z,w^-1*x^-1*w*x,
  w^-1*y^-1*w*y,w^-1*z^-1*w*z,
  x^-1*y^-1*x*y,x^-1*z^-1*x*z,
  y^-1*z^-1*y*z,a^-1*d*a*d^-1,
  a^-1*w*a*z^-1,a^-1*x*a*x^-1,
  a^-1*y*a*(w^-1*x^-1*y^-1*z^-1)
  ^-1,a^-1*z*a*w^-1,
  b^-1*d*b*(d*w*x^-1*z)^-1,
  b^-1*w*b*x^-1,b^-1*x*b*y^-1,
  b^-1*y*b*w^-1,b^-1*z*b*z^-1,
  c^-1*d*c*(d*x)^-1,
  c^-1*w*c*(w^-1*x*y^-1*z^-1)^-1,
  c^-1*x*c*(x^-1*z)^-1,
  c^-1*y*c*(w*x^-1)^-1,c^-1*z*c*x],
  [[b*w^-1,c*a*b*c]]];
  end,
  [30]],
  "A6 3^1 E 3^4' II",[14,5,2],1,
  3,30],
  # 87480.6
  [[1,"abcwxyzf",
  function(a,b,c,w,x,y,z,f)
  return
  [[a^2,b^3,c^3,(b*c)^4,(b*c^-1)^5,a^-1*b^-1*c
  *b*c*b^-1*c*b*c^-1,w^3,x^3,y^3,
  z^3,f^3,w^-1*f^-1*w*f,x^-1*f^-1*x*f
  ,y^-1*f^-1*y*f,z^-1*f^-1*z*f,
  w^-1*x^-1*w*x,w^-1*y^-1*w*y,
  w^-1*z^-1*w*z,x^-1*y^-1*x*y,
  x^-1*z^-1*x*z,y^-1*z^-1*y*z,
  a^-1*w*a*z^-1,a^-1*x*a*x^-1,
  a^-1*y*a*(w^-1*x^-1*y^-1*z^-1)
  ^-1,a^-1*z*a*w^-1,
  a^-1*f*a*f^-1,b^-1*w*b*x^-1,
  b^-1*x*b*y^-1,b^-1*y*b*w^-1,
  b^-1*z*b*z^-1,b^-1*f*b*f^-1,
  c^-1*w*c*(w^-1*x*y^-1*z^-1*f)^-1
  ,c^-1*x*c*(x^-1*z*f)^-1,
  c^-1*y*c*(w*x^-1*f)^-1,
  c^-1*z*c*(x^-1*f^-1)^-1,
  c^-1*f*c*f^-1],[[a,b,w]]];
  end,
  [18]],
  "A6 3^4' E 3^1 I",[14,5,3],3,
  3,18],
  # 87480.7
  [[1,"abcwxyze",
  function(a,b,c,w,x,y,z,e)
  return
  [[a^2,b^3,c^3,(b*c)^4,(b*c^-1)^5,a^-1*b^-1*c
  *b*c*b^-1*c*b*c^-1,w^3,x^3,y^3,
  z^3,e^3,w^-1*e^-1*w*e,x^-1*e^-1*x*e
  ,y^-1*e^-1*y*e,z^-1*e^-1*z*e,
  w^-1*x^-1*w*x,w^-1*y^-1*w*y,
  w^-1*z^-1*w*z,x^-1*y^-1*x*y,
  x^-1*z^-1*x*z,y^-1*z^-1*y*z,
  a^-1*w*a*z^-1,a^-1*x*a*x^-1,
  a^-1*y*a*(w^-1*x^-1*y^-1*z^-1)
  ^-1,a^-1*z*a*w^-1,
  a^-1*e*a*e^-1,b^-1*w*b*x^-1,
  b^-1*x*b*(y*e^-1)^-1,
  b^-1*y*b*(w*e)^-1,b^-1*z*b*(z*e)^-1,
  b^-1*e*b*e^-1,
  c^-1*w*c*(w^-1*x*y^-1*z^-1*e^-1)
  ^-1,c^-1*x*c*(x^-1*z*e^-1)^-1,
  c^-1*y*c*(w*x^-1*e^-1)^-1,
  c^-1*z*c*(x^-1*e)^-1,
  c^-1*e*c*e^-1],
  [[a*b,b*a*b*a*b^-1*a*b^-1,w*e]]];
  end,
  [108]],
  "A6 3^4' E 3^1 II",[14,5,4],3,
  3,108],
  # 87480.8
  [[1,"abcwxyzd",
  function(a,b,c,w,x,y,z,d)
  return
  [[a^2*d^-1,b^3,c^3,(b*c)^4,(b*c^-1)^5,a^-1
  *b^-1*c*b*c*b^-1*c*b*c^-1,
  d^3,b^-1*d*b*d^-1,c^-1*d*c*d^-1,
  w^3,x^3,y^3,z^3,w^-1*d^-1*w*d,
  x^-1*d^-1*x*d,y^-1*d^-1*y*d,
  z^-1*d^-1*z*d,w^-1*x^-1*w*x,
  w^-1*y^-1*w*y,w^-1*z^-1*w*z,
  x^-1*y^-1*x*y,x^-1*z^-1*x*z,
  y^-1*z^-1*y*z,a^-1*w*a*z^-1,
  a^-1*x*a*x^-1,
  a^-1*y*a*(w^-1*x^-1*y^-1*z^-1)
  ^-1,a^-1*z*a*w^-1,
  b^-1*w*b*x^-1,b^-1*x*b*y^-1,
  b^-1*y*b*w^-1,b^-1*z*b*z^-1,
  c^-1*w*c*(w^-1*x*y^-1*z^-1)^-1,
  c^-1*x*c*(x^-1*z)^-1,
  c^-1*y*c*(w*x^-1)^-1,
  c^-1*z*c*x],
  [[a*d,c*d,w],[b,c*a*b*c,z]]];
  end,
  [18,30]],
  "A6 3^1 x 3^4'",[14,5,5],3,
  3,[18,30]]
  ];