Spracherkennung für: .tbl vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
#############################################################################
##
#W ctomisc6.tbl GAP table library Thomas Breuer
##
## This file contains the ordinary character tables of miscellaneous
## CAS tables (alphabetical order, 'pap' to 'w(f4)')
##
#H ctbllib history
#H ---------------
#H $Log: ctomisc6.tbl,v $
#H Revision 4.34 2012/04/23 16:16:14 gap
#H next step of consolidation:
#H
#H - removed a few unnecessary duplicate tables,
#H and changed some related fusions, names of maxes, table constructions
#H - make sure that duplicate tables arise only via `ConstructPermuted'
#H constructions
#H - added some relative names
#H - added fusions A11.2 -> A12.2, L2(11).2 -> A12.2, D8x2F4(2)'.2 -> B,
#H L2(41) -> M, (A5xA12):2 -> A17,
#H - added maxes of A12.2, L6(2), 2.M22.2
#H - added table of QD16.2,
#H - fixed the syntax of two `ALN' calls
#H TB
#H
#H Revision 4.33 2012/01/30 08:31:58 gap
#H removed #H entries from the headers
#H TB
#H
#H Revision 4.32 2011/09/28 14:32:22 gap
#H removed revision entry and SET_TABLEFILENAME call
#H TB
#H
#H Revision 4.31 2010/12/01 17:47:57 gap
#H renamed "Sym(4)" to "Symm(4)";
#H note that the table constructed with `CharacterTable( "Symmetric", 4 )'
#H gets the identifier `"Sym(4)"', and this table is sorted differently
#H TB
#H
#H Revision 4.30 2010/05/05 13:20:07 gap
#H - added many class fusions,
#H - changed several class fusions according to consistency conditions,
#H after systematic checks of consistency
#H - with Brauer tables w.r.t. the restriction of characters,
#H - of subgroup fusions with the corresponding subgroup fusions between
#H proper factors where the factor fusions are stored,
#H - of subgroup fusions from maximal subgroups with subgroup fusions of
#H extensions inside automorphic extensions
#H
#H TB
#H
#H Revision 4.29 2009/04/22 12:39:06 gap
#H added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H TB
#H
#H Revision 4.28 2007/07/03 08:50:15 gap
#H added fusions,
#H encoded several tables as index two subdirect products
#H TB
#H
#H Revision 4.27 2004/01/20 10:26:13 gap
#H added several names of the forms `<name>C<class>', `<name>N<class>'
#H TB
#H
#H Revision 4.26 2003/06/10 16:19:11 gap
#H store in several fusions between character tables to which subgroup number
#H in the table of marks of the supergroup the subgroup belongs
#H (in order to make the commutative diagrams testable)
#H TB
#H
#H Revision 4.25 2003/05/15 17:38:18 gap
#H next step towards the closer connection to the library of tables of marks:
#H added fusions tbl -> tom, adjusted fusions between character tables
#H in order to make the diagrams commute, adjusted orderings of maxes
#H TB
#H
#H Revision 4.24 2003/03/07 15:53:40 gap
#H added tables of `Isoclinic(2.A5.2)' and `L2(125)',
#H and many `tomidentifier' components (still several are missing)
#H TB
#H
#H Revision 4.23 2003/01/29 15:51:54 gap
#H added admissible names, fusions, tables for certain maxes (which are
#H available in Rob's ATLAS and thus should be available in the table
#H library, too)
#H TB
#H
#H Revision 4.22 2003/01/24 15:57:34 gap
#H replaced several fusions by ones that are compatible with Brauer tables
#H TB
#H
#H Revision 4.21 2003/01/21 16:25:32 gap
#H further standardizations of `InfoText' strings,
#H added and corrected `Maxes' infos,
#H added some fusions
#H TB
#H
#H Revision 4.20 2002/11/04 16:31:43 gap
#H inserted a comma (fixes the newly added 2nd power map of suzs2)
#H TB
#H
#H Revision 4.19 2002/10/22 12:44:13 gap
#H added 215 factor fusions for cases <tbl> -> <tbl> / O_{<p>}(<tbl>)
#H (they make it possible to construct <p>-modular Brauer tables
#H for tables of the type [p^n].<fact> where the <p>-modular Brauer table
#H of <fact> is in the library)
#H TB
#H
#H Revision 4.18 2002/09/18 15:22:01 gap
#H changed the `text' components of many fusions,
#H in order to use them as a status information (for evaluation)
#H TB
#H
#H Revision 4.17 2002/08/21 14:53:59 gap
#H removed names s2m21, s2m23, s2m23 (now M24C2A)
#H added fusion M24C2A -> M24
#H TB
#H
#H Revision 4.16 2002/07/18 17:55:46 gap
#H added power map of suzs2
#H TB
#H
#H Revision 4.15 2002/07/12 06:45:56 gap
#H further tidying up: removed `irredinfo' stuff, rearranged constructions
#H TB
#H
#H Revision 4.14 2001/05/04 16:49:09 gap
#H first revision for ctbllib
#H
#H
#H tbl history (GAP 4)
#H -------------------
#H (Rev. 4.14 of ctbllib coincides with Rev. 4.13 of tbl in GAP 4)
#H
#H RCS file: /gap/CVS/GAP/4.0/tbl/ctomisc6.tbl,v
#H Working file: ctomisc6.tbl
#H head: 4.13
#H branch:
#H locks: strict
#H access list:
#H symbolic names:
#H GAP4R2: 4.13.0.6
#H GAP4R2PRE2: 4.13.0.4
#H GAP4R2PRE1: 4.13.0.2
#H GAP4R1: 4.9.0.2
#H keyword substitution: kv
#H total revisions: 15; selected revisions: 15
#H description:
#H ----------------------------
#H revision 4.13
#H date: 2000/01/06 13:52:06; author: gap; state: Exp; lines: +12 -2
#H added maxes of S5 with fusions (I needed them ...)
#H
#H TB
#H ----------------------------
#H revision 4.12
#H date: 1999/08/25 17:32:28; author: gap; state: Exp; lines: +3 -2
#H added name `2^2' for `V4'
#H
#H TB
#H ----------------------------
#H revision 4.11
#H date: 1999/08/20 13:40:25; author: gap; state: Exp; lines: +2 -69
#H removed corrupted table with name `u4q3c'
#H
#H (Apparently this should be $3_2.U_4(3).2_3^{\prime}$,
#H but the characters are wrong, consistent power maps do not exist,
#H already the table of the factor group by the normal $3$ is fishy
#H --it has no elements of order $9$--, even the info text is rubbish!
#H I hate these old CAS tables ...)
#H
#H TB
#H ----------------------------
#H revision 4.10
#H date: 1999/07/30 07:55:20; author: gap; state: Exp; lines: +6 -5
#H corrected table `s61p'
#H (I hate these old CAS tables ...)
#H
#H TB
#H ----------------------------
#H revision 4.9
#H date: 1999/07/19 16:08:09; author: gap; state: Exp; lines: +5 -2
#H added character parameters for table of S4 ...
#H
#H TB
#H ----------------------------
#H revision 4.8
#H date: 1999/07/16 10:53:37; author: gap; state: Exp; lines: +4 -3
#H changed `classtext' components of tables of alternating and symmetric
#H groups to `ClassParameters' values (same format as computed from
#H generic tables)
#H
#H TB
#H ----------------------------
#H revision 4.7
#H date: 1999/07/14 11:39:41; author: gap; state: Exp; lines: +4 -3
#H cosmetic changes for the release ...
#H
#H TB
#H ----------------------------
#H revision 4.6
#H date: 1999/06/23 11:59:17; author: gap; state: Exp; lines: +2 -88
#H added admissible name L4(3).2^2 to the table of this group,
#H added fusions from index 2 subgroups
#H
#H TB
#H ----------------------------
#H revision 4.5
#H date: 1998/08/18 13:54:57; author: gap; state: Exp; lines: +2 -214
#H added table of S15 mod 3 (constructed by J"urgen M"uller)
#H
#H TB
#H ----------------------------
#H revision 4.4
#H date: 1998/03/12 15:52:22; author: gap; state: Exp; lines: +3 -71
#H tables with names `mo81p' and `y' are both `2^6:A8';
#H cleaned this situation, added some fusions
#H
#H TB
#H ----------------------------
#H revision 4.3
#H date: 1997/11/25 15:45:34; author: gap; state: Exp; lines: +5 -4
#H first attempt to link the library of character tables and the
#H library of tables of marks
#H TB
#H ----------------------------
#H revision 4.2
#H date: 1997/08/05 15:03:54; author: gap; state: Exp; lines: +6 -6
#H removed unnecessary (and ugly) `return' statements in the calls of
#H `ConstructPermuted' and `ConstructSubdirect'
#H ----------------------------
#H revision 4.1
#H date: 1997/07/17 15:45:22; author: fceller; state: Exp; lines: +2 -2
#H for version 4
#H ----------------------------
#H revision 1.2
#H date: 1997/04/04 12:20:25; author: sam; state: Exp; lines: +199 -335
#H added 'ConstructPermuted', 'ConstructSubdirect',
#H changed table constructions involving 'CharTable', 'RecFields'
#H 'Sort...' up to now
#H ----------------------------
#H revision 1.1
#H date: 1996/10/21 16:00:51; author: sam; state: Exp;
#H first proposal of the table library
#H ==========================================================================
##
MOT("L3(4)Syl2",
[
"origin: CAS library,\n",
"Sylow 2 subgroup of M21 = L3(4)\n",
"tests: 1.o.r., pow[2],\n",
"2nd power map determined only up to matrix automorphisms,"
],
[64,64,64,64,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16],
[,[1,1,1,1,1,1,1,1,2,3,2,1,4,4,2,1,3,3,4]],
[[1,1,1,1,1,-1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,1],[1,1,1,1,1,1,-1,-1,1,1,-1,-1,
1,-1,-1,-1,1,1,-1],
[TENSOR,[1,2]],[1,1,1,1,1,-1,1,-1,-1,-1,1,-1,1,1,-1,-1,1,-1,1],
[TENSOR,[1,4]],
[TENSOR,[2,4]],
[TENSOR,[1,6]],[1,1,1,1,-1,-1,1,-1,1,-1,1,1,1,-1,1,-1,-1,1,-1],
[TENSOR,[1,8]],
[TENSOR,[2,8]],
[TENSOR,[1,10]],
[TENSOR,[4,8]],
[TENSOR,[1,12]],
[TENSOR,[2,12]],
[TENSOR,[1,14]],
[TENSOR,[1,1]],[4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[4,-4,4,-4,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],[4,4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[( 5, 6)( 7,12)( 8,16)(10,17)(11,15)(14,19),( 2, 4)( 7, 8)( 9,13)(10,17)
(11,19)(12,16)(14,15),( 3, 4)( 6, 7)( 9,11)(10,19)(12,16)(13,17)(14,18)]);
ALF("L3(4)Syl2","L3(4)",[1,2,2,2,2,2,2,2,4,5,6,2,4,6,5,2,6,4,5],[
"determined using that the three root classes of each central involution\n",
"map to different classes in L3(4)"
]);
ALN("L3(4)Syl2",["L3(4)C2A","L3(4)N2A"]);
MOT("M23C2A",
[
"involution centralizer in sporadic Mathieu group M23,\n",
"origin: CAYLEY, tests: 1.o.r., pow[2,3,7]"
],
0,
0,
0,
0,
["ConstructPermuted",["2^(1+3):L3(2)"],(4,6)(5,7)(8,9,10,11,14,16,15,12),(2,3)
(6,9,12,8)(10,14)(11,13)(15,16)]);
ARC("M23C2A","CAS",[rec(name:="s2m23",
permchars:=( 8, 9)(10,11),
permclasses:=( 5, 7, 6)( 8,11, 9,10)(12,13,15,14))]);
ALF("M23C2A","M23",[1,2,2,2,3,4,4,4,6,6,6,7,8,9,12,13],[
"fusion map is unique up to table automorphisms,\n",
"the map on the CAS table is wrong"
]);
ALF("M23C2A","L3(2)",[1,1,1,2,3,2,2,4,3,3,3,5,6,4,5,6]);
ALN("M23C2A",["M23C2","M23N2A"]);
MOT("U72CT",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,5,11]"
],
[168170618880,168170618880,169869312,159252480,254803968,254803968,4718592,
3538944,663552,3538944,3538944,589824,73728,49152,466560,466560,373248,373248,
20736,31104,1492992,1492992,20736,27648,15552,15552,2592,884736,884736,49152,
73728,9216,73728,73728,12288,3072,18432,18432,3072,768,720,720,120,10368,
10368,31104,31104,5184,41472,41472,2304,3456,1728,1728,41472,41472,6912,1728,
3456,3456,576,2592,2592,432,1728,1728,288,768,768,128,324,324,648,648,108,66,
66,864,864,6912,6912,384,576,1728,1728,288,144,144,576,576,96,90,90,108,108,
46080,92160,92160,3072,3072,768,1536,1536,256,256,288,576,576,96,96,72,144,
144,3072,3072,512,384,3072,3072,512,384,256,512,512,128,128,128,20,40,40,24,
48,48,64,64,32,64,64,32,96,96,48,96,96,48,82114560,82114560,497664,497664,
27648,27648,119439360,119439360,497664,442368,1866240,1866240,311040,1492992,
1492992,20736,27648,23328,23328,46656,46656,7776,31104,31104,1728,2592,6912,
6912,2304,2304,576,576,90,90,663552,663552,36864,55296,6912,41472,41472,6912,
497664,497664,6912,9216,7776,7776,41472,41472,6912,1728,2592,2592,27648,27648,
1536,2304,6912,6912,1152,5184,5184,864,13824,13824,2304,576,864,864,10368,
10368,576,864,2592,2592,432,864,864,144,96,96,5184,5184,288,432,324,324,162,
162,648,648,108,66,66,66,66,13824,13824,2304,576,3456,3456,576,1728,1728,288,
432,432,864,864,144,576,576,96,576,576,96,576,576,96,144,144,360,360,60,90,90,
432,432,72,108,108],
[,[1,1,1,2,1,1,1,2,3,1,1,2,3,3,15,15,17,17,17,18,21,21,22,21,25,25,26,5,5,5,6,
8,5,5,7,8,10,10,11,14,41,41,42,15,15,17,17,19,17,17,17,18,15,15,21,21,22,24,
17,17,19,25,25,26,25,25,26,33,33,35,71,71,73,73,74,76,76,44,44,49,49,49,50,55,
55,57,53,53,49,49,51,92,92,71,71,1,4,4,3,4,10,12,12,14,14,21,23,23,24,23,25,
27,27,28,28,30,32,28,28,30,32,28,30,30,31,32,32,41,43,43,65,67,67,68,68,70,68,
68,70,84,84,86,84,84,86,146,146,146,146,146,146,152,152,153,152,156,156,157,
159,159,160,159,163,163,165,165,166,168,168,168,169,148,148,148,148,150,150,
178,178,152,152,152,153,155,156,156,157,159,159,160,159,163,163,159,159,160,
162,163,163,152,152,155,155,156,156,157,165,165,166,159,159,160,162,163,163,
168,168,168,169,168,168,170,168,168,170,174,174,228,228,228,229,232,232,234,
234,236,236,237,239,239,241,241,180,180,181,183,185,185,186,194,194,196,198,
198,207,207,208,200,200,202,204,204,205,194,194,196,198,198,269,269,270,272,
272,228,228,230,232,232],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,2,1,2,3,4,1,2,4,
3,1,2,4,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,5,6,5,6,9,5,6,7,8,10,
11,5,6,8,9,10,11,13,5,6,8,10,11,12,68,69,70,17,18,17,18,20,76,77,28,29,28,29,
30,31,28,29,32,37,38,33,34,35,41,42,46,47,96,97,98,99,100,101,102,103,104,105,
96,98,97,99,100,96,97,98,114,115,116,117,118,119,120,121,122,123,124,125,126,
127,128,129,130,101,103,102,134,135,136,137,138,139,118,119,121,114,115,117,1,
2,5,6,10,11,1,2,4,3,1,2,4,1,2,4,3,1,2,1,2,4,1,2,3,4,28,29,33,34,37,38,41,42,5,
6,7,8,9,5,6,8,5,6,8,7,5,6,5,6,8,9,5,6,10,11,14,13,10,11,12,5,6,8,10,11,12,13,
10,11,5,6,7,8,5,6,9,10,11,13,68,69,17,18,19,20,17,18,17,18,17,18,20,76,77,76,
77,28,29,31,32,28,29,31,28,29,32,28,29,28,29,31,37,38,40,37,38,39,33,34,36,33,
34,41,42,43,41,42,46,47,48,46,47],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,1,2,4,44,
45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,15,16,94,95,96,
98,97,99,100,101,103,102,104,105,106,108,107,109,110,111,113,112,118,119,120,
121,114,115,116,117,122,124,123,125,127,126,96,97,98,131,133,132,137,138,139,
134,135,136,143,144,145,140,141,142,146,147,148,149,150,151,152,153,154,155,
156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,
175,176,177,146,147,180,181,182,183,184,185,186,187,188,189,190,191,192,193,
194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,
213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,
232,233,234,235,236,237,238,241,242,239,240,243,244,245,246,247,248,249,250,
251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,156,
157,158,152,153,274,275,276,277,278],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
67,68,69,70,71,72,73,74,75,1,2,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,
93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,
114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,
133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,
152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,
171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,
190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,
209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,
228,229,230,231,232,233,234,235,236,237,238,146,147,146,147,243,244,245,246,
247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,
266,267,268,269,270,271,272,273,274,275,276,277,278]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
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[TENSOR,[4,2]],[20,20,20,20,-12,-12,-12,-12,-12,4,4,4,4,4,-10,-10,2,2,2,2,8,8,
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3,0,0,0,1,1,1,1,1,1,-2,-2,-2,1,1,-1,-1,-1,2,2,-1,-1,-1,2,2],[44,44,44,44,12,
12,12,12,12,-4,-4,-4,-4,-4,14,14,-1,-1,-1,-1,5,5,5,5,2,2,2,4,4,4,4,4,4,4,4,4,
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[TENSOR,[10,2]],[55,55,55,55,23,23,23,23,23,7,7,7,7,7,10,10,1,1,1,1,10,10,10,
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10,10,10,10,10,10,1,1,1,1,1,1,10,10,10,1,1,1,1,-1,-1,-1,-1,3,3,0,0,2,2,2,2,2,
2,2,2,5,5,5,5,5,5,5,5,5,5,5,5,-2,-2,-2,-2,-2,-2,-2,2,2,2,1,1,1,1,1,1,-1,-1,-1,
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-1,-1,2,2,2,0,0,0,0,0,0,-1,-1,-1,-1,-1,0,0,0,0,0,-1,-1,-1,-1,-1],
[TENSOR,[12,2]],[88,88,88,88,24,24,24,24,24,-8,-8,-8,-8,-8,28,28,-2,-2,-2,-2,
10,10,10,10,4,4,4,8,8,8,8,8,8,8,8,8,0,0,0,0,-2,-2,-2,12,12,6,6,6,6,6,6,6,4,4,
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0,0],[110,110,110,110,46,46,46,46,46,14,14,14,14,14,20,20,2,2,2,2,20,20,20,20,
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0,0,0,0,1,1,1,1,1],[110,110,110,110,14,14,14,14,14,-2,-2,-2,-2,-2,-25,-25,2,2,
2,2,2,2,2,2,2,2,2,14,14,14,14,14,6,6,6,6,-2,-2,-2,-2,0,0,0,-1,-1,-4,-4,-4,2,2,
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2,2,2,2,2,2,2,2,14,14,14,14,14,6,6,6,6,-2,-2,-2,-2,0,0,0,-1,-1,-4,-4,-4,2,2,2,
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2,2,-1,-1],[110,110,110,110,14,14,14,14,14,-2,-2,-2,-2,-2,-25,-25,2,2,2,2,2,2,
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0,4,-4,-2,2,0,-2,2,0,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[65536,-65536,0,0,
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0,0,0,-24,24,0,0,-24,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,4,-4,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,-E(33)-E(33)^2-E(33)^4
-E(33)^8-E(33)^16-E(33)^17-E(33)^25-E(33)^29-E(33)^31-E(33)^32,
E(33)+E(33)^2+E(33)^4+E(33)^8+E(33)^16+E(33)^17+E(33)^25+E(33)^29+E(33)^31
+E(33)^32,-E(33)^5-E(33)^7-E(33)^10-E(33)^13-E(33)^14-E(33)^19-E(33)^20
-E(33)^23-E(33)^26-E(33)^28,E(33)^5+E(33)^7+E(33)^10+E(33)^13+E(33)^14
+E(33)^19+E(33)^20+E(33)^23+E(33)^26+E(33)^28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[277,5]]],
[(239,241)(240,242),( 97, 98)(102,103)(107,108)(112,113)(114,115)(118,119)
(123,124)(129,130)(132,133)(134,135)(137,138)(140,141)(143,144),( 97, 98)
(102,103)(107,108)(112,113)(114,118)(115,119)(116,120)(117,121)(123,124)
(126,127)(129,130)(132,133)(134,137)(135,138)(136,139)(140,143)(141,144)
(142,145),(114,119)(115,118)(116,120)(117,121)(126,127)(134,138)(135,137)
(136,139)(140,144)(141,143)(142,145)]);
ALF("U72CT","(3xU5(2)).2",[1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,5,5,5,5,6,6,6,
6,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,10,11,11,11,12,12,13,13,13,14,14,14,14,
15,15,16,16,16,16,17,17,17,18,18,18,19,19,19,20,20,20,21,21,22,22,22,23,
23,24,24,25,25,25,25,26,26,26,27,27,28,28,28,29,29,30,30,78,78,78,78,78,
79,79,79,79,79,80,80,80,80,80,81,81,81,82,82,82,82,83,83,83,83,84,84,84,
84,84,84,85,85,85,86,86,86,87,87,87,88,88,88,90,90,90,89,89,89,31,31,32,
32,33,33,34,34,34,34,35,35,35,36,36,36,36,37,37,38,38,38,39,39,39,39,40,
40,41,41,42,42,43,43,44,44,44,44,44,45,45,45,46,46,46,46,47,47,48,48,48,
48,49,49,50,50,50,50,51,51,51,52,52,52,53,53,53,53,54,54,56,56,56,56,55,
55,55,57,57,57,58,58,59,59,59,59,60,60,61,61,62,62,62,63,63,64,64,65,65,
65,65,66,66,66,67,67,67,68,68,69,69,69,70,70,70,71,71,71,72,72,72,73,73,
74,74,74,75,75,76,76,76,77,77]);
MOT("pap",
[
"origin: CAS library,\n",
"names:=pap\n",
" order: 2^2.3^3 = 108\n",
" number of classes: 11\n",
" source:norman, j.f.\n",
" the group characters for a group of\n",
" order 108 associated with a pappus\n",
" theorem of projective geometry,\n",
" [romanian summary]\n",
" an. univ. timisoara ser. sti.mat.11\n",
" (1973),115-122\n",
" generated by dixon algorithm\n",
" aachen (1980)\n",
" comments:degree:4\n",
" generators:a,b,c,d\n",
" relations: a^2=b^2=c^2=d^3=1\n",
" (ac)^3=(acd)^3=(bd)^2=1\n",
" (ad)^2=(da)^2\n",
" [ab]=[bc]=[cd]=1 \n",
"tests: 1.o.r., pow[2,3]"
],
0,
0,
0,
0,
["ConstructPermuted",["M12N3"],(2,8,6)(4,7)(5,9,11,10),(1,3,4)(5,8,6)(10,11)
]);
MOT("V4",
0,
[4,4,4,4],
[,[1,1,1,1]],
[[1,1,1,1],[1,1,-1,-1],[1,-1,1,-1],[1,-1,-1,1]],
[(2,3),(3,4)]);
ARC("V4","projectives",["Q8",[[2,0,0,0]],]);
ALF("V4","D8",[1,2,4,4],[
"fusion map is unique up to table automorphisms"
]);
ALN("V4",["2^2"]);
MOT("Q8",
0,
[8,8,4,4,4],
[,[1,1,2,2,2]],
0,
[(3,4),(4,5)],
["ConstructProj",[["V4",[]],["Q8",[]]]]);
ALF("Q8","V4",[1,1,2,3,4]);
MOT("M24C2A",
[
"origin: CAS library (name was s2m24),\n",
"tests: 1.o.r., pow[2,3,7]"
],
0,
0,
0,
0,
["ConstructPermuted",["2^1+6.psl(3,2)"],(6,12,10,9,8,7)(11,13,15,14)(17,22,18,
23,19,24,20,25)(21,26)(28,29),(2,25,23,20,17,16,8,10,13,6,4)(3,26,28,30,29,24,
22,21,19,18,15,9,12,5)(7,11,14)]);
ALF("M24C2A","M24",[1,2,2,2,3,2,3,2,3,7,6,6,7,6,7,8,8,7,6,7,14,4,10,10,10,
17,12,13,19,20],[
"fusion map is unique up to table autom."
]);
ALF("M24C2A","L3(2)",[1,1,1,1,1,2,2,2,2,2,2,1,2,2,2,2,4,4,4,4,4,3,3,3,3,3,
5,6,5,6]);
ALN("M24C2A",["M24N2A"]);
MOT("s2wrs2",
[
"origin: CAS library,\n",
"names:=s2wrs2; d8\n",
" order: 2^3 = 8\n",
" number of classes: 5\n",
" source:saenger, f.\n",
" einige charakterentafeln von symmetrien\n",
" symmetrischer gruppen\n",
" mitt.math.sem.giessen\n",
" heft 98 [1973], 21-38\n",
" comments:wreath-product of s2 with s2\n",
" test: orth.1, minus \n",
"tests: 1.o.r., pow[2]"
],
0,
0,
0,
0,
["ConstructPermuted",["D8"],(3,5),(2,4)]);
MOT("s2wrs3",
[
"origin: CAS library,\n",
"names:=s2wrs3\n",
" order: 2^4.3 = 48\n",
" number of classes: 10\n",
" source:saenger, f.\n",
" einige charakterentafeln von symmetrien\n",
" symmetrischer gruppen\n",
" mitt.math.sem. giessen\n",
" heft 98 [1973], 21 - 38\n",
" comments:wreath-product of s2 with s3\n",
" test: orth.1, minus, sym(3) \n",
"tests: 1.o.r., pow[2,3]"
],
0,
0,
0,
0,
["ConstructPermuted",["2xSymm(4)"],(),(4,5)(9,10)]);
ALF("s2wrs3","A6.2_1",[1,8,2,7,4,11,2,8,5,9],[
"fusion 2xSymm(4) -> A6.2_1 mapped under A6.2^2"
]);
MOT("s2wrs4",
[
"origin: CAS library,\n",
"names:=s2wrs4\n",
" order: 2^7.3 = 384\n",
" number of classes: 20\n",
" source:saenger, f.\n",
" einige charakterentafeln von symmetrien\n",
" symmetrischer gruppen\n",
" mitt.math.sem. giessen\n",
" heft 98 [1973], 21 - 38\n",
" comments:wreath-product of s2 with s4\n",
" test: orth.1, minus, sym(3) \n",
"tests: 1.o.r., pow[2,3]"
],
[384,384,64,32,32,12,12,96,96,16,12,12,32,32,16,8,32,32,16,8],
[,[1,1,1,1,2,6,6,1,1,3,6,6,1,1,3,4,3,3,1,5],[1,2,3,4,5,1,2,8,9,10,9,8,13,14,
15,16,17,18,19,20]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,
-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1],
[TENSOR,[2,3]],[2,2,2,2,2,-1,-1,2,2,2,-1,-1,0,0,0,0,0,0,0,0],
[TENSOR,[5,3]],[3,3,3,-1,-1,0,0,3,3,-1,0,0,1,1,1,-1,1,1,1,-1],
[TENSOR,[7,2]],
[TENSOR,[7,3]],
[TENSOR,[7,4]],[6,6,-2,2,-2,0,0,0,0,0,0,0,2,2,-2,0,0,0,0,0],[6,6,-2,-2,2,0,0,
0,0,0,0,0,0,0,0,0,2,2,-2,0],
[TENSOR,[12,2]],
[TENSOR,[11,2]],[4,-4,0,0,0,1,-1,2,-2,0,1,-1,2,-2,0,0,2,-2,0,0],
[TENSOR,[15,2]],
[TENSOR,[15,3]],
[TENSOR,[15,4]],[8,-8,0,0,0,-1,1,4,-4,0,-1,1,0,0,0,0,0,0,0,0],
[TENSOR,[19,3]]],
[(13,14)(17,18),( 8, 9)(11,12)(17,18)]);
ARC("s2wrs4","tomfusion",rec(name:="2^4:S4",map:=[1,2,4,3,11,10,41,5,9,16,
43,44,7,8,19,30,31,14,6,49],text:=[
"fusion map is unique up to table autom."
]));
ALF("s2wrs4","A8.2",[1,2,3,2,6,5,10,13,14,16,19,18,2,3,7,6,16,15,14,20],[
"fusion map is unique up to table autom."
]);
ALF("s2wrs4","U4(2).2",[1,2,3,3,7,5,11,2,3,8,13,11,16,17,19,19,18,19,17,
23],[
"determined using the fusion 2^4:A4 -> U4(2)"
]);
ALN("s2wrs4",["w(b4)"]);
MOT("s2wrs5",
[
"origin: CAS library,\n",
"names:=s2wrs5\n",
" order: 2^8.3.5 = 3,840\n",
" number of classes: 36\n",
" source:saenger, f.\n",
" einige charakterentafeln von symmetrien\n",
" symmetrischer gruppen\n",
" mitt.math.sem. giessen\n",
" heft 98 [1973], 21 -38\n",
" comments:wreath-product of s2 with s5\n",
" test: orth.1, minus, sym(3) \n",
"tests: 1.o.r., pow[2,3,5]"
],
[3840,768,384,64,64,32,48,48,24,10,3840,768,384,64,64,32,48,48,24,10,192,192,
64,64,16,16,24,24,192,192,64,64,16,16,24,24],
[,[1,1,1,1,2,3,7,7,7,10,1,1,1,1,2,3,7,7,7,10,1,3,3,1,4,5,7,8,3,1,1,3,4,5,7,
8],[1,2,3,4,5,6,1,3,2,10,11,12,13,14,15,16,13,11,12,20,21,22,23,24,25,26,21,
22,29,30,31,32,33,34,30,29],,[1,2,3,4,5,6,7,8,9,1,11,12,13,14,15,16,17,18,19,
11,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,
-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[2,3]],[4,4,4,0,0,0,1,1,1,-1,4,4,4,0,0,0,1,1,1,-1,2,2,2,2,0,0,-1,-1,2,
2,2,2,0,0,-1,-1],
[TENSOR,[5,2]],
[TENSOR,[5,3]],
[TENSOR,[5,4]],[5,5,5,1,1,1,-1,-1,-1,0,5,5,5,1,1,1,-1,-1,-1,0,1,1,1,1,-1,-1,1,
1,1,1,1,1,-1,-1,1,1],
[TENSOR,[9,2]],
[TENSOR,[9,3]],
[TENSOR,[9,4]],[5,-3,1,1,1,-1,2,-2,0,0,-5,3,-1,-1,-1,1,2,-2,0,0,3,-3,1,-1,1,
-1,0,0,3,-3,1,-1,-1,1,0,0],
[TENSOR,[13,2]],
[TENSOR,[13,3]],
[TENSOR,[13,4]],[6,6,6,-2,-2,-2,0,0,0,1,6,6,6,-2,-2,-2,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],
[TENSOR,[17,3]],[10,-6,2,2,2,-2,-2,2,0,0,10,-6,2,2,2,-2,2,-2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],[10,2,-2,2,-2,0,1,1,-1,0,10,2,-2,2,-2,0,1,1,-1,0,4,2,-2,
0,0,0,1,-1,2,4,0,-2,0,0,1,-1],[10,2,-2,-2,2,0,1,1,-1,0,10,2,-2,-2,2,0,1,1,-1,
0,2,4,0,-2,0,0,-1,1,4,2,-2,0,0,0,-1,1],
[TENSOR,[20,2]],
[TENSOR,[21,2]],
[TENSOR,[19,3]],
[TENSOR,[20,3]],
[TENSOR,[21,3]],
[TENSOR,[20,4]],
[TENSOR,[21,4]],[15,-9,3,-1,-1,1,0,0,0,0,15,-9,3,-1,-1,1,0,0,0,0,3,-3,1,-1,-1,
1,0,0,-3,3,-1,1,-1,1,0,0],
[TENSOR,[29,2]],
[TENSOR,[29,3]],
[TENSOR,[29,4]],[20,4,-4,0,0,0,-1,-1,1,0,20,4,-4,0,0,0,-1,-1,1,0,2,-2,-2,2,0,
0,-1,1,-2,2,2,-2,0,0,-1,1],
[TENSOR,[33,2]],
[TENSOR,[33,3]],
[TENSOR,[33,4]]],
[(21,30)(22,29)(23,32)(24,31)(25,33)(26,34)(27,35)(28,36)]);
ARC("s2wrs5","tomfusion",rec(name:="2^5:S5`",map:=[1,4,5,12,31,60,13,76,85,
75,2,3,6,10,36,42,78,79,83,259,7,22,28,11,72,185,90,264,17,8,9,34,67,210,
86,277],text:=[
"fusion map is unique up to table autom."
]));
ALF("s2wrs5","A10.2",[1,3,2,3,9,7,5,13,14,11,24,23,25,24,28,27,30,33,32,
37,2,7,8,3,9,16,13,20,26,24,25,27,28,35,33,39],[
"fusion map is unique up to table autom."
]);
ALF("s2wrs5","A5.2",[1,1,1,2,2,2,3,3,3,4,1,1,1,2,2,2,3,3,3,4,5,5,5,5,6,6,
7,7,5,5,5,5,6,6,7,7]);
ALN("s2wrs5",["w(b5)"]);
MOT("s3wrs2",
[
"origin: CAS library,\n",
"names:=s3wrs2, o4p2\n",
" order: 2^3.3^2 = 72\n",
" number of classes: 9\n",
" source:saenger, f.\n",
" einige charakterentafeln von symmetrien\n",
" symmetrischer gruppen\n",
" mitt.math.sem. giessen\n",
" heft 98 [1973], 21 - 38\n",
" comments:wreath-product of s3 with s2\n",
" test: orth.1, minus, sym(3) \n",
"tests: 1.o.r., pow[2,3]"
],
[72,18,18,8,12,6,12,6,4],
[,[1,2,3,1,1,2,1,3,4],[1,1,1,4,5,5,7,7,9]],
[[1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,-1,-1,-1],[1,1,1,1,-1,-1,1,1,-1],
[TENSOR,[2,3]],[2,2,2,-2,0,0,0,0,0],[4,-2,1,0,0,0,2,-1,0],
[TENSOR,[6,2]],[4,1,-2,0,2,-1,0,0,0],
[TENSOR,[8,3]]],
[(2,3)(5,7)(6,8)]);
ALF("s3wrs2","A6.2_1",[1,3,4,2,7,10,8,11,5],[
"fusion map is unique up to table automorphisms"
]);
ALF("s3wrs2","3^2:Q8.2",[1,4,4,2,3,7,3,7,5],[
"fusion map is unique"
]);
ALF("s3wrs2","A7.2",[1,3,4,2,9,12,10,13,5],[
"fusion map is unique up to table aut."
]);
ALF("s3wrs2","A8",[1,4,5,3,3,9,2,10,7],[
"fusion map is unique up to table aut."
]);
ALN("s3wrs2",["3^2:D8","A8N3"]);
MOT("s3wrs3",
[
"origin: CAS library,\n",
"names:=s3wrs3\n",
" order: 2^4.3^4 = 1,296\n",
" number of classes: 22\n",
" source:generated by dixon-algorithm\n",
" aachen [1980]\n",
" comments:wreath-product of s3 with s3,\n",
" degree: 9\n",
" generators: a = (1,2,3); b = (1,2);\n",
" c = (1,4,7)(2,5,8)(3,6,9);\n",
" d = (1,4)(2,5)(3,6)\n",
" test: orth.1, minus,sym(3) \n",
"tests: 1.o.r., pow[2,3]"
],
[1296,216,162,108,48,24,18,9,144,36,36,48,6,72,36,36,18,8,24,12,24,12],
[,[1,2,3,4,1,2,7,8,1,2,4,1,7,1,4,2,3,5,5,6,1,4],[1,1,1,1,5,5,1,3,9,9,9,12,12,
14,14,14,14,18,19,19,21,21]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,-1,
-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,
-1],
[TENSOR,[2,3]],[2,2,2,2,2,2,-1,-1,2,2,2,2,-1,0,0,0,0,0,0,0,0,0],
[TENSOR,[5,3]],[3,3,3,3,-1,-1,0,0,1,1,1,-3,0,1,1,1,1,-1,1,1,-1,-1],
[TENSOR,[7,2]],
[TENSOR,[7,3]],
[TENSOR,[7,4]],[6,3,-3,0,2,-1,0,0,-4,-1,2,0,0,2,2,-1,-1,0,-2,1,0,0],
[TENSOR,[11,2]],
[TENSOR,[11,4]],
[TENSOR,[11,3]],[8,-4,-1,2,0,0,2,-1,0,0,0,0,0,4,-2,-2,1,0,0,0,0,0],
[TENSOR,[15,2]],[12,0,3,-3,0,0,0,0,4,-2,1,0,0,-2,1,-2,1,0,0,0,-2,1],
[TENSOR,[17,4]],
[TENSOR,[17,3]],[12,6,-6,0,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[17,2]],[16,-8,-2,4,0,0,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[]);
ARC("s3wrs3","tomfusion",rec(name:="3^3:(2xS4)",map:=[1,10,9,7,5,20,8,49,
6,38,35,3,24,2,37,22,27,18,17,63,4,25],text:=[
"fusion map is unique"
]));
ALF("s3wrs3","A9.2",[1,4,5,6,2,10,5,13,17,21,23,18,25,18,24,22,25,20,7,15,
3,11],[
"fusion map is unique"
]);
ALF("s3wrs3","S6(2)",[1,6,7,8,4,18,8,25,2,15,19,5,21,3,20,16,17,13,10,27,
5,21],[
"fusion map is unique"
]);
ALF("s3wrs3","U4(2).2",[1,5,4,6,3,13,6,14,16,20,21,17,22,2,12,11,10,8,18,
25,17,22],[
"fusion map is unique"
]);
MOT("s4",
[
"origin: CAS library,\n",
" names:= s4\n",
" order: 2^3.3 = 24\n",
" number of classes: 5\n",
" source: generated by dixon-algorithm aachen [1982]\n",
" comments: symmetric group, catalogue nr.24.15\n",
" test: orth, min, sym(3) \n",
"constructions: AGL(2,2),\n",
"tests: 1.o.r., pow[2,3]"
],
[24,8,3,4,4],
[,[1,1,3,1,2],[1,2,1,4,5]],
[[1,1,1,1,1],[1,1,1,-1,-1],[2,2,-1,0,0],[3,-1,0,1,-1],
[TENSOR,[4,2]]],
[]);
ARC("s4","tomfusion",rec(name:="S4",map:=[1,2,4,3,6],text:=[
"fusion map is unique"
]));
ARC("s4","ClassParameters",[[1,[1,1,1,1]],[1,[2,2]],[1,[3,1]],[1,[2,1,1]],[1,
[4]]]);
ARC("s4","CharacterParameters",[[1,[4]],[1,[1,1,1,1]],[1,[2,2]],[1,[3,1]],[1,
[2,1,1]]]);
ALF("s4","A5.2",[1,2,3,5,6],[
"fusion map is unique"
]);
ALF("s4","A6",[1,2,3,2,5],[
"fusion map is unique up to table automorphisms"
],"tom:18");
ALF("s4","L2(11).2",[1,2,3,8,9],[
"fusion map is unique"
]);
ALF("s4","L2(13).2",[1,2,3,9,10],[
"fusion map is unique"
]);
ALF("s4","L2(17)",[1,2,3,2,4],[
"fusion map is unique"
]);
ALF("s4","L2(23)",[1,2,3,2,4],[
"fusion map is unique"
]);
ALF("s4","L2(113)",[1,31,50,31,17],[
"fusion map is unique"
]);
ALF("s4","L3(2)",[1,2,3,2,4],[
"fusion map is unique"
]);
ALF("s4","L3(3)",[1,2,4,2,5],[
"fusion map is unique"
]);
ALF("s4","M11",[1,2,3,2,4],[
"fusion map is unique"
]);
ALF("s4","A7",[1,2,4,2,5]);
ALF("s4","2xSymm(4)",[1,3,5,7,9],[
"fusion map is unique up to table aut."
]);
ALN("s4",["AGL(2,2)"]);
MOT("A6M5",
[
"5th maximal subgroup of A6,\n",
"differs from A6M4 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["s4"]]);
ALF("A6M5","A6",[1,2,4,2,5],[
"fusion s4 -> A6 mapped under A6.2_2"
]);
ALF("A6M5","s2wrs3",[1,3,5,7,9],[
"fusion map is unique up to table aut."
]);
MOT("s4wrs2",
[
"solvable subgroup of maximal order in M22.2,\n",
"origin: CAS library,\n",
"names:=s4wrs2\n",
" order: 2^7.3^2 = 1,152\n",
" number of classes: 20\n",
" source:saenger, f.\n",
" einige charakterentafeln von symmetrien\n",
" symmetrischer gruppen\n",
" mitt.math.sem. giessen\n",
" heft 98 [1973], 21 - 38\n",
" comments:wreath-product of s4 with s2\n",
" test: orth.1, minus, sym(3) \n",
"tests: 1.o.r., pow[2,3]"
],
[1152,192,128,18,72,24,32,32,16,96,96,32,32,12,12,48,16,6,8,8],
[,[1,1,1,4,5,5,1,3,2,1,2,1,2,5,6,1,3,4,7,8],[1,2,3,1,1,2,7,8,9,10,11,12,13,10,
11,16,17,16,19,20]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,
-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1],
[TENSOR,[2,3]],[2,2,2,2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0],[4,4,4,1,-2,-2,0,
0,0,0,0,0,0,0,0,2,2,-1,0,0],
[TENSOR,[6,2]],[4,4,4,-2,1,1,0,0,0,2,2,2,2,-1,-1,0,0,0,0,0],
[TENSOR,[8,3]],[6,2,-2,0,3,-1,2,-2,0,4,2,0,-2,1,-1,0,0,0,0,0],[6,2,-2,0,3,-1,
-2,2,0,2,4,-2,0,-1,1,0,0,0,0,0],
[TENSOR,[11,3]],
[TENSOR,[10,3]],[12,4,-4,0,-3,1,0,0,0,2,-2,2,-2,-1,1,0,0,0,0,0],
[TENSOR,[14,3]],[9,-3,1,0,0,0,1,1,-1,3,-3,-1,1,0,0,3,-1,0,1,-1],
[TENSOR,[16,2]],
[TENSOR,[16,3]],
[TENSOR,[16,4]],[18,-6,2,0,0,0,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0]],
[]);
ALF("s4wrs2","M22.2",[1,2,2,3,3,7,2,4,5,12,14,13,14,16,19,12,15,16,4,10],[
"fusion map is unique"
]);
MOT("s5wrs2",
[
"origin: CAS library,\n",
"names:=s5wrs2;\n",
" order: 2^7.3^2.5^2 = 28,800\n",
" number of classes: 35\n",
" source:saenger, f\n",
" einige charakterentafeln von symmetrien\n",
" symmetrischer gruppen\n",
" mitt.math.sem. giessen\n",
" heft 98 [1973], 21 - 38\n",
" comments:wreath-product of s5 with s2\n",
" test: orth.1, minus, sym(3) \n",
"tests: 1.o.r., pow[2,3,5]"
],
[28800,960,128,720,72,600,50,48,40,30,288,48,32,72,72,24,1440,96,480,32,720,
72,48,36,60,24,20,30,240,16,12,10,24,8,12],
[,[1,1,1,4,5,6,7,4,6,10,1,2,3,4,5,8,1,1,2,2,4,4,4,5,6,8,9,10,1,3,5,7,11,13,
15],[1,2,3,1,1,6,7,2,9,6,11,12,13,11,11,12,17,18,19,20,17,17,18,17,25,19,27,
25,29,30,29,32,33,34,33],,[1,2,3,4,5,1,1,8,2,4,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,17,26,19,21,29,30,31,29,33,34,35]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1],[1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,
-1,-1],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[8,4,0,5,2,3,-2,1,-1,0,4,2,0,1,-2,-1,6,2,4,0,3,3,-1,0,1,1,-1,
-2,0,0,0,0,0,0,0],
[TENSOR,[6,3]],[8,4,0,5,2,3,-2,1,-1,0,-4,-2,0,-1,2,1,2,-2,4,0,5,-1,1,2,-3,1,
-1,0,0,0,0,0,0,0,0],
[TENSOR,[8,3]],[10,6,2,4,-2,5,0,0,1,-1,2,0,-2,2,2,0,6,2,4,0,6,0,2,0,1,-2,-1,1,
0,0,0,0,0,0,0],
[TENSOR,[10,3]],[10,6,2,4,-2,5,0,0,1,-1,-2,0,2,-2,-2,0,4,0,6,2,4,-2,0,-2,-1,0,
1,-1,0,0,0,0,0,0,0],
[TENSOR,[12,3]],[12,4,-4,6,0,7,2,-2,-1,1,0,0,0,0,0,0,6,-2,6,-2,6,0,-2,0,1,0,1,
1,0,0,0,0,0,0,0],
[TENSOR,[14,3]],[16,0,0,4,1,-4,1,0,0,-1,4,0,0,-2,1,0,8,0,0,0,-4,2,0,-1,-2,0,0,
1,4,0,1,-1,2,0,-1],
[TENSOR,[16,2]],
[TENSOR,[16,3]],
[TENSOR,[16,4]],[25,5,1,-5,1,0,0,-1,0,0,1,-1,1,1,1,-1,5,1,-5,-1,5,-1,1,-1,0,1,
0,0,5,1,-1,0,1,-1,1],
[TENSOR,[20,2]],
[TENSOR,[20,3]],
[TENSOR,[20,4]],[32,0,0,8,2,-8,2,0,0,-2,-8,0,0,4,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[36,-12,4,0,0,6,1,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,
-2,0,1,0,0,0],
[TENSOR,[25,2]],[40,4,0,1,-2,-5,0,1,-1,1,4,-2,0,1,-2,1,14,2,-4,0,-1,-1,-1,2,
-1,-1,1,-1,0,0,0,0,0,0,0],
[TENSOR,[27,3]],[40,4,0,1,-2,-5,0,1,-1,1,-4,2,0,-1,2,-1,6,2,4,0,-9,-3,-1,0,1,
1,-1,1,0,0,0,0,0,0,0],
[TENSOR,[29,3]],[48,-8,0,6,0,-2,-2,-2,2,1,0,0,0,0,0,0,12,-4,0,0,-6,0,2,0,2,0,
0,-1,0,0,0,0,0,0,0],
[TENSOR,[31,3]],[50,10,2,-10,2,0,0,-2,0,0,-2,2,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[60,-4,-4,-6,0,5,0,2,1,-1,0,0,0,0,0,0,6,-2,-6,2,6,0,-2,0,1,
0,-1,1,0,0,0,0,0,0,0],
[TENSOR,[34,3]]],
[]);
ARC("s5wrs2","tomfusion",rec(name:="(S5xS5):2",map:=[1,3,6,8,9,33,34,46,
102,151,4,19,24,39,41,126,2,7,11,20,36,38,44,47,98,122,209,279,5,32,52,
104,26,88,140],text:=[
"fusion map is unique"
]));
ALF("s5wrs2","A10.2",[1,2,3,4,5,10,11,12,18,21,2,8,9,12,13,19,23,25,26,27,
29,29,31,32,36,38,41,42,24,28,33,37,7,16,20],[
"fusion map is unique"
]);
ALF("s5wrs2","He.2",[1,2,3,4,4,9,9,10,16,21,2,6,7,10,10,17,27,27,28,28,29,
30,30,30,35,36,40,43,2,7,10,16,28,34,36],[
"fusion map is unique, equal to that on the CAS table"
]);
MOT("S4wrS3",
[
"8th maximal subgroup of S12"
],
0,
0,
0,
[],
["ConstructWreathSymmetric",["Symm(4)"],3]);
ALF("S4wrS3","A12.2",[1,2,5,41,44,4,15,42,46,6,49,64,2,9,10,3,16,43,45,17,
51,66,4,11,12,8,52,65,15,30,32,42,46,48,47,4,10,19,46,58,3,12,18,45,59,16,
32,21,66,72,43,48,57,11,23,45,47,67,12,24,7,20,26,55,68],[
"fusion map is unique"
]);
MOT("S3wrS4",
[
"10th maximal subgroup of S12"
],
0,
0,
0,
[],
["ConstructWreathSymmetric",["S3"],4]);
ALF("S3wrS4","A12.2",[1,5,41,6,49,2,8,52,15,42,7,54,17,51,4,42,50,9,51,56,
30,4,19,46,53,55,31,16,21,66,43,57,11,3,18,45,20,67,12,8,25,56,7,26,55,54,
70,21,47,68,24],[
"fusion map is unique"
]);
MOT("2^6:S6",
[
"maximal subgroup of S12,\n",
"origin: Dixon's Algorithm"
],
[46080,46080,3072,3072,7680,7680,2304,256,256,128,256,256,128,128,128,64,288,
288,288,288,96,96,96,96,72,72,36,32,32,32,32,20,20,20,20,1536,1536,384,384,256
,1536,1536,384,384,256,384,384,128,128,64,64,32,64,64,32,48,48,48,48,48,48,48,
48,12,12],
[,[1,1,1,1,1,1,1,1,1,1,3,3,4,3,4,4,17,17,17,17,17,17,17,17,25,25,25,8,9,11,12,
32,32,32,32,1,1,1,1,1,4,4,4,4,4,1,2,4,3,8,8,8,11,11,11,17,17,17,17,24,24,24,24
,25,26],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,7,7,2,5,3,6,4,1,2,7,28,29,30
,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,36
,37,39,38,42,41,43,44,46,47],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19
,20,21,22,23,24,25,26,27,28,29,30,31,1,6,5,2,36,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[5,5,5,5,5,5,5,1,
1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,3,3,3,3,3,3,3,3,3
,3,-1,-1,-1,-1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,-1,-1],
[TENSOR,[3,2]],[5,5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2
,-1,-1,-1,-1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,3,3,3,3,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,-1,-1,0,0],
[TENSOR,[5,2]],[16,16,16,16,16,16,16,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,
-2,-2,-2,-2,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],[9,9,9,9,9,9,9,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,-1,
-1,-1,-1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[8,2]],[10,10,10,10,10,10,10,-2,-2,-2,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1
,1,1,1,1,0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,0,0,0,0,0,0,-1,-1,-1,
-1,-1,-1,-1,-1,1,1],
[TENSOR,[10,2]],[1,1,1,1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,-1,1,-1,1,1
,1,-1,1,-1,-1,1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1,-1,1,1,1,-1,-1,-1,1,1,
1,-1,-1,-1,-1,1,1,1,-1],
[TENSOR,[2,12]],
[TENSOR,[3,12]],
[TENSOR,[3,13]],
[TENSOR,[5,13]],
[TENSOR,[5,12]],
[TENSOR,[8,13]],
[TENSOR,[8,12]],
[TENSOR,[10,12]],
[TENSOR,[10,13]],
[TENSOR,[7,12]],[15,15,-1,-1,-5,-5,3,-1,-1,3,3,3,-1,-1,-1,-1,3,-3,-3,3,1,-1,1
,-1,0,0,0,-1,-1,1,1,0,0,0,0,-5,-5,-1,-1,3,7,7,-1,-1,-1,3,3,-1,-1,-1,-1,-1,1,1,
1,1,1,-1,-1,1,1,-1,-1,0,0],[15,15,-1,-1,-5,-5,3,3,3,-1,-1,-1,-1,3,-1,-1,3,-3,
-3,3,1,-1,1,-1,0,0,0,1,1,-1,-1,0,0,0,0,-7,-7,1,1,1,5,5,1,1,-3,-3,-3,1,1,-1,-1,
-1,1,1,1,-1,-1,1,1,-1,-1,1,1,0,0],
[TENSOR,[23,2]],
[TENSOR,[24,2]],
[TENSOR,[23,12]],
[TENSOR,[24,12]],
[TENSOR,[23,13]],
[TENSOR,[24,13]],[30,30,-2,-2,-10,-10,6,2,2,2,2,2,-2,2,-2,-2,-3,3,3,-3,-1,1,
-1,1,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,2,2,2,-2,-2,2,6,6,-2,-2,0,0,0,0,0,0,-1,-1
,1,1,-1,-1,1,1,0,0],
[TENSOR,[31,2]],
[TENSOR,[31,13]],
[TENSOR,[31,12]],[45,45,-3,-3,-15,-15,9,1,1,-3,-3,-3,1,1,1,1,0,0,0,0,0,0,0,0,
0,0,0,-1,-1,1,1,0,0,0,0,9,9,-3,-3,1,-3,-3,-3,-3,5,-3,-3,1,1,-1,-1,-1,1,1,1,0,0
,0,0,0,0,0,0,0,0],
[TENSOR,[35,2]],
[TENSOR,[35,12]],
[TENSOR,[35,13]],[45,45,-3,-3,-15,-15,9,-3,-3,1,1,1,1,-3,1,1,0,0,0,0,0,0,0,0,
0,0,0,1,1,-1,-1,0,0,0,0,-3,-3,-3,-3,5,9,9,-3,-3,1,-3,-3,1,1,1,1,1,-1,-1,-1,0,0
,0,0,0,0,0,0,0,0],
[TENSOR,[39,2]],
[TENSOR,[39,13]],
[TENSOR,[39,12]],[6,-6,-2,2,-4,4,0,2,-2,0,2,-2,2,0,-2,0,3,3,-3,-3,-1,1,1,-1,0
,0,0,0,0,0,0,1,-1,1,-1,-4,4,-2,2,0,-4,4,-2,2,0,0,0,0,0,2,-2,0,2,-2,0,-1,1,-1,1
,1,-1,1,-1,0,0],
[TENSOR,[43,2]],
[TENSOR,[43,12]],
[TENSOR,[43,13]],[20,-20,4,-4,0,0,0,4,-4,0,-4,4,0,0,0,0,2,0,0,-2,0,-2,0,2,2,
-2,0,0,0,0,0,0,0,0,0,-8,8,0,0,0,0,0,4,-4,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,-2
,2,0,0],
[TENSOR,[47,2]],[20,-20,4,-4,0,0,0,-4,4,0,4,-4,0,0,0,0,2,0,0,-2,0,-2,0,2,2,-2
,0,0,0,0,0,0,0,0,0,0,0,4,-4,0,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,2,-2,0,0
,0,0],
[TENSOR,[49,2]],[24,-24,-8,8,-16,16,0,0,0,0,0,0,0,0,0,0,3,3,-3,-3,-1,1,1,-1,0
,0,0,0,0,0,0,-1,1,-1,1,8,-8,4,-4,0,8,-8,4,-4,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,1
,-1,1,-1,0,0],
[TENSOR,[51,2]],
[TENSOR,[51,12]],
[TENSOR,[51,13]],[30,-30,-10,10,-20,20,0,2,-2,0,2,-2,2,0,-2,0,-3,-3,3,3,1,-1,
-1,1,0,0,0,0,0,0,0,0,0,0,0,4,-4,2,-2,0,4,-4,2,-2,0,0,0,0,0,2,-2,0,2,-2,0,1,-1,
1,-1,-1,1,-1,1,0,0],
[TENSOR,[55,2]],
[TENSOR,[55,12]],
[TENSOR,[55,13]],[36,-36,-12,12,-24,24,0,-4,4,0,-4,4,-4,0,4,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0],
[TENSOR,[59,12]],[40,-40,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,1,-3,3,-1,-3,-1,3,1,-2,
2,0,0,0,0,0,0,0,0,0,-8,8,-4,4,0,8,-8,4,-4,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,1,-1
,1,-1,0,0],
[TENSOR,[61,13]],
[TENSOR,[61,12]],
[TENSOR,[61,2]],[80,-80,16,-16,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,4,0,4,0,-4,2,-2
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
]],
[(36,37)(38,39)(41,42)(43,44)(50,51)(53,54)(56,57)(58,59)(60,61)(62,63),
( 5, 6)(13,15)(18,19)(21,23)(33,34)(36,37)(43,44)(50,51)(56,57)(62,63)]);
ALF("2^6:S6","A6.2_1",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,4,
4,4,5,5,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,9,9,9,9,9,9,10,10,10,10,
10,10,10,10,11,11]);
ALF("2^6:S6","A12.2",[1,3,4,2,41,43,42,4,3,43,10,12,45,48,46,11,6,53,50,
18,52,19,57,17,7,20,55,12,47,59,24,14,63,62,28,2,3,43,42,4,45,44,9,11,46,
3,47,45,12,12,10,48,58,59,23,17,18,53,57,65,67,31,33,20,68],[
"fusion map is unique up to table automorphisms"
]);
MOT("A8.2N2",
[
"origin: CAS library,\n",
"names:=s61; s6[1]\n",
" order: 2^7 = 128\n",
" number of classes: 20\n",
" source:dye, r.h.\n",
" the classes and characters of\n",
" certain maximal and other subgroups\n",
" of o 2n+2(2)\n",
" ann.mat.pura appl.(4) 107\n",
" (1975), 13-47\n",
" comments:table blown up using cas-system \n",
"Sylow 2 subgroup in S8,\n",
"tests: 1.o.r., pow[2]"
],
0,
0,
0,
0,
["ConstructPermuted",["A11Syl2"],(3,5,7,6,4)(8,13,17,16,9,14,18,12)(11,15),(3,
6,4,5,7)(9,10)(11,14,12)(17,18,20,19)]);
ALF("A8.2N2","A8.2",[1,2,2,2,3,3,3,6,7,2,6,6,13,14,14,16,16,15,16,20],[
"fusion map is unique up to table aut."
]);
ALN("A8.2N2",["A8.2Syl2"]);
MOT("s61p",
[
"origin: CAS library,\n",
"names:=s61p; s6[1]+\n",
" order: 2^6 = 64\n",
" number of classes: 16\n",
" source:dye, r.h.\n",
" the classes and characters of\n",
" certain maximal and other subgroups\n",
" of o 2n+2[2]\n",
" ann.mat.pura appl.[4] 107\n",
" [1975], 13-47\n",
" comments:table blown up using cas-system.\n",
"The element orders on the CAS table were incorrect,\n",
"the correct power map was computed from the group (T. Breuer, July 1999)."
],
0,
0,
0,
0,
["ConstructPermuted",["2^3.D8"],(5,6)(8,11,12,14)(9,13,16,10,15),(2,3,5,7)(4,
6,8)(11,14,13)(15,16)]);
ALF("s61p","A8.2N2",[1,2,3,3,4,5,6,7,8,9,10,10,11,11,12,12],[
"fusion map is unique up to table automorphisms"
]);
ALF("s61p","A8",[1,2,2,2,2,3,3,3,6,7,2,2,6,6,6,6],[
"fusion map is unique up to table aut."
]);
ALN("s61p",["A8Syl2","A8N2"]);
MOT("sl25ex",
[
"origin: CAS library,\n",
"names:=sl25ex; 3**[1+4].sl2(5)\n",
" order: 29,160\n",
" number of classes: 33\n",
" source: koichiro harada\n",
" on the simple group f of order\n",
" 2^14.3^6.5^6.7.11.19\n",
" proceedings of the conference\n",
" on finite groups,\n",
" park city, utah (1975)\n",
" comments: \n",
"tests: 1.o.r., pow[2,3,5],\n",
"3rd power map determined only up to matrix automorphisms,"
],
[29160,29160,29160,243,243,360,162,162,162,27,27,12,30,30,360,360,18,18,18,27,
27,30,30,12,12,30,30,30,30,30,30,30,30],
[,[1,3,2,4,5,1,7,9,8,11,10,6,14,13,3,2,7,9,8,21,20,14,13,16,15,29,28,27,26,29,
28,27,26],[1,1,1,1,1,6,1,1,1,1,1,12,14,13,6,6,6,6,6,2,3,23,22,12,12,14,14,13,
13,23,23,22,22],,[1,3,2,4,5,6,7,9,8,11,10,12,1,1,16,15,17,19,18,21,20,6,6,25,
24,3,2,3,2,16,15,16,15]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[3,3,3,3,
3,3,0,0,0,0,0,-1,-E(5)^2-E(5)^3,-E(5)-E(5)^4,3,3,0,0,0,0,0,-E(5)^2-E(5)^3,
-E(5)-E(5)^4,-1,-1,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(5)-E(5)^4],
[GALOIS,[2,2]],[4,4,4,4,4,4,1,1,1,1,1,0,-1,-1,4,4,1,1,1,1,1,-1,-1,0,0,-1,-1,
-1,-1,-1,-1,-1,-1],[5,5,5,5,5,5,-1,-1,-1,-1,-1,1,0,0,5,5,-1,-1,-1,-1,-1,0,0,1,
1,0,0,0,0,0,0,0,0],[2,2,2,2,2,-2,-1,-1,-1,-1,-1,0,E(5)+E(5)^4,E(5)^2+E(5)^3,
-2,-2,1,1,1,-1,-1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,E(5)+E(5)^4,E(5)+E(5)^4,
E(5)^2+E(5)^3,E(5)^2+E(5)^3,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,
-E(5)^2-E(5)^3],
[GALOIS,[6,2]],[4,4,4,4,4,-4,1,1,1,1,1,0,-1,-1,-4,-4,-1,-1,-1,1,1,1,1,0,0,-1,
-1,-1,-1,1,1,1,1],[6,6,6,6,6,-6,0,0,0,0,0,0,1,1,-6,-6,0,0,0,0,0,-1,-1,0,0,1,1,
1,1,-1,-1,-1,-1],[40,40,40,4,-5,0,4,4,4,-2,-2,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,
0,0,0,0,0,0],[40,40,40,4,-5,0,-2,-2,-2,1,1,0,0,0,0,0,0,0,0,2*E(3)-E(3)^2,
-E(3)+2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[11,2]],[40,40,40,-5,4,0,4,4,4,1,1,0,0,0,0,0,0,0,0,-2,-2,0,0,0,0,0,0,
0,0,0,0,0,0],[40,40,40,-5,4,0,-2,-2,-2,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,0,0,0,0,0,
0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[14,2]],[9,9*E(3),9*E(3)^2,0,0,1,3,3*E(3),3*E(3)^2,0,0,1,-1,-1,E(3),
E(3)^2,1,E(3),E(3)^2,0,0,1,1,E(3),E(3)^2,-E(3),-E(3)^2,-E(3),-E(3)^2,E(3),
E(3)^2,E(3),E(3)^2],
[GALOIS,[16,2]],[27,27*E(3),27*E(3)^2,0,0,3,0,0,0,0,0,-1,E(5)^2+E(5)^3,
E(5)+E(5)^4,3*E(3),3*E(3)^2,0,0,0,0,0,-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(3),
-E(3)^2,E(15)^11+E(15)^14,E(15)+E(15)^4,E(15)^2+E(15)^8,E(15)^7+E(15)^13,
-E(15)^11-E(15)^14,-E(15)-E(15)^4,-E(15)^2-E(15)^8,-E(15)^7-E(15)^13],
[GALOIS,[18,11]],
[GALOIS,[18,7]],
[GALOIS,[18,2]],[36,36*E(3),36*E(3)^2,0,0,4,3,3*E(3),3*E(3)^2,0,0,0,1,1,
4*E(3),4*E(3)^2,1,E(3),E(3)^2,0,0,-1,-1,0,0,E(3),E(3)^2,E(3),E(3)^2,-E(3),
-E(3)^2,-E(3),-E(3)^2],
[GALOIS,[22,2]],[45,45*E(3),45*E(3)^2,0,0,5,-3,-3*E(3),-3*E(3)^2,0,0,1,0,0,
5*E(3),5*E(3)^2,-1,-E(3),-E(3)^2,0,0,0,0,E(3),E(3)^2,0,0,0,0,0,0,0,0],
[GALOIS,[24,2]],[18,18*E(3),18*E(3)^2,0,0,-2,-3,-3*E(3),-3*E(3)^2,0,0,0,
-E(5)-E(5)^4,-E(5)^2-E(5)^3,-2*E(3),-2*E(3)^2,1,E(3),E(3)^2,0,0,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,0,0,-E(15)^2-E(15)^8,-E(15)^7-E(15)^13,-E(15)^11-E(15)^14,
-E(15)-E(15)^4,-E(15)^2-E(15)^8,-E(15)^7-E(15)^13,-E(15)^11-E(15)^14,
-E(15)-E(15)^4],
[GALOIS,[26,11]],
[GALOIS,[26,7]],
[GALOIS,[26,2]],[36,36*E(3),36*E(3)^2,0,0,-4,3,3*E(3),3*E(3)^2,0,0,0,1,1,
-4*E(3),-4*E(3)^2,-1,-E(3),-E(3)^2,0,0,1,1,0,0,E(3),E(3)^2,E(3),E(3)^2,E(3),
E(3)^2,E(3),E(3)^2],
[GALOIS,[30,2]],[54,54*E(3),54*E(3)^2,0,0,-6,0,0,0,0,0,0,-1,-1,-6*E(3),
-6*E(3)^2,0,0,0,0,0,-1,-1,0,0,-E(3),-E(3)^2,-E(3),-E(3)^2,-E(3),-E(3)^2,-E(3),
-E(3)^2],
[GALOIS,[32,2]]],
[(13,14)(22,23)(26,28)(27,29)(30,32)(31,33),(10,11),( 2, 3)( 8, 9)(10,11)
(15,16)(18,19)(20,21)(24,25)(26,27)(28,29)(30,31)(32,33),( 2, 3)( 8, 9)(15,16)
(18,19)(20,21)(24,25)(26,27)(28,29)(30,31)(32,33)]);
ALF("sl25ex","2.A5",[1,1,1,1,1,2,4,4,4,4,4,3,6,8,2,2,5,5,5,4,4,7,9,3,3,6,
6,8,8,7,7,9,9]);
MOT("D8x3^2:Q8",
0,
0,
0,
0,
[( 5,11)( 6,12),(19,25)(20,26)(21,27)(22,28)(23,29)(24,30),
( 5, 6)(11,12)(17,18)(23,24)(29,30),( 4, 5)(10,11)(16,17)(22,23)(28,29)],
["ConstructDirectProduct",[["D8"],["3^2:Q8"]]]);
ALF("D8x3^2:Q8","Suz",[1,2,6,7,9,9,3,3,17,9,8,8,10,10,30,10,10,10,3,3,17,
9,9,9,3,3,17,9,8,8],[
"unique fusion that is compatible with 2.(D8x3^(1+2)_+:Q8) -> 6.Suz"
]);
MOT("suzd2",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3]"
],
0,
0,
0,
0,
["ConstructPermuted",["D8x3^2:Q8"],
( 2, 5,12,14,17,25, 3, 9,27,28,19, 4,11,13,10,16,24,21,29,26, 7)
( 6,15,30,23,18,22,20, 8)
,
( 1,11,22,16, 6,26,18,28,20,12,29,25,17,21, 7)( 2, 4, 8,10,14)( 3,15,13, 9, 5,
23,24,27,19)
]);
MOT("suzdx",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,5]"
],
0,
0,
0,
0,
["ConstructPermuted",["(3^2:4xa6).2"],(2,5,3)(4,10,9,7)(6,24,25,35,31,20,18,
28,13)(8,17,11,22,33,29,15,23,34,32,19,16,26,36,30,14)(12,27),(1,4,13)(2,3,12)
(5,9,21,19,17,6,7,15,10,20,22,25,24,23)(8,16)(11,26,28,29,30,14)(31,32)(33,34)
]);
ALF("suzdx","3^2:Q8",[1,2,1,2,3,1,1,3,3,4,1,5,6,6,5,2,4,4,6,5,1,2,2,3,2,4,
4,3,5,6,5,6,3,3,4,4]);
ALF("suzdx","A6.2_1",[1,1,2,2,1,4,3,4,3,1,5,7,7,8,8,5,2,5,9,9,6,3,4,2,6,4,
3,5,10,11,11,10,6,6,6,6]);
MOT("suzs2",
[
"Sylow 2 subgroup in sporadic simple group Suz,\n",
"origin: CAS library,\n",
"2nd power map computed from the group"
],
[8192,8192,4096,2048,1024,512,512,512,512,256,256,256,256,256,256,256,256,256,
256,256,128,128,128,1024,1024,1024,1024,1024,1024,512,512,512,512,512,512,512,
512,512,512,256,256,256,256,256,256,256,256,256,256,256,256,256,256,256,256,
256,256,256,256,256,256,256,256,256,256,128,128,128,128,128,128,128,128,128,
128,32,32,32,32,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,32,32,
32,32,32,32,32,32,32,32],
[,[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,2,3,3,2,3,3,2,
3,2,3,3,4,2,4,2,3,3,3,2,3,3,3,4,2,3,3,2,3,2,3,2,4,4,2,4,5,5,5,4,4,4,4,5,5,5,7,
6,9,8,24,29,25,26,25,27,24,28,24,28,25,29,27,29,26,26,27,28,34,31,30,36,39,38,
35,37,32,33]],
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1,1,1,1,-1,1,1,1,-1,-1,1,1,1,-1],[1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,1,
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-1,1,1,-1,1,-1,-1,1,-1,-1,1,1,1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,1,1,1,-1,1,1,1],[1,1,1,1,1,1,1,1,1,1,-1,-1,-1,1,1,1,1,-1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,-1,
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1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,1,1,
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1,1,-1,-1],[1,1,1,1,1,1,1,1,1,-1,1,1,1,1,1,1,-1,1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,-1,1,1,1,1,1,-1,1,1,1,1,1,1,1,1,1,1,1,-1,1,1,-1,1,1,1,1,
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-1,-1,1,1,-1,1,1,-1,1,1],
[TENSOR,[1,8]],
[TENSOR,[1,7]],
[TENSOR,[1,6]],
[TENSOR,[1,5]],
[TENSOR,[1,4]],
[TENSOR,[1,3]],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,2,2,2,2,2,-2,-2,2,2,0,0,0,2,-2,-2,2,0,0,0,2,0,0,2,2,2,2,2,2,
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0,0,0,0,0,0,0,0],
[TENSOR,[17,1]],[2,2,2,2,2,2,2,-2,-2,0,0,0,0,-2,2,-2,-2,0,-2,0,0,2,0,2,2,2,2,
2,2,-2,-2,2,-2,2,-2,2,2,-2,-2,0,-2,2,-2,0,0,0,0,0,0,2,-2,2,0,0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[19,1]],[2,2,2,2,2,2,-2,2,-2,0,0,0,0,-2,-2,2,-2,0,0,-2,0,0,2,2,2,2,2,
2,2,-2,-2,-2,2,2,-2,-2,-2,2,2,0,2,0,0,2,0,0,0,0,-2,2,-2,-2,0,0,0,0,0,0,0,0,0,
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2,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[21,2]],
[TENSOR,[17,7]],
[TENSOR,[17,5]],
[TENSOR,[19,6]],
[TENSOR,[19,5]],
[TENSOR,[21,5]],
[TENSOR,[21,6]],[2,2,2,2,2,-2,-2,-2,-2,0,0,0,0,2,2,2,0,0,0,0,-2,-2,2,2,2,2,2,
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0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[29,3]],[2,2,2,2,2,-2,2,2,-2,0,0,0,0,2,-2,-2,0,0,-2,-2,2,0,0,2,2,2,2,
2,2,2,-2,-2,-2,-2,2,-2,2,-2,2,0,2,0,-2,0,0,0,0,0,-2,-2,-2,2,2,0,0,0,0,0,0,0,0,
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2,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[31,3]],
[TENSOR,[29,2]],
[TENSOR,[29,1]],
[TENSOR,[31,2]],
[TENSOR,[31,1]],[2,2,2,2,2,-2,-2,2,2,-2,0,0,0,-2,2,-2,0,0,0,-2,0,2,0,2,2,2,2,
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[TENSOR,[37,3]],[2,2,2,2,2,-2,2,-2,2,2,0,0,0,-2,-2,2,0,0,-2,0,0,0,-2,2,2,2,2,
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[TENSOR,[39,3]],
[TENSOR,[37,2]],
[TENSOR,[37,1]],
[TENSOR,[39,2]],
[TENSOR,[39,1]],[4,4,4,4,-4,4,0,0,0,0,-2,2,2,0,0,0,4,2,0,0,0,0,0,4,4,4,-4,-4,
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[TENSOR,[45,9]],
[TENSOR,[45,5]],
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0,0,0,0,0,0,0,0],
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MOT("twd5a",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,5]"
],
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ARC("twd5a","tomfusion",rec(name:="2.(2^4:S5)",map:=[1,2,3,7,11,9,10,36,5,
15,47,19,14,45,8,4,22,22,30,43,44,44,49,98,98],text:=[
"fusion map is unique"
]));
ALF("twd5a","A5.2",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,5,5,5,5,5,6,6,6,7,7,7]);
ALF("twd5a","2.U4(2).2",[1,2,3,4,4,11,12,13,7,8,20,18,14,15,25,26,27,28,
29,29,34,33,30,38,37],[
"fusion map is unique up to table autom."
]);
MOT("w(d4)",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3]"
],
0,
0,
0,
0,
["ConstructPermuted",["2^3.S4v2"],(11,13),(4,5)(6,7)(11,12)]);
MOT("w(d5)",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,5]"
],
0,
0,
0,
0,
["ConstructPermuted",["mo62"],(2,3)(5,6)(12,13,14)(15,17)(16,18),(7,8,9)(11,
13,14,16,12,15)]);
ALF("w(d5)","A5.2",[1,1,1,2,2,2,3,3,3,4,5,5,5,5,6,6,7,7]);
MOT("w(f4)",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3]"
],
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12],
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[TENSOR,[12,3]],
[TENSOR,[12,4]],
[TENSOR,[12,2]],[12,12,-4,4,-3,-3,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[4,
-4,0,0,-2,2,1,-1,1,-1,0,0,2,-2,0,2,-2,2,-2,0,0,1,-1,-1,1],
[TENSOR,[17,2]],
[TENSOR,[17,3]],
[TENSOR,[17,4]],[8,-8,0,0,2,-2,-1,1,2,-2,0,0,0,0,0,0,0,4,-4,0,0,0,0,1,-1],
[TENSOR,[21,2]],[8,-8,0,0,2,-2,2,-2,-1,1,0,0,0,0,0,4,-4,0,0,0,0,-1,1,0,0],
[TENSOR,[23,2]],[16,-16,0,0,-2,2,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(13,14)(18,19)(24,25),(13,14)(16,17)(22,23),( 7, 9)( 8,10)(16,18)(17,19)
(20,21)(22,25)(23,24)]);
ARC("w(f4)","tomfusion",rec(name:="2.(A4xA4).2.2",map:=[1,2,4,25,11,40,9,
38,10,48,108,3,18,32,76,5,6,8,7,13,14,43,39,44,50],text:=[
"fusion map is unique up to table autom."
]));
ALF("w(f4)","U4(2).2",[1,2,3,7,4,10,5,11,6,12,15,17,18,19,23,16,17,2,3,19,
8,22,21,11,13],[
"fusion map is unique up to table autom."
]);
ALN("w(f4)",["weylf(4)"]);
LIBTABLE.LOADSTATUS.ctomisc6:="userloaded";
#############################################################################
##
#E