Spracherkennung für: .tbl vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
#############################################################################
##
#W ctoatres.tbl GAP table library Thomas Breuer
##
## This file contains the ordinary character tables related to the groups
## $F_4(2)$, $G_2(q)$ for $q$ in [3,4,5], $R(27)$, $Sz(8)$ and $Sz(32)$ of
## the ATLAS (``rest of the ATLAS tables'').
##
#H ctbllib history
#H ---------------
#H $Log: ctoatres.tbl,v $
#H Revision 4.39 2012/06/20 14:45:29 gap
#H added tables and fusions, as documented in ctbldiff.dat
#H TB
#H
#H Revision 4.38 2012/06/06 12:43:48 gap
#H "R(27)" is "2G2(27)"
#H TB
#H
#H Revision 4.37 2012/04/23 16:16:06 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 4.36 2012/03/28 13:16:36 gap
#H added a permutation (of the maximal subgroups) for the fusion to the
#H table of marks of Sz(8).3, L2(11).2, HS.2, He.2, S4(5), U3(3), U4(2).2
#H TB
#H
#H Revision 4.35 2012/01/26 11:00:19 gap
#H added fusion G2(5) -> O7(5)
#H TB
#H
#H Revision 4.34 2011/09/28 12:26:14 gap
#H - removed revision entry and SET_TABLEFILENAME call,
#H - changed the construction of the table of 2.(2xF4(2)).2 from an
#H explicit function to (the now generalized) `ConstructIsoclinic',
#H - added maxes entry for G2(5),
#H - added fusion from Sz(8).3 to the table of marks
#H TB
#H
#H Revision 4.33 2010/05/05 13:20:00 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 4.32 2010/01/19 17:05:30 gap
#H added several tables of maximal subgroups of central extensions of
#H simple groups (many of them were contributed by S. Dany)
#H TB
#H
#H Revision 4.31 2009/07/29 13:52:15 gap
#H break a too long line
#H TB
#H
#H Revision 4.30 2009/06/15 15:12:12 gap
#H added tables of 2E6(2)M3, 2E6(2)M4, 2E6(2)M5, 2E6(2)M7, 2E6(2)M8,
#H 2E6(2)M9, and corresponding fusions
#H TB
#H
#H Revision 4.29 2009/04/27 08:27:20 gap
#H removed some superfluous explicit <nam>M<n> names,
#H which are created automatically
#H TB
#H
#H Revision 4.28 2009/01/12 17:33:57 gap
#H added missing maxes of Fi22.2 and their fusions
#H TB
#H
#H Revision 4.27 2008/06/24 16:23:05 gap
#H added several fusions and names
#H TB
#H
#H Revision 4.26 2006/06/07 07:54:26 gap
#H unified ConstructMixed and ConstructMGA (for better programmatic access)
#H TB
#H
#H Revision 4.25 2005/01/26 15:04:55 gap
#H fixed construction function for "2.(2xF4(2)).2",
#H the table is constructed from a direct product
#H but itself is not a direct product,
#H so the flag must not be copied over
#H TB
#H
#H Revision 4.24 2005/01/18 15:16:51 gap
#H fixed maxes of Sz(8).3
#H TB
#H
#H Revision 4.23 2004/08/31 12:33:33 gap
#H added tables of 4.L2(25).2_3,
#H L2(49).2^2,
#H L2(81).2^2,
#H L2(81).(2x4),
#H 3.L3(4).3.2_2,
#H L3(9).2^2,
#H L4(4).2^2,
#H 2x2^3:L3(2)x2,
#H (2xA6).2^2,
#H 2xL2(11).2,
#H S3xTh,
#H 41:40,
#H 7^(1+4):(3x2.S7),
#H 7xL2(8),
#H (7xL2(8)).3,
#H O7(3)N3A,
#H O8+(3).2_1',
#H O8+(3).2_1'',
#H O8+(3).2_2',
#H O8+(3).(2^2)_{122},
#H S4(9),
#H S4(9).2_i,
#H 2.U4(3).2_2',
#H 2.U4(3).(2^2)_{133},
#H 2.U4(3).D8,
#H 3.U6(2).S3,
#H added fusions 3.A6.2_i -> 3.A6.2^2,
#H L2(49).2_i -> L2(49).2^2,
#H L3(9).2_i -> L3(9).2^2,
#H L4(4).2_i -> L4(4).2^2,
#H G2(3) -> O7(3),
#H L2(17) -> S8(2),
#H 2.L3(4).2_2 -> 2.M22.2
#H 3.L3(4).2_2 -> 3.L3(4).3.2_2
#H 3.L3(4).3 -> 3.L3(4).3.2_2
#H 2^5:S6 -> 2.M22.2
#H O8+(3) -> O8+(3).2_1',
#H O8+(3) -> O8+(3).2_1'',
#H O8+(3) -> O8+(3).2_2',
#H O8+(3) -> O8+(3).(2^2)_{122},
#H O8+(3).2_1 -> O8+(3).(2^2)_{122},
#H O8+(3).2_2 -> O8+(3).(2^2)_{122},
#H 2.U4(3) -> 2.U4(3).2_2',
#H 2.U4(3).2_1 -> 2.U4(3).(2^2)_{133},
#H 2.U4(3).2_2 -> O7(3),
#H 2.U4(3).2_2' -> U4(3).2_2,
#H 2.U4(3).2_3 -> 2.U4(3).(2^2)_{133},
#H 2.U4(3).2_3' -> 2.U4(3).(2^2)_{133},
#H 2.U4(3).4 -> 2.U4(3).D8,
#H 3.U6(2).2 -> 3.U6(2).S3,
#H 3.U6(2).3 -> 3.U6(2).S3,
#H replaced table of psl(3,4):d12 by L3(4).D12,
#H changed table of O8+(3).S4 to a construction table,
#H changed encoding of the table of 12.A6.2_3,
#H added maxes of Sz(8), Sz(8).3,
#H TB
#H
#H Revision 4.22 2004/02/17 17:33:14 gap
#H added certain tables of isoclinic groups of ATLAS groups
#H (which are available in atlasrep),
#H added missing maxes of U5(2)
#H TB
#H
#H Revision 4.21 2003/05/15 17:38:02 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 4.20 2003/01/21 16:25:31 gap
#H further standardizations of `InfoText' strings,
#H added and corrected `Maxes' infos,
#H added some fusions
#H TB
#H
#H Revision 4.19 2003/01/14 17:28:49 gap
#H changed `InfoText' values (for a better programmatic access)
#H and replaced `ConstructDirectProduct' by `ConstructPermuted' where
#H there is only one factor (again better programmatic handling)
#H TB
#H
#H Revision 4.18 2002/10/22 12:44:06 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 4.17 2002/09/23 14:45:42 gap
#H added comment to fusion 2^2.Sz(8) -> 2^2.Sz(8).3
#H TB
#H
#H Revision 4.16 2002/07/15 15:19:35 gap
#H added table automorphisms of 2.F4(2).2
#H TB
#H
#H Revision 4.15 2002/07/12 06:45:55 gap
#H further tidying up: removed `irredinfo' stuff, rearranged constructions
#H TB
#H
#H Revision 4.14 2002/07/08 16:06:56 gap
#H changed `construction' component from function (call) to list of function
#H name and arguments
#H TB
#H
#H Revision 4.13 2001/11/06 08:40:46 gap
#H adjustments that make it easier to use the data under GAP 3
#H TB
#H
#H Revision 4.12 2001/06/18 16:01:33 gap
#H moved `ctblpope.tst' here
#H TB
#H
#H Revision 4.11 2001/05/14 15:44:36 gap
#H added table of 2.(2xF4(2)).2 (computed by Simon Norton)
#H TB
#H
#H Revision 4.10 2001/05/04 16:47:04 gap
#H first revision for ctbllib
#H
#H
#H tbl history (GAP 4)
#H -------------------
#H (Rev. 4.10 of ctbllib coincides with Rev. 4.9 of tbl in GAP 4)
#H
#H RCS file: /gap/CVS/GAP/4.0/tbl/ctoatres.tbl,v
#H Working file: ctoatres.tbl
#H head: 4.9
#H branch:
#H locks: strict
#H access list:
#H symbolic names:
#H GAP4R2: 4.8.0.6
#H GAP4R2PRE2: 4.8.0.4
#H GAP4R2PRE1: 4.8.0.2
#H GAP4R1: 4.5.0.2
#H keyword substitution: kv
#H total revisions: 10; selected revisions: 10
#H description:
#H ----------------------------
#H revision 4.9
#H date: 2000/03/27 09:54:44; author: gap; state: Exp; lines: +7 -2
#H added some tables of maxes of 2.Suz and corresponding fusions,
#H added table of 3.Fi22M5
#H
#H TB
#H ----------------------------
#H revision 4.8
#H date: 1999/10/21 14:15:46; author: gap; state: Exp; lines: +7 -5
#H added many `tomidentifer' and `tomfusion' values, which yields a better
#H interface between `tom' and `tbl';
#H
#H added maxes of McL.2,
#H
#H unified tables `J2.2M4', `2^(2+4):(3x3):2^2', `2^(2+4):(S3xS3)'.
#H
#H TB
#H ----------------------------
#H revision 4.7
#H date: 1999/09/28 15:34:04; author: gap; state: Exp; lines: +6 -2
#H added maxes of Sz(32)
#H
#H TB
#H ----------------------------
#H revision 4.6
#H date: 1999/08/31 13:16:13; author: gap; state: Exp; lines: +6 -2
#H added missing tables and fusions of maximal subgroups of Suz.2
#H
#H TB
#H ----------------------------
#H revision 4.5
#H date: 1999/07/14 11:39:37; author: gap; state: Exp; lines: +4 -3
#H cosmetic changes for the release ...
#H
#H TB
#H ----------------------------
#H revision 4.4
#H date: 1998/04/03 13:26:47; author: gap; state: Exp; lines: +4 -2
#H added tables of maxes of G2(3) and fusions into G2(3)
#H
#H TB
#H ----------------------------
#H revision 4.3
#H date: 1998/03/11 08:05:15; author: gap; state: Exp; lines: +8 -2
#H mainly new fusions to tables of marks added
#H
#H TB
#H ----------------------------
#H revision 4.2
#H date: 1997/11/25 15:44:35; author: gap; state: Exp; lines: +7 -3
#H first attempt to link the library of character tables and the
#H library of tables of marks
#H TB
#H ----------------------------
#H revision 4.1
#H date: 1997/07/17 15:38:10; author: fceller; state: Exp; lines: +2 -2
#H for version 4
#H ----------------------------
#H revision 1.1
#H date: 1996/10/21 15:59:06; author: sam; state: Exp;
#H first proposal of the table library
#H ==========================================================================
##
MOT("2.F4(2)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[6622253206732800,6622253206732800,95126814720,95126814720,95126814720,
95126814720,1509949440,1509949440,18874368,18874368,8709120,8709120,8709120,
8709120,93312,93312,7077888,7077888,11010048,11010048,11010048,11010048,
2949120,2949120,2949120,2949120,196608,196608,131072,131072,98304,98304,98304,
98304,49152,49152,16384,12288,8192,7200,7200,138240,138240,138240,138240,
27648,27648,27648,27648,10368,10368,10368,10368,9216,9216,9216,9216,2304,2304,
2304,2304,1152,1152,2352,2352,2352,2352,4096,4096,2048,3072,3072,3072,3072,
3072,3072,3072,3072,1024,1024,1024,128,256,256,108,108,108,108,480,480,480,
480,160,160,2304,2304,2304,2304,864,864,1152,1152,1152,1152,1152,1152,1152,
1152,768,768,768,768,192,192,192,192,96,96,96,96,48,48,26,26,112,112,112,112,
180,180,180,180,128,128,128,128,64,64,34,34,34,34,36,36,36,36,80,80,80,80,42,
42,42,42,96,96,96,96,96,96,96,96,56,56,56,56,60,60,60,60],
[,[1,1,1,1,1,1,1,1,1,1,11,11,13,13,15,15,3,5,3,3,5,5,7,7,7,7,3,5,8,8,7,7,7,7,
9,9,7,10,9,40,40,11,11,13,13,11,11,13,13,15,15,15,15,11,11,13,13,11,11,13,13,
15,15,64,64,66,66,29,29,29,19,19,21,21,17,17,18,18,29,29,30,35,39,39,85,85,87,
87,40,40,40,40,40,40,46,46,48,48,50,52,54,54,56,56,54,54,56,56,46,46,48,48,54,
54,56,56,50,52,62,62,63,63,123,123,64,64,66,66,129,129,131,131,68,68,70,70,81,
81,139,139,141,141,85,85,87,87,93,93,93,93,151,151,153,153,109,109,111,111,95,
95,97,97,125,125,127,127,129,129,131,131],[1,2,3,4,5,6,7,8,9,10,1,2,1,2,1,2,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,3,
4,5,6,5,6,3,4,3,4,5,6,7,8,7,8,9,10,9,10,9,10,64,65,66,67,68,69,70,71,72,73,74,
75,76,77,78,79,80,81,82,83,84,15,16,15,16,89,90,91,92,93,94,18,18,17,17,17,18,
23,24,23,24,25,26,25,26,21,22,19,20,31,32,33,34,27,28,35,36,38,38,123,124,125,
126,127,128,40,41,40,41,134,133,135,136,138,137,141,142,139,140,50,51,52,53,
147,148,149,150,64,65,66,67,73,74,71,72,77,78,75,76,163,164,165,166,90,89,91,
92],,[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,
28,29,30,31,32,33,34,35,36,37,38,39,1,2,42,43,44,45,46,47,48,49,50,51,52,53,
54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,
80,81,82,83,84,85,86,87,88,3,4,5,6,7,8,95,96,97,98,99,100,101,102,103,104,105,
106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,122,121,123,124,
125,126,127,128,11,12,13,14,134,133,135,136,137,138,141,142,139,140,143,144,
145,146,23,24,25,26,151,152,153,154,155,156,157,158,159,160,161,162,163,164,
165,166,43,42,44,45],,[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,
48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,1,2,1,2,68,69,70,71,72,73,74,
75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,
100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,
119,120,121,122,123,124,3,4,5,6,129,130,131,132,133,134,135,136,138,137,141,
142,139,140,143,144,145,146,147,148,149,150,11,12,13,14,155,156,157,158,159,
160,161,162,19,20,21,22,167,168,169,170],,,,,,[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,
66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,
92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,
113,114,115,116,117,118,119,120,121,122,1,2,125,126,127,128,129,130,131,132,
134,133,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,
152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,
170],,,,[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,
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,
79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,122,
121,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,1,2,1,2,
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]],
0,
[(139,141)(140,142),(137,138),(133,134),(133,134)(137,138),(121,122),( 3, 5)
( 4, 6)( 11, 13)( 12, 14)( 17, 18)( 19, 21)( 20, 22)( 25, 26)( 27, 28)
( 31, 33)( 32, 34)( 42, 44)( 43, 45)( 46, 48)( 47, 49)( 50, 52)( 51, 53)
( 54, 56)( 55, 57)( 58, 60)( 59, 61)( 64, 66)( 65, 67)( 71, 73)( 72, 74)
( 75, 77)( 76, 78)( 79, 80)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 95, 97)
( 96, 98)( 99,100)(101,103)(102,104)(105,108)(106,107)(109,111)(110,112)
(113,115)(114,116)(117,118)(125,127)(126,128)(129,131)(130,132)(143,145)
(144,146)(149,150)(151,153)(152,154)(155,157)(156,158)(159,161)(160,162)
(163,165)(164,166)(167,170)(168,169)],
["ConstructProj",[["F4(2)",[]],["2.F4(2)",[]]]]);
ARC("2.F4(2)","CAS",[rec(name:="2.f4f2",
permchars:=(9,10)(16,17)(22,23)(30,31)(35,36)(38,39)(50,51)(56,57)(59,60)
(61,62)(63,64)(69,70)(75,76)(78,79)(80,81)(88,89)(97,98)(99,100)(106,107)
(111,112)(113,114)(121,122)(123,124)(125,126)(127,128)(130,131)(132,133)
(134,135)(142,143)(144,145)(146,147)(152,153)(159,160)(161,162)(163,164)
(165,166),
permclasses:=(46,47)(48,49)(62,63)(89,90)(101,102)(103,104)(105,106)(109,
110)(111,112)(119,120)(125,126)(127,128)(143,144)(145,146)(147,148)(155,
156)(157,158)(159,160)(161,162),
text:="")]);
ALF("2.F4(2)","F4(2)",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,12,
13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,27,
27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,
40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,
54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,67,
68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,81,
82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,
94,94,95,95]);
ALF("2.F4(2)","2E6(2)M4",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,11,12,
12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,26,
27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,
39,40,40,41,41,42,42,43,43,44,45,46,47,48,48,49,49,50,50,51,51,52,52,53,
53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,
67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,79,80,80,81,
81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,
93,94,94,95,95]);
ALF("2.F4(2)","2.F4(2).2",[1,2,3,4,3,4,5,6,7,8,9,10,9,10,11,12,13,13,14,
15,14,15,16,17,18,18,19,19,20,21,22,23,22,23,24,25,26,27,28,29,30,31,32,
31,32,33,34,33,34,35,36,35,36,37,38,37,38,39,40,39,40,41,42,43,44,43,44,
45,46,47,48,49,48,49,50,51,50,51,52,52,53,54,55,56,57,58,57,58,59,60,59,
60,61,62,63,64,63,64,65,65,66,67,66,67,68,69,69,68,70,71,70,71,72,73,72,
73,74,74,75,76,77,78,79,80,81,82,81,82,83,84,83,84,85,86,87,88,89,90,91,
92,91,92,93,94,93,94,95,96,97,97,98,99,98,99,100,101,100,101,102,103,102,
103,104,105,104,105,106,107,107,106],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.F4(2)","2.2E6(2)",[1,2,3,4,6,5,5,6,7,7,8,9,10,11,12,13,16,20,14,15,
20,20,24,23,24,23,22,27,27,27,31,31,23,24,29,30,31,32,33,34,35,36,37,45,
44,41,40,38,39,42,43,48,47,40,41,44,45,46,46,50,49,52,51,55,56,53,54,73,
73,73,57,57,64,64,58,59,64,64,69,73,69,75,76,77,80,81,78,79,82,83,85,84,
84,85,101,101,92,93,91,105,108,107,112,111,108,107,112,111,101,101,97,98,
109,109,111,112,110,123,117,118,125,126,127,128,131,132,130,129,135,136,
133,134,146,146,146,146,142,142,148,149,150,151,156,157,159,158,167,166,
167,166,170,171,168,169,183,183,177,176,183,183,178,179,189,190,187,187,
194,193,192,191],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("2.F4(2)",["2.2E6(2)M4"]);
MOT("2.F4(2).2",
[
"origin: ATLAS of finite groups\n",
"the 2nd power map had been incorrect up to version 1.3,\n",
"(the map had 85,85,86,86 instead of 86,86,85,85)"
],
[13244506413465600,13244506413465600,95126814720,95126814720,3019898880,
3019898880,37748736,37748736,8709120,8709120,186624,186624,7077888,11010048,
11010048,5898240,5898240,2949120,196608,262144,262144,98304,98304,98304,98304,
32768,24576,16384,14400,14400,138240,138240,27648,27648,10368,10368,9216,9216,
2304,2304,2304,2304,2352,2352,8192,8192,4096,3072,3072,3072,3072,1024,2048,
256,512,512,108,108,480,480,320,320,2304,2304,864,1152,1152,1152,1152,768,768,
192,192,96,192,192,96,96,52,52,112,112,180,180,256,256,256,256,128,128,34,34,
36,36,160,160,80,42,42,96,96,96,96,56,56,60,60,71884800,40960,6144,432,2560,
2560,1536,1536,512,768,768,256,256,200,48,256,256,128,64,64,64,64,64,40,48,48,
48,48,48,48,52,52,64,64,64,64,64,64,64,64,80,80,80,80],
[,[1,1,1,1,1,1,1,1,9,9,11,11,3,3,3,5,5,5,3,6,6,5,5,7,7,5,8,7,29,29,9,9,9,9,11,
11,9,9,9,9,11,11,43,43,20,20,20,14,14,13,13,20,21,24,28,28,57,57,29,29,29,29,
33,33,35,37,37,37,37,33,33,37,37,35,41,41,42,42,79,79,43,43,83,83,45,45,47,47,
53,53,91,91,57,57,61,61,61,98,98,70,70,63,63,81,81,83,83,1,6,7,11,16,17,24,24,
21,27,27,25,26,29,41,53,53,53,46,56,56,56,56,62,75,75,78,78,77,77,79,79,86,86,
85,85,88,88,88,88,95,95,96,96],[1,2,3,4,5,6,7,8,1,2,1,2,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,3,4,3,4,3,4,5,6,7,8,7,8,43,44,45,46,47,48,49,
50,51,52,53,54,55,56,11,12,59,60,61,62,13,13,13,16,17,18,18,14,15,22,23,19,24,
25,27,27,79,80,81,82,29,30,86,85,87,88,90,89,91,92,35,36,95,96,97,43,44,48,49,
50,51,104,105,60,59,108,109,110,108,112,113,114,115,116,117,118,119,120,121,
110,123,124,125,126,130,129,128,127,131,114,115,117,118,117,118,138,139,142,
143,141,140,144,145,146,147,148,149,150,151],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,1,2,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,3,4,5,6,63,64,65,66,
67,68,69,70,71,72,73,74,75,76,78,77,79,80,81,82,9,10,86,85,87,88,89,90,91,92,
93,94,16,17,18,98,99,100,101,102,103,104,105,32,31,108,109,110,111,112,113,
114,115,116,118,117,119,120,108,122,124,123,125,126,128,127,130,129,109,132,
133,137,136,135,134,139,138,143,142,140,141,146,147,144,145,112,112,113,
113],,[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,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,1,2,45,46,47,48,49,50,51,52,
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,
79,80,3,4,83,84,85,86,87,88,90,89,91,92,93,94,95,96,97,9,10,100,101,102,103,
14,15,106,107,108,109,110,111,112,113,114,115,116,118,117,119,120,121,122,124,
123,125,126,129,130,127,128,131,132,133,135,134,137,136,139,138,141,140,143,
142,146,147,144,145,149,148,151,150],,,,,,[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,
67,68,69,70,71,72,73,74,75,76,77,78,1,2,81,82,83,84,86,85,87,88,89,90,91,92,
93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,
114,115,116,118,117,119,120,121,122,124,123,125,126,128,127,130,129,131,132,
133,135,134,137,136,108,108,142,143,141,140,146,147,144,145,148,149,150,
151],,,,[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,
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,78,77,
79,80,81,82,83,84,85,86,87,88,89,90,1,2,93,94,95,96,97,98,99,100,101,102,103,
104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,
123,124,125,126,127,128,129,130,131,132,133,136,137,134,135,138,139,140,141,
142,143,144,145,146,147,149,148,151,150]],
0,
[(148,149)(150,151),(138,139),(117,118)(123,124)(127,128)(129,130)(134,135)
(136,137)(144,146)(145,147),(114,115)(132,133)(144,147)(145,146),(89,90)(127,
130)(128,129),(77,78)(134,136)(135,137),(140,141)(142,143),(85,86)(140,142,
141,143)],
["ConstructProj",[["F4(2).2",[]],["2.F4(2).2",[]]]]);
ALF("2.F4(2).2","F4(2).2",[1,1,2,2,3,3,4,4,5,5,6,6,7,8,8,9,9,10,11,12,12,
13,13,14,14,15,16,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,
26,27,28,28,29,29,30,31,32,33,33,34,34,35,35,36,36,37,37,38,39,39,40,40,
41,41,42,42,43,44,44,45,46,47,47,48,48,49,49,50,50,51,51,52,53,54,54,55,
55,56,56,57,58,58,59,59,60,60,61,61,62,62,63,64,65,66,67,68,69,69,70,71,
71,72,73,74,75,76,76,77,78,79,79,80,80,81,82,82,83,83,84,84,85,85,86,86,
87,87,88,88,89,89,90,90,91,91]);
MOT("Isoclinic(2.F4(2).2)",
[
"isoclinic group of the 2.F4(2).2 given in the ATLAS"
],
0,
0,
0,
[(148,149)(150,151),(138,139),(117,118)(123,124)(127,128)(129,130)(134,135)
(136,137)(144,146)(145,147),(114,115)(132,133)(144,147)(145,146),(89,90)(127,
130)(128,129),(77,78)(134,136)(135,137),(140,141)(142,143),(85,86)(140,142,
141,143)],
["ConstructIsoclinic",[["2.F4(2).2"]]]);
ALF("Isoclinic(2.F4(2).2)","F4(2).2",[1,1,2,2,3,3,4,4,5,5,6,6,7,8,8,9,9,10,
11,12,12,13,13,14,14,15,16,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,
25,26,26,27,28,28,29,29,30,31,32,33,33,34,34,35,35,36,36,37,37,38,39,39,40,
40,41,41,42,42,43,44,44,45,46,47,47,48,48,49,49,50,50,51,51,52,53,54,54,55,
55,56,56,57,58,58,59,59,60,60,61,61,62,62,63,64,65,66,67,68,69,69,70,71,
71,72,73,74,75,76,76,77,78,79,79,80,80,81,82,82,83,83,84,84,85,85,86,86,
87,87,88,88,89,89,90,90,91,91]);
MOT("Isoclinic(2x2.F4(2).2)",
[
"central product of C4 and 2.F4(2).2"
],
0,
0,
0,
[(295,297)(296,298)(299,301)(300,302),(275,277)(276,278),
(227,229)(228,230)(263,265)(264,266)(287,293)(288,294)(289,291)(290,292),
(177,179)(178,180)(253,259)(254,260)(255,257)(256,258),
(169,171)(170,172)(233,235)(234,236)(245,247)(246,248)(253,255)(254,256)
(257,259)(258,260)(267,269)(268,270)(271,273)(272,274)(279,285,281,283)
(280,286,282,284)(287,291)(288,292)(289,293)(290,294)(295,297)(296,298)
(299,301)(300,302)
,(153,155)(154,156)(267,271)(268,272)(269,273)(270,274),
( 2, 4)( 6, 8)( 10, 12)( 14, 16)( 18, 20)( 22, 24)( 28, 30)( 32, 34)
( 40, 42)( 44, 46)( 48, 50)( 58, 60)( 62, 64)( 66, 68)( 70, 72)( 74, 76)
( 78, 80)( 82, 84)( 86, 88)( 90, 92)( 96, 98)(100,102)(110,112)(114,116)
(118,120)(122,124)(126,128)(132,134)(136,138)(140,142)(144,146)(150,152)
(158,160)(162,164)(166,168)(170,172)(174,176)(177,179)(178,180)(182,184)
(186,188)(190,192)(196,198)(200,202)(204,206)(208,210)(212,214)(228,230)
(233,235)(245,247)(253,257)(254,260)(255,259)(256,258)(264,266)(267,269)
(271,273)(276,278)(280,282)(284,286)(287,291)(288,294)(289,293)(290,292)
(296,298)(300,302)
,(279,281)(280,282)(283,285)(284,286),
(233,235)(234,236)(245,247)(246,248)(253,255)(254,256)(257,259)(258,260)
(267,269)(268,270)(271,273)(272,274)(287,291)(288,292)(289,293)(290,294)
],
["ConstructIsoclinic",[["2.F4(2).2"],["Cyclic",2]],[1,3..301]]);
MOT("2.(2xF4(2)).2",
[
"4B centralizer in the Monster group,\n",
"constructed by Simon Norton, Dec. 2000"
],
0,
0,
0,
[(153,155)(154,156)(267,271)(268,272)(269,273)(270,274),(177,179)(178,180)
(253,258)(254,257)(255,260)(256,259),(227,228)(229,230)(263,264)(265,266)(287,
292)(288,291)(289,294)(290,293),(233,234)(235,236)(245,246)(247,248)(253,254)
(255,256)(257,258)(259,260)(267,268)(269,270)(271,272)(273,274)(287,291)(288,
292)(289,293)(290,294),(275,276)(277,278),(295,296)(297,298)(299,300)(301,
302),(279,280)(281,282)(283,284)(285,286),(169,170)(171,172)(279,283,280,284)
(281,285,282,286),(3,4)(7,8)(11,12)(15,16)(19,20)(23,24)(29,30)(33,34)(41,42)
(45,46)(49,50)(59,60)(63,64)(67,68)(71,72)(75,76)(79,80)(83,84)(87,88)(91,92)
(97,98)(101,102)(111,112)(115,116)(119,120)(123,124)(127,128)(133,134)(137,
138)(141,142)(145,146)(151,152)(159,160)(163,164)(167,168)(171,172)(175,176)
(183,184)(187,188)(191,192)(197,198)(201,202)(205,206)(209,210)(213,214)(215,
216)(217,218)(219,220)(221,222)(223,224)(225,226)(227,229)(228,230)(231,232)
(233,235)(234,236)(237,238)(239,240)(241,242)(243,244)(245,247)(246,248)(249,
250)(251,252)(253,255)(254,256)(257,259)(258,260)(261,262)(263,265)(264,266)
(267,269)(268,270)(271,273)(272,274)(275,277)(276,278)(279,281)(280,282)(283,
285)(284,286)(287,289)(288,290)(291,293)(292,294)(295,297)(296,298)(299,301)
(300,302)],
["ConstructIsoclinic",[["Isoclinic(2x2.F4(2).2)"]],[1..214],[1..4],
(2,3)(6,7)(10,11)(14,15)(18,19)(22,23)(28,29)(32,33)(40,41)(44,45)(48,49)
(58,59)(62,63)(66,67)(70,71)(74,75)(78,79)(82,83)(86,87)(90,91)(96,97)(100,
101)(110,111)(114,115)(118,119)(122,123)(126,127)(132,133)(136,137)(140,141)
(144,145)(150,151)(158,159)(162,163)(166,167)(170,171)(174,175)(182,183)
(186,187)(190,191)(196,197)(200,201)(204,205)(208,209)(212,213)(228,229)
(234,235)(246,247)(254,255)(258,259)(264,265)(268,269)(272,273)(276,277)
(280,281)(284,285)(288,289)(292,293)(296,297)(300,301),
(184,186)(192,194)(196,198)(200,202)(210,212)(218,220)(224,226)(238,240)
(266,268)(272,274)(276,278)(288,290)(292,294)(296,298)(300,302)]);
ALF("2.(2xF4(2)).2","M",[1,2,8,8,3,2,8,8,2,3,8,8,3,3,8,8,4,13,37,37,5,16,41,
41,7,8,7,7,8,8,8,8,7,7,8,7,9,8,9,9,8,8,8,8,9,9,7,9,10,10,8,9,10,9,9,10,11,
29,65,65,15,13,37,37,15,13,37,37,17,16,41,41,13,15,37,37,15,15,37,37,17,
14,41,41,19,47,93,93,25,25,21,21,25,21,22,22,22,22,22,22,22,22,25,25,21,
25,22,24,21,25,25,25,27,59,116,116,30,29,65,65,29,30,65,65,35,35,37,37,36,
41,37,37,35,35,37,37,35,35,35,35,37,37,37,37,39,39,42,41,36,42,40,40,40,
43,40,43,45,89,144,144,48,47,93,93,50,99,154,154,55,55,55,55,56,56,56,56,
54,54,54,54,57,111,164,164,60,59,116,116,65,65,64,64,65,64,70,128,174,174,
78,78,78,78,78,78,78,78,94,94,93,93,99,100,154,154,23,23,23,23,23,23,84,
84,22,22,22,22,26,26,26,26,23,23,25,21,25,21,26,26,24,24,123,123,84,84,56,
56,56,56,56,56,54,54,55,56,55,56,56,55,56,55,123,123,83,83,83,83,86,80,86,
80,86,80,86,80,189,190,189,190,107,107,107,107,107,107,107,107,108,108,
108,108,108,108,108,108,124,124,124,124,124,124,124,124]);
ALF("2.(2xF4(2)).2","F4(2).2",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,
6,6,6,7,7,8,8,8,8,9,9,9,9,10,10,11,11,12,12,12,12,13,13,13,13,14,14,14,14,
15,15,16,16,17,17,18,18,18,18,19,19,19,19,20,20,20,20,21,21,21,21,22,22,
22,22,23,23,23,23,24,24,24,24,25,25,25,25,26,26,26,26,27,27,28,28,28,28,
29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,34,34,35,35,35,35,36,36,
36,36,37,37,37,37,38,38,39,39,39,39,40,40,40,40,41,41,41,41,42,42,42,42,
43,43,44,44,44,44,45,45,46,46,47,47,47,47,48,48,48,48,49,49,49,49,50,50,
50,50,51,51,51,51,52,52,53,53,54,54,54,54,55,55,55,55,56,56,56,56,57,57,
58,58,58,58,59,59,59,59,60,60,60,60,61,61,61,61,62,62,62,62,63,63,64,64,
65,65,66,66,67,67,68,68,69,69,69,69,70,70,71,71,71,71,72,72,73,73,74,74,
75,75,76,76,76,76,77,77,78,78,79,79,79,79,80,80,80,80,81,81,82,82,82,82,
83,83,83,83,84,84,84,84,85,85,85,85,86,86,86,86,87,87,87,87,88,88,88,88,
89,89,89,89,90,90,90,90,91,91,91,91]);
ALN("2.(2xF4(2)).2",["4.F4(2).2","MC4B"]);
MOT("2.G2(4)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[503193600,503193600,122880,122880,3840,120960,120960,360,360,3072,3072,768,
512,600,600,600,600,600,600,600,600,384,384,12,42,42,32,64,64,40,40,40,40,20,
20,96,96,48,48,26,26,26,26,30,30,30,30,30,30,30,30,42,42,42,42],
[,[1,1,1,1,2,6,6,8,8,3,3,4,3,16,16,14,14,20,20,18,18,6,6,9,25,25,10,13,13,20,
20,18,18,17,15,22,22,23,23,42,42,40,40,46,46,44,44,50,50,48,48,54,54,52,52],[
1,2,3,4,5,1,2,1,2,10,11,12,13,16,17,14,15,20,21,18,19,3,4,5,25,26,27,28,29,32,
33,30,31,35,34,10,11,12,12,40,41,42,43,16,17,14,15,20,21,18,19,25,26,25,26],,[
1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,1,2,1,2,1,2,22,23,24,25,26,27,28,29,3,4,3,4,
5,5,36,37,39,38,42,43,40,41,6,7,6,7,8,9,8,9,52,53,54,55],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,16,17,14,15,20,21,18,19,22,23,24,1,2,27,28,29,32,33,30,31,35,34,
36,37,38,39,42,43,40,41,46,47,44,45,50,51,48,49,6,7,6,7],,,,,,[1,2,3,4,5,6,7,
8,9,10,11,12,13,16,17,14,15,20,21,18,19,22,23,24,25,26,27,28,29,32,33,30,31,
35,34,36,37,38,39,1,2,1,2,46,47,44,45,50,51,48,49,54,55,52,53]],
0,
[(52,54)(53,55),(40,42)(41,43),(38,39),(38,39)(52,54)(53,55),(14,16)(15,17)
(18,20)(19,21)(30,32)(31,33)(34,35)(44,46)(45,47)(48,50)(49,51)],
["ConstructProj",[["G2(4)",[]],["2.G2(4)",[]]]]);
ARC("2.G2(4)","maxes",["2.J2","2.2^(2+8).(3xA5)","2.2^(4+6).(A5x3)",
"Isoclinic(2xU3(4).2)","Isoclinic(6.L3(4).2_3)","Isoclinic(2xU3(3).2)",
"2.A5xA5","2.L2(13)"]);
ALF("2.G2(4)","G2(4)",[1,1,2,2,3,4,4,5,5,6,6,7,8,9,9,10,10,11,11,12,12,13,
13,14,15,15,16,17,17,18,18,19,19,20,21,22,22,23,24,25,25,26,26,27,27,28,
28,29,29,30,30,31,31,32,32]);
ALF("2.G2(4)","2.G2(4).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,14,15,16,
17,16,17,18,19,20,21,22,23,24,25,26,27,26,27,28,28,29,30,31,32,33,34,33,
34,35,36,35,36,37,38,37,38,39,40,39,40],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.G2(4)","Isoclinic(2.G2(4).2)",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
14,15,16,17,16,17,18,19,20,21,22,23,24,25,26,27,26,27,28,28,29,30,31,32,
33,34,33,34,35,36,35,36,37,38,37,38,39,40,39,40],[
"fusion map is unique up to table aut."
]);
ALF("2.G2(4)","2.Suz",[1,2,3,4,5,6,7,10,11,12,13,15,14,19,20,19,20,17,18,
17,18,21,22,29,30,31,32,33,34,40,41,40,41,42,42,45,46,49,49,54,55,56,57,
63,64,63,64,59,60,61,62,71,72,73,74],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
MOT("2.G2(4).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[1006387200,1006387200,245760,245760,7680,241920,241920,720,720,6144,6144,
1536,1024,600,600,600,600,768,768,24,84,84,64,128,128,40,40,20,192,192,96,96,
26,26,30,30,30,30,42,42,24192,384,192,192,432,36,192,192,192,64,48,24,24,28,
28,32,32,32,32,48,48,48,48,48,48],
[,[1,1,1,1,2,6,6,8,8,3,3,4,3,14,14,16,16,6,6,9,21,21,10,13,13,16,16,15,18,18,
19,19,33,33,35,35,37,37,39,39,1,3,5,5,6,8,11,12,12,10,18,20,20,21,21,25,25,25,
25,30,30,31,31,32,32],[1,2,3,4,5,1,2,1,2,10,11,12,13,14,15,16,17,3,4,5,21,22,
23,24,25,26,27,28,10,11,12,12,33,34,14,15,16,17,21,22,41,42,43,44,41,41,47,49,
48,50,42,43,44,55,54,59,58,57,56,47,47,49,48,49,48],,[1,2,3,4,5,6,7,8,9,10,11,
12,13,1,2,1,2,18,19,20,21,22,23,24,25,3,4,5,29,30,32,31,33,34,6,7,8,9,39,40,
41,42,44,43,45,46,47,49,48,50,51,53,52,55,54,57,56,59,58,61,60,65,64,63,62],,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,2,23,24,25,26,27,28,29,
30,31,32,33,34,35,36,37,38,6,7,41,42,44,43,45,46,47,48,49,50,51,53,52,41,41,
58,59,56,57,60,61,62,63,64,65],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,1,2,35,36,37,38,39,40,41,42,
44,43,45,46,47,49,48,50,51,53,52,55,54,57,56,59,58,60,61,63,62,65,64]],
0,
[(60,61),(54,55),(48,49)(56,59)(57,58)(62,63)(64,65),(43,44)(52,53)(56,58)
(57,59),(31,32)(62,64)(63,65),(31,32)(60,61)(62,64)(63,65)],
["ConstructProj",[["G2(4).2",[]],["2.G2(4).2",[]]]]);
ARC("2.G2(4).2","CAS",[rec(name:="g2f4c",
permchars:=(17,18),
permclasses:=())]);
ALF("2.G2(4).2","G2(4).2",[1,1,2,2,3,4,4,5,5,6,6,7,8,9,9,10,10,11,11,12,
13,13,14,15,15,16,16,17,18,18,19,20,21,21,22,22,23,23,24,24,25,26,27,27,
28,29,30,31,31,32,33,34,34,35,35,36,36,37,37,38,38,39,39,40,40]);
ALN("2.G2(4).2",["g2f4c"]);
MOT("Isoclinic(2.G2(4).2)",
[
"isoclinic group of the 2.G2(4).2 given in the ATLAS"
],
0,
0,
0,
[(60,61),(54,55),(43,44)(48,49)(52,53)(56,57)(58,59)(62,63)(64,65),(31,32)(62,
64)(63,65),(43,44)(52,53)(56,58)(57,59)],
["ConstructIsoclinic",[["2.G2(4).2"]]]);
ALF("Isoclinic(2.G2(4).2)","G2(4).2",[1,1,2,2,3,4,4,5,5,6,6,7,8,9,9,10,10,11,
11,12,13,13,14,15,15,16,16,17,18,18,19,20,21,21,22,22,23,23,24,24,25,26,27,
27,28,29,30,31,31,32,33,34,34,35,35,36,36,37,37,38,38,39,39,40,40]);
ALF("Isoclinic(2.G2(4).2)","2.Suz.2",[1,2,3,4,5,6,7,10,11,12,13,15,14,19,
20,17,18,21,22,27,28,29,30,31,32,36,37,38,41,42,45,45,48,49,53,54,51,52,
59,60,62,64,65,65,66,68,72,76,77,75,83,85,85,86,86,87,88,87,88,93,93,98,
99,98,99],[
"fusion map is unique up to table automorphisms"
]);
ALN("Isoclinic(2.G2(4).2)",["2.Suz.2M2"]);
MOT("2.Sz(8)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[58240,58240,64,16,16,10,10,14,14,14,14,14,14,26,26,26,26,26,26],
[,[1,1,1,3,3,6,6,10,10,12,12,8,8,16,16,18,18,14,14],,,[1,2,3,4,5,1,2,10,11,12,
13,8,9,14,15,16,17,18,19],,[1,2,3,5,4,6,7,1,2,1,2,1,2,18,19,14,15,16,
17],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,1,2,1,2]],
0,
[(14,16,18)(15,17,19),( 8,12,10)( 9,13,11),(4,5)],
["ConstructProj",[["Sz(8)",[]],["2.Sz(8)",[]]]]);
ARC("2.Sz(8)","maxes",["2.2^(3+3):7","2x13:4","2x5:4","D28"]);
ALF("2.Sz(8)","Sz(8)",[1,1,2,3,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11]);
MOT("2^2.Sz(8)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"
],
[116480,116480,116480,116480,64,16,16,20,20,20,20,28,28,28,28,28,28,28,28,28,
28,28,28,52,52,52,52,52,52,52,52,52,52,52,52],
[,[1,1,1,1,1,5,5,8,8,8,8,16,16,16,16,20,20,20,20,12,12,12,12,28,28,28,28,32,
32,32,32,24,24,24,24],,,[1,2,3,4,5,6,7,1,2,3,4,16,17,18,19,20,21,22,23,12,13,
14,15,24,25,26,27,28,29,30,31,32,33,34,35],,[1,2,3,4,5,7,6,8,9,10,11,1,2,3,4,
1,2,3,4,1,2,3,4,32,33,34,35,24,25,26,27,28,29,30,31],,,,,,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,1,2,3,4,1,2,3,4,1,2,3,4]],
0,
[(24,28,32)(25,29,33)(26,30,34)(27,31,35),(12,20,16)(13,21,17)(14,22,18)
(15,23,19),(6,7),( 3, 4)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35),
( 2, 3)( 9,10)(13,14)(17,18)(21,22)(25,26)(29,30)(33,34)],
["ConstructV4G","2.Sz(8)",( 2, 3, 4)( 9,10,11)(12,16,20)
(13,18,23)(14,19,21)(15,17,22)(24,28,32)(25,30,35)(26,31,33)(27,29,34)]);
ARC("2^2.Sz(8)","maxes",["2^2.2^(3+3):7","2^2x13:4","5:4x2^2","2^2xD14"]);
ALF("2^2.Sz(8)","2.Sz(8)",[1,1,2,2,3,4,5,6,6,7,7,8,8,9,9,10,10,11,11,12,
12,13,13,14,14,15,15,16,16,17,17,18,18,19,19]);
ALF("2^2.Sz(8)","Sz(8)",[1,1,1,1,2,3,4,5,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,9,
9,9,9,10,10,10,10,11,11,11,11]);
ALF("2^2.Sz(8)","2^2.Sz(8).3",[1,2,2,2,3,4,5,6,7,7,7,8,9,10,11,8,11,9,10,
8,10,11,9,12,13,14,15,12,15,13,14,12,14,15,13],[
"fusion map determined up to table autom.\n",
"by Brauer tables and factors"
]);
ALN("2^2.Sz(8)",["2^2.Sz(8).3M1"]);
MOT("2^2.Sz(8).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11],\n",
"(all possibilities of an order 3 table automorphism of 2^2.Sz(8)\n",
"to represent a group automorphism of Sz(8) lead to equivalent tables)"
],
[349440,116480,192,48,48,60,20,28,28,28,28,52,52,52,52,60,60,12,12,12,12,12,
12,15,15],
[,[1,1,1,3,3,6,6,8,8,8,8,12,12,12,12,17,16,17,16,19,18,19,18,25,24],[1,2,3,5,
4,6,7,8,10,11,9,12,15,13,14,1,1,3,3,5,5,4,4,6,6],,[1,2,3,4,5,1,2,8,11,9,10,12,
13,14,15,17,16,19,18,21,20,23,22,17,16],,[1,2,3,5,4,6,7,1,2,2,2,12,14,15,13,
16,17,18,19,22,23,20,21,24,25],,,,,,[1,2,3,4,5,6,7,8,9,10,11,1,2,2,2,16,17,18,
19,20,21,22,23,24,25]],
0,
[(16,17)(18,19)(20,21)(22,23)(24,25),(13,15,14),( 9,10,11),( 4, 5)(20,22)
(21,23)],
["ConstructMGA","2^2.Sz(8)","Sz(8).3",[[12,20,28],[13,21,29],[14,22,30],[15,
23,31],[16,24,32],[17,25,33],[18,26,34],[19,27,35]],()]);
ALF("2^2.Sz(8).3","Sz(8).3",[1,1,2,3,4,5,5,6,6,6,6,7,7,7,7,8,9,10,11,12,
13,14,15,16,17]);
MOT("3.G2(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[12737088,12737088,12737088,1728,1728,1728,5832,5832,729,162,162,288,288,288,
288,288,288,72,72,18,18,21,21,21,24,24,24,24,24,24,27,27,27,36,36,36,36,36,36,
39,39,39,39,39,39],
[,[1,3,2,1,3,2,7,8,9,10,11,4,6,5,4,6,5,7,8,10,11,22,24,23,12,14,13,15,17,16,
31,33,32,18,18,18,19,19,19,43,45,44,40,42,41],[1,1,1,4,4,4,1,1,1,1,1,12,12,12,
15,15,15,4,4,4,4,22,22,22,25,25,25,28,28,28,9,9,9,12,12,12,15,15,15,40,40,40,
43,43,43],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,1,2,3,25,
26,27,28,29,30,31,32,33,34,35,36,37,38,39,43,44,45,40,41,42],,,,,,[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,
33,34,35,36,37,38,39,1,2,3,1,2,3]],
0,
[(40,43)(41,44)(42,45),(32,33),( 2, 3)( 5, 6)(13,14)(16,17)(23,24)(26,27)
(29,30)(32,33)(35,36)(38,39)(41,42)(44,45),( 2, 3)( 5, 6)(13,14)(16,17)(23,24)
(26,27)(29,30)(35,36)(38,39)(41,42)(44,45),( 7, 8)(12,15)(13,16)(14,17)(18,19)
(25,28)(26,29)(27,30)(34,37)(35,38)(36,39)],
["ConstructProj",[["G2(3)",[]],,["3.G2(3)",[-1,-1,-25,-25,-1,-1,-1,-1,-1,-1,
-1]]]]);
ARC("3.G2(3)","maxes",["3xU3(3).2","3.G2(3)M2","3.(3^(1+2)+x3^2):2S4",
"3.G2(3)M4","3xL3(3).2","3.G2(3)M6","3xL2(8).3","3x2^3.L3(2)","3xL2(13)",
"3.2^(1+4)+:3^2.2"]);
ALF("3.G2(3)","G2(3)",[1,1,1,2,2,2,3,4,5,6,7,8,8,8,9,9,9,10,11,12,13,14,
14,14,15,15,15,16,16,16,17,18,19,20,20,20,21,21,21,22,22,22,23,23,23]);
ALF("3.G2(3)","3.G2(3).2",[1,2,2,3,4,4,5,5,6,7,8,9,10,11,9,11,10,12,12,13,
14,15,16,16,17,18,19,17,19,18,20,21,22,23,24,25,23,25,24,26,27,28,26,28,
27],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.G2(3)","3.O7(3)",[1,2,3,10,11,12,13,18,18,21,20,28,29,30,25,26,27,
51,60,64,63,65,66,67,71,72,73,68,69,70,78,78,78,94,95,96,97,97,97,105,106,
107,102,103,104],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
MOT("3.G2(3).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[25474176,12737088,3456,1728,5832,1458,324,324,288,288,288,72,36,36,42,21,24,
24,24,54,54,54,36,36,36,39,39,39,3024,48,54,36,36,12,12,14,18,18,18],
[,[1,2,1,2,5,6,7,8,3,4,4,5,7,8,15,16,9,11,10,20,22,21,12,12,12,26,27,28,1,3,6,
8,8,13,13,15,20,22,21],[1,1,3,3,1,1,1,1,9,9,9,3,3,3,15,15,17,17,17,6,6,6,9,9,
9,26,26,26,29,30,29,29,29,30,30,36,31,31,31],,,,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,1,2,17,18,19,20,21,22,23,24,25,26,28,27,29,30,31,32,33,35,34,29,37,38,
39],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,1,
2,2,29,30,31,32,33,34,35,36,37,38,39]],
0,
[(34,35),(27,28),(21,22)(32,33)(38,39),(10,11)(18,19)(24,25),(10,11)(18,19)
(21,22)(24,25)(27,28)(32,33)(34,35)(38,39)],
["ConstructMGA","3.G2(3)","G2(3).2",[[24,27],[25,26],[28,31],[29,30],[32,
33],[34,37],[35,36],[38,41],[39,40],[42,43],[44,45]],()]);
ALF("3.G2(3).2","G2(3).2",[1,1,2,2,3,4,5,6,7,7,7,8,9,10,11,11,12,12,12,13,
14,15,16,16,16,17,17,17,18,19,20,21,22,23,24,25,26,27,28]);
MOT("F4(2)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[3311126603366400,47563407360,47563407360,754974720,9437184,4354560,4354560,
46656,7077888,7077888,5505024,5505024,1474560,1474560,196608,196608,65536,
49152,49152,24576,16384,12288,8192,3600,69120,69120,13824,13824,5184,5184,
4608,4608,1152,1152,576,1176,1176,2048,2048,1536,1536,1536,1536,1024,1024,
1024,128,128,54,54,240,240,80,1152,1152,864,864,576,576,576,576,384,384,96,96,
96,96,48,48,48,13,56,56,90,90,64,64,64,64,17,17,18,18,40,40,21,21,48,48,48,48,
28,28,30,30],
[,[1,1,1,1,1,6,7,8,2,3,2,3,4,4,2,3,4,4,4,5,4,5,5,24,6,7,6,7,8,8,6,7,6,7,8,36,
37,17,17,11,12,9,10,17,17,17,20,23,49,50,24,24,24,27,28,29,30,31,32,31,32,27,
28,31,32,29,30,35,35,35,71,36,37,74,75,38,39,46,46,80,81,49,50,53,53,86,87,62,
63,54,55,72,73,74,75],[1,2,3,4,5,1,1,1,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,2,3,3,2,2,3,4,4,5,5,5,36,37,38,39,40,41,42,43,44,45,46,47,48,8,8,51,
52,53,10,9,9,10,13,13,14,14,12,11,18,19,15,16,20,22,22,71,72,73,24,24,76,77,
79,78,81,80,29,30,84,85,36,37,41,40,43,42,92,93,51,52],,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,20,21,22,23,1,25,26,27,28,29,30,31,32,33,34,35,36,
37,38,39,40,41,42,43,44,45,46,47,48,49,50,2,3,4,54,55,56,57,58,59,60,61,62,63,
64,65,66,67,68,70,69,71,72,73,6,7,76,77,78,79,81,80,82,83,13,14,86,87,88,89,
90,91,92,93,25,26],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,1,1,38,39,40,41,42,43,44,45,46,47,48,
49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,2,3,74,
75,76,77,79,78,81,80,82,83,84,85,6,7,88,89,90,91,11,12,94,95],,,,,,[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,
59,60,61,62,63,64,65,66,67,68,69,70,1,72,73,74,75,76,77,78,79,80,81,82,83,84,
85,86,87,88,89,90,91,92,93,94,95],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
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ARC("F4(2)","isSimple",true);
ARC("F4(2)","extInfo",["2","2"]);
ARC("F4(2)","maxes",["(2^(1+8)x2^6):S6(2)","F4(2)M2","S8(2)","F4(2)M4",
"[2^20]:(S3xL3(2))","F4(2)M6","O8+(2).3.2","F4(2)M8","3D4(2).3","F4(2)M10",
"2F4(2)'.2","L4(3).2_2","F4(2)M13","(L3(2)xL3(2)):2"]);
ALF("F4(2)","F4(2).2",[1,2,2,3,4,5,5,6,7,7,8,8,9,10,11,11,12,13,13,14,15,
16,17,18,19,19,20,20,21,21,22,22,23,23,24,25,25,26,27,28,28,29,29,30,30,
31,32,33,34,34,35,35,36,37,37,38,38,39,39,40,40,41,41,42,42,43,43,44,45,
46,47,48,48,49,49,50,51,52,53,54,54,55,55,56,57,58,58,59,59,60,60,61,61,
62,62]);
ALF("F4(2)","2E6(2)",[1,2,3,3,4,5,6,7,9,11,8,11,15,15,14,16,16,20,15,19,
20,21,22,23,24,28,26,25,27,30,26,28,29,31,32,34,33,46,46,35,39,36,39,43,
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81,82,83,85,84,87,86,94,94,91,91,97,98,101,102,106,106,108,107,114,111,
114,112,120,117,122,121]);
ALF("F4(2)","E6(2)",[1,2,3,3,4,5,6,7,8,11,9,11,13,13,12,14,14,17,13,18,17,
15,16,19,20,25,23,22,21,26,23,25,24,27,28,32,31,40,40,34,37,33,37,38,40,
38,42,41,44,43,45,46,46,51,52,47,53,54,57,54,57,51,50,55,57,56,58,60,61,
62,63,71,70,75,74,78,78,77,77,79,80,81,82,84,84,91,92,94,95,94,96,107,108,
113,114],[
"fusion map is unique up to table automorphisms"
]);
ALN("F4(2)",["f4f2","2E6(2)M3"]);
MOT("F4(2).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: Aut(F4(2))"
],
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0],
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ARC("F4(2).2","maxes",["F4(2)","[2^20]:A6.2^2","[2^22]:(S3xS3):2","2F4(2)x2",
"L4(3).2^2","S4(4).4","(S6wr2).2","F4(2).2M8","(L3(2)xL3(2)).4",
"7^2:(3x2S4)"]);
MOT("G2(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
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13],
[,[1,1,3,4,5,6,7,2,2,3,4,6,7,14,8,9,17,19,18,10,11,23,22],[1,2,1,1,1,1,1,8,9,
2,2,2,2,14,15,16,5,5,5,8,9,22,23],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,15,16,
17,18,19,20,21,23,22],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,1,1]],
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-2,1,0,0,0,2,-1,-1,-1,-1,1,1],[64,0,-8,-8,1,4,-2,0,0,0,0,0,0,1,0,0,1,
2*E(3)-E(3)^2,-E(3)+2*E(3)^2,0,0,-1,-1],
[GALOIS,[3,2]],[78,-2,-3,-3,-3,-3,6,2,2,1,1,1,-2,1,0,0,0,0,0,-1,-1,0,0],[91,
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E(13)^2+E(13)^5+E(13)^6+E(13)^7+E(13)^8+E(13)^11],
[GALOIS,[15,2]],[546,2,-21,6,6,-3,-3,-2,6,-1,2,-1,-1,0,0,0,0,0,0,1,0,0,0],[
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[(22,23),(18,19),( 3, 4)( 8, 9)(10,11)(15,16)(20,21)]);
ARC("G2(3)","CAS",[rec(name:="g2f3",
permchars:=(),
permclasses:=())]);
ARC("G2(3)","projectives",["3.G2(3)",[[27,3,0,0,0,0,0,-1,3,0,0,0,0,-1,-1,1,0,
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0,0,0,-3,-3,0,0,0,0,0,1,1,0,0,0,0,0,-E(13)-E(13)^3-E(13)^4-E(13)^9-E(13)^10
-E(13)^12,-E(13)^2-E(13)^5-E(13)^6-E(13)^7-E(13)^8-E(13)^11],
[GALOIS,[3,2]],[351,15,0,0,0,0,0,3,3,0,0,0,0,1,1,1,0,0,0,0,0,0,0],[351,-9,0,0,
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1,0,0,0,0,2,0,0],[378,-6,0,0,0,0,0,-2,6,0,0,0,0,0,0,0,0,0,0,-2,0,1,1],[378,-6,
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-1]],]);
ARC("G2(3)","isSimple",true);
ARC("G2(3)","extInfo",["3","2"]);
ARC("G2(3)","maxes",["U3(3).2","G2(3)M2","(3^(1+2)+x3^2):2S4","G2(3)M4",
"L3(3).2","G2(3)M6","L2(8).3","2^3.L3(2)","L2(13)","2^(1+4)+:3^2.2"]);
ARC("G2(3)","tomfusion",rec(name:="G2(3)",map:=[1,2,6,3,4,5,7,9,8,14,12,
13,15,23,33,34,50,51,51,52,53,60,60],text:=[
"unique fusion map compatible with AtlasRep"
]));
ALF("G2(3)","G2(3).2",[1,2,3,3,4,5,6,7,7,8,8,9,10,11,12,12,13,14,15,16,16,
17,17],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("G2(3)","O7(3)",[1,4,5,8,8,11,10,14,13,23,28,32,31,33,35,34,38,38,38,
46,47,51,50],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("G2(3)","3D4(3)",[1,2,3,4,4,5,6,8,7,9,10,11,12,16,18,17,20,20,20,22,
21,29,30],[
"fusion map is unique up to table automorphisms"
]);
ALN("G2(3)",["g2f3"]);
MOT("G2(3).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: Aut(G2(3))"
],
[8491392,1152,5832,1458,324,324,96,72,36,36,14,8,54,54,54,12,13,3024,48,54,36,
36,12,12,14,18,18,18],
[,[1,1,3,4,5,6,2,3,5,6,11,7,13,15,14,8,17,1,2,4,6,6,9,9,11,13,15,14],[1,2,1,1,
1,1,7,2,2,2,11,12,4,4,4,7,17,18,19,18,18,18,19,19,25,20,20,20],,,,[1,2,3,4,5,
6,7,8,9,10,1,12,13,14,15,16,17,18,19,20,21,22,24,23,18,26,27,28],,,,,,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,1,18,19,20,21,22,23,24,25,26,27,28]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,
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E(3)-E(3)^2],
[TENSOR,[3,2]],[64,0,-8,1,4,-2,0,0,0,0,1,0,1,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,0,
-1,8,0,-1,2*E(3),2*E(3)^2,0,0,1,-1,-E(3)^2,-E(3)],
[TENSOR,[5,2]],
[GALOIS,[5,2]],
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0,0],
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1,1],
[TENSOR,[11,2]],[182,6,11,2,8,-4,2,3,0,0,0,0,-4,2,2,-1,0,0,0,0,0,0,0,0,0,0,0,
0],[104,8,14,5,2,-1,0,2,2,-1,-1,0,2,-1,-1,0,0,8,0,-1,-1,-1,0,0,1,2,-1,-1],
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2,2,2,0,0,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0],[729,9,0,0,0,0,-3,0,0,0,1,-1,0,
0,0,0,1,27,3,0,0,0,0,0,-1,0,0,0],
[TENSOR,[23,2]],[819,3,9,9,0,0,-1,-3,0,0,0,1,0,0,0,-1,0,21,-3,3,0,0,0,0,0,0,0,
0],
[TENSOR,[25,2]],[832,0,-32,-5,4,4,0,0,0,0,-1,0,1,1,1,0,0,8,0,-1,2,2,0,0,1,-1,
-1,-1],
[TENSOR,[27,2]]],
[(23,24),(14,15)(21,22)(27,28),(14,15)(21,22)(23,24)(27,28)]);
ARC("G2(3).2","CAS",[rec(name:="g2f3b",
permchars:=(),
permclasses:=())]);
ARC("G2(3).2","maxes",["G2(3)","3^2.(3x3^(1+2)+):D8","L2(8):3x2",
"2^3.L3(2):2","L2(13).2","2^(1+4)+.(S3xS3)"]);
ARC("G2(3).2","tomfusion",rec(name:="G2(3).2",map:=[1,3,4,5,6,7,11,19,22,21,
24,34,45,46,46,55,58,2,12,20,23,23,56,56,61,99,100,100],text:=[
"fusion map is unique"
]));
ALF("G2(3).2","Fi22.2",[1,4,6,6,8,7,12,21,25,22,26,30,32,32,32,41,47,62,
67,74,78,78,95,95,97,101,101,101],[
"fusion map is unique"
]);
ALN("G2(3).2",["g2f3b"]);
MOT("G2(4)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[251596800,61440,3840,60480,180,1536,768,512,300,300,300,300,192,12,21,32,32,
20,20,20,20,48,48,48,13,13,15,15,15,15,21,21],
[,[1,1,1,4,5,2,2,2,10,9,12,11,4,5,15,6,8,12,11,10,9,13,13,13,26,25,28,27,30,
29,32,31],[1,2,3,1,1,6,7,8,10,9,12,11,2,3,15,16,17,19,18,21,20,6,7,7,25,26,10,
9,12,11,15,15],,[1,2,3,4,5,6,7,8,1,1,1,1,13,14,15,16,17,2,2,3,3,22,24,23,26,
25,4,4,5,5,31,32],,[1,2,3,4,5,6,7,8,10,9,12,11,13,14,1,16,17,19,18,21,20,22,
23,24,26,25,28,27,30,29,4,4],,,,,,[1,2,3,4,5,6,7,8,10,9,12,11,13,14,15,16,17,
19,18,21,20,22,23,24,1,1,28,27,30,29,32,31]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[65,1,5,20,
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[GALOIS,[4,2]],[350,30,10,35,5,6,2,-2,0,0,0,0,3,1,0,2,-2,0,0,0,0,3,-1,-1,-1,
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0,0],
[GALOIS,[11,2]],[819,51,-13,0,3,3,3,3,-3*E(5)-3*E(5)^4,-3*E(5)^2-3*E(5)^3,
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[GALOIS,[13,2]],[1300,20,20,85,-5,4,4,4,0,0,0,0,5,-1,-2,0,0,0,0,0,0,1,1,1,0,0,
0,0,0,0,1,1],[1365,85,21,-21,0,5,5,5,5,5,0,0,-5,0,0,1,1,0,0,1,1,-1,-1,-1,0,0,
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[GALOIS,[17,2]],[2925,45,-15,90,0,5,-7,-3,0,0,0,0,-6,0,-1,1,1,0,0,0,0,2,2,2,0,
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[(31,32),(25,26),(23,24),(23,24)(31,32),( 9,10)(11,12)(18,19)(20,21)(27,28)
(29,30)]);
ARC("G2(4)","CAS",[rec(name:="g2f4",
permchars:=(),
permclasses:=(),
text:=[
" maximal subgroup index\n",
"2^2+8:[a5xz3] 1365\n",
"2^4+6:[z3xa5] 1365\n",
"maximal subgroup of sporadic simple Suzuki group Suz,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly\n",
""])]);
ARC("G2(4)","projectives",["2.G2(4)",[[12,-4,0,-6,0,-4,0,0,2,2,-3,-3,2,0,-2,0,
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[GALOIS,[2,2]],[364,-36,0,-14,4,-4,0,0,4,4,-1,-1,-6,0,0,0,2,-1,-1,0,0,2,0,0,0,
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ARC("G2(4)","isSimple",true);
ARC("G2(4)","extInfo",["2","2"]);
ARC("G2(4)","maxes",["J2","2^(2+8):(3xA5)","2^(4+6):(A5x3)","U3(4).2",
"3.L3(4).2_3","U3(3).2","A5xA5","L2(13)"]);
ARC("G2(4)","tomfusion",rec(name:="G2(4)",map:=[1,2,3,4,5,15,16,17,19,19,18,
18,20,21,25,79,80,87,87,86,86,105,106,106,110,110,112,112,113,113,292,292],
text:=[
"fusion map is unique"
]));
ALF("G2(4)","G2(4).2",[1,2,3,4,5,6,7,8,9,9,10,10,11,12,13,14,15,16,16,17,
17,18,19,20,21,21,22,22,23,23,24,24],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("G2(4)","Suz",[1,2,3,4,6,7,9,8,12,12,11,11,13,17,18,19,20,24,24,25,25,
27,29,29,32,33,37,37,35,36,41,42],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("G2(4)","3D4(4)",[1,2,3,4,5,6,6,7,9,10,12,11,13,14,18,19,20,26,27,25,
24,28,28,28,35,36,44,43,45,46,68,69],[
"fusion map is unique up to table automorphisms"
]);
ALN("G2(4)",["g2f4"]);
MOT("G2(4).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: Aut(G2(4))"
],
[503193600,122880,7680,120960,360,3072,1536,1024,300,300,384,24,42,64,64,20,
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24],
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[TENSOR,[39,2]]],
[(36,37),(19,20)(39,40)]);
ARC("G2(4).2","CAS",[rec(name:="g2f4b",
permchars:=(17,18),
permclasses:=())]);
ARC("G2(4).2","projectives",["2.G2(4).2",[[12,-4,0,-6,0,-4,0,0,2,-3,2,0,-2,0,
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-E(7)^6,0,0,0,0,0],[11648,-128,0,56,-4,0,0,0,-2,-2,-8,0,0,0,0,2,0,0,0,0,0,1,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[7488,64,0,36,0,0,0,0,-2,3,4,0,-2,0,0,-1,
0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,2*E(3)-2*E(3)^2,0,0]],]);
ARC("G2(4).2","maxes",["G2(4)","J2.2","2^(2+8):(3xA5):2","2^(4+6):(A5x3):2",
"U3(4).4","3.L3(4).2^2","2xU3(3).2","(A5xA5):2","L2(13).2"]);
ALF("G2(4).2","Suz.2",[1,2,3,4,6,7,9,8,12,11,13,16,17,18,19,22,23,25,27,
27,30,33,32,36,38,40,41,42,44,47,50,49,54,56,57,58,58,61,64,64],[
"fusion map is unique"
]);
ALN("G2(4).2",["g2f4b"]);
MOT("G2(5)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[5859000000,14400,378000,720,480,480,375000,15000,3750,1875,1250,720,720,36,
21,24,24,600,600,50,50,24,24,750,75,75,75,30,20,20,21,21,24,24,24,24,25,30,30,
31,31,31,31,31],
[,[1,1,3,4,2,2,7,8,9,10,11,3,4,4,15,5,6,7,8,9,11,12,13,24,25,27,26,28,19,18,
32,31,22,22,23,23,37,24,28,41,42,43,44,40],[1,2,1,1,5,6,7,8,9,10,11,2,2,2,15,
16,17,18,19,20,21,5,6,7,9,10,10,8,29,30,15,15,16,16,17,17,37,18,19,44,40,41,
42,43],,[1,2,3,4,5,6,1,1,1,1,1,12,13,14,15,16,17,2,2,2,2,22,23,3,3,3,3,4,5,6,
31,32,33,34,35,36,7,12,13,40,41,42,43,44],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
1,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,3,3,34,33,36,35,37,38,39,42,43,
44,40,41],,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,32,31,34,33,36,35,37,38,39,1,1,1,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1],[124,4,-20,1,0,4,-1,4,9,-6,-1,4,1,1,-2,0,-2,-1,4,-1,-1,0,1,5,0,0,
0,1,0,-1,1,1,0,0,1,1,-1,-1,1,0,0,0,0,0],[280,-8,28,4,0,0,30,-10,0,-5,5,4,4,-2,
0,0,0,2,2,2,-3,0,0,3,3,-2,-2,-1,0,0,0,0,0,0,0,0,0,-1,-1,1,1,1,1,1],[651,11,21,
-3,-5,-5,26,26,1,1,1,5,5,-1,0,-1,-1,6,6,1,1,1,1,-4,1,1,1,2,0,0,0,0,-1,-1,-1,
-1,1,0,0,0,0,0,0,0],[930,18,48,0,6,6,55,15,0,-5,5,0,0,0,-1,0,0,3,3,-2,3,0,0,
-2,3,-2,-2,0,1,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],[960,0,-48,0,0,0,-40,0,-10,-5,
10,0,0,0,1,0,0,0,0,0,0,0,0,2,2,3*E(3)-2*E(3)^2,-2*E(3)+3*E(3)^2,0,0,0,1,1,0,0,
0,0,0,0,0,-1,-1,-1,-1,-1],
[GALOIS,[6,2]],[1085,5,77,-1,1,5,-40,5,0,-10,10,5,-1,-1,0,1,-1,0,5,0,0,1,-1,2,
-3,2,2,-1,1,0,0,0,1,1,-1,-1,0,0,-1,0,0,0,0,0],[1085,5,-49,5,5,1,85,0,-10,-5,
10,-1,5,-1,0,-1,1,5,0,0,0,-1,1,1,-4,1,1,0,0,1,0,0,-1,-1,1,1,0,-1,0,0,0,0,0,
0],[1240,-8,-20,4,0,0,-10,-10,15,15,-10,4,4,-2,1,0,0,2,2,-3,2,0,0,5,0,0,0,-1,
0,0,1,1,0,0,0,0,0,-1,-1,0,0,0,0,0],[1890,18,0,0,6,6,15,15,15,15,-10,0,0,0,0,0,
0,3,3,3,-2,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1],[2480,-16,104,
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0,0,-2,1,0,0,0,0,0],[2604,20,84,-3,0,4,-21,-16,14,-1,4,-4,5,-1,0,0,2,-5,0,0,0,
0,1,9,-1,-1,-1,2,0,-1,0,0,0,0,-1,-1,-1,1,0,0,0,0,0,0],[2604,-12,21,0,4,0,104,
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0,0,0],[2604,20,21,0,4,0,104,-21,4,4,4,5,8,2,0,2,0,0,-5,0,0,1,0,-4,1,1,1,0,-1,
0,0,0,-1,-1,0,0,-1,0,-2,0,0,0,0,0],[3255,31,-21,9,-1,-5,130,5,5,5,5,-5,1,1,0,
1,-1,6,1,1,1,-1,1,4,-1,-1,-1,-1,-1,0,0,0,1,1,-1,-1,0,0,1,0,0,0,0,0],[3255,31,
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1,1,0,1,0,0,0,0,0,0],[3906,-30,126,0,-2,6,31,36,16,1,6,6,0,0,0,0,0,-5,0,0,0,
-2,0,1,1,1,1,0,-2,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0],[3906,-30,0,6,6,-2,156,31,6,
6,6,0,6,0,0,0,0,0,-5,0,0,0,-2,0,0,0,0,1,1,-2,0,0,0,0,0,0,1,0,1,0,0,0,0,0],[
10416,-16,84,0,0,0,-84,36,-19,-4,-9,-4,8,2,0,0,0,4,4,-1,-1,0,0,9,-1,-1,-1,0,0,
0,0,0,0,0,0,0,1,1,-2,0,0,0,0,0],[12096,0,0,0,0,0,96,-24,6,-9,-4,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,E(31)+E(31)^5+E(31)^6+E(31)^25
+E(31)^26+E(31)^30,E(31)^2+E(31)^10+E(31)^12+E(31)^19+E(31)^21+E(31)^29,
E(31)^4+E(31)^7+E(31)^11+E(31)^20+E(31)^24+E(31)^27,E(31)^8+E(31)^9+E(31)^14
+E(31)^17+E(31)^22+E(31)^23,E(31)^3+E(31)^13+E(31)^15+E(31)^16+E(31)^18
+E(31)^28],
[GALOIS,[21,3]],
[GALOIS,[21,8]],
[GALOIS,[21,4]],
[GALOIS,[21,2]],[13020,4,-84,9,0,4,-105,20,-5,-5,-5,4,1,1,0,0,2,-1,4,-1,-1,0,
1,-9,1,1,1,-1,0,-1,0,0,0,0,-1,-1,0,-1,1,0,0,0,0,0],[13020,36,105,0,4,0,20,15,
-15,0,-5,9,0,0,0,-2,0,-4,-9,1,1,1,0,5,0,0,0,0,-1,0,0,0,1,1,0,0,0,-1,0,0,0,0,0,
0],[13020,4,105,0,4,0,20,15,-15,0,-5,1,-8,-2,0,2,0,4,-1,-1,-1,1,0,5,0,0,0,0,
-1,0,0,0,-1,-1,0,0,0,1,2,0,0,0,0,0],[15500,20,20,5,0,4,-125,0,0,0,0,-4,5,-1,2,
0,-2,-5,0,0,0,0,1,-5,0,0,0,0,0,-1,-1,-1,0,0,1,1,0,1,0,0,0,0,0,0],[15624,-24,
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0,0,0,-1,2,0,0,0,0,0,0],[15624,24,126,0,-8,0,124,-6,-11,4,-1,6,0,0,0,0,0,4,-6,
-1,-1,-2,0,1,1,1,1,0,2,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0],[15624,-24,126,0,0,0,
124,-6,-11,4,-1,-6,0,0,0,0,0,-4,6,1,1,0,0,1,1,1,1,0,0,0,0,0,
E(24)-E(24)^11-E(24)^17+E(24)^19,-E(24)+E(24)^11+E(24)^17-E(24)^19,0,0,-1,-1,
0,0,0,0,0,0],
[GALOIS,[32,7]],[15624,-24,0,-12,0,0,-126,4,9,-6,-1,0,12,0,0,0,0,6,-4,1,1,0,0,
0,0,0,0,-2,0,0,0,0,0,0,0,0,-1,0,2,0,0,0,0,0],[15624,24,0,6,0,-8,-126,4,9,-6,
-1,0,6,0,0,0,0,-6,4,-1,-1,0,-2,0,0,0,0,1,0,2,0,0,0,0,0,0,-1,0,1,0,0,0,0,0],[
15624,-24,0,6,0,0,-126,4,9,-6,-1,0,-6,0,0,0,0,6,-4,1,1,0,0,0,0,0,0,1,0,0,0,0,
0,0,E(24)-E(24)^11-E(24)^17+E(24)^19,-E(24)+E(24)^11+E(24)^17-E(24)^19,-1,0,
-1,0,0,0,0,0],
[GALOIS,[36,7]],[15625,25,-125,-5,5,5,0,0,0,0,0,-5,-5,1,1,-1,-1,0,0,0,0,-1,-1,
0,0,0,0,0,0,0,1,1,-1,-1,-1,-1,0,0,0,1,1,1,1,1],[16275,35,-105,-9,-1,-1,25,25,
0,0,0,-1,-1,-1,0,1,1,5,5,0,0,-1,-1,-5,0,0,0,1,-1,-1,0,0,1,1,1,1,0,-1,-1,0,0,0,
0,0],[17856,0,-288,0,0,0,-144,-24,-4,11,6,0,0,0,-1,0,0,0,0,0,0,0,0,12,2,2,2,0,
0,0,-1,-1,0,0,0,0,1,0,0,0,0,0,0,0],[17856,0,144,0,0,0,-144,-24,-4,11,6,0,0,0,
-1,0,0,0,0,0,0,0,0,-6,-1,-1,-1,0,0,0,E(21)^2+E(21)^8+E(21)^10+E(21)^11
+E(21)^13+E(21)^19,E(21)+E(21)^4+E(21)^5+E(21)^16+E(21)^17+E(21)^20,0,0,0,0,
1,0,0,0,0,0,0,0],
[GALOIS,[41,2]],[19530,-6,-126,0,-10,6,155,30,5,5,5,-6,0,0,0,0,0,-1,-6,-1,-1,
2,0,-1,-1,-1,-1,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0],[19530,-6,0,-6,6,-10,30,
35,15,0,5,0,-6,0,0,0,0,-6,-1,-1,-1,0,2,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,-1,0,0,
0,0,0]],
[(40,44,43,42,41),(35,36),(33,34),(33,34)(35,36),(31,32),(26,27),(26,27)
(31,32)(33,34)(35,36)]);
ARC("G2(5)","CAS",[rec(name:="g2f5",
permchars:=(),
permclasses:=())]);
ARC("G2(5)","isSimple",true);
ARC("G2(5)","extInfo",["",""]);
ARC("G2(5)","maxes",["5^(1+4):GL(2,5)","5^2.5.5^2.4S5","3.U3(5).2","L3(5).2",
"2.(A5xA5).2","U3(3).2","2^3.L3(2)"]);
ALF("G2(5)","Ly",[1,2,3,4,5,5,6,6,7,7,7,8,9,10,11,12,13,15,15,16,16,19,20,
22,24,24,24,23,26,26,28,27,31,31,32,33,34,36,37,39,40,41,42,38],[
"fusion is unique up to table automorphisms,\n",
"chosen representative is the unique one that is compatible with the\n",
"5-modular tables,\n",
"the representative differs from the fusion map on the CAS table"
]);
ALF("G2(5)","O7(5)",[1,4,6,7,9,11,12,15,17,17,18,28,23,29,30,31,32,39,45,
50,51,60,58,68,74,74,74,72,82,80,83,84,88,89,90,91,93,111,112,114,115,116,
117,118],[
"fusion map is unique up to table automorphisms"
]);
ALN("G2(5)",["g2f5"]);
MOT("G2(7)",
[
"computed using Magma V2.27-3 Tue Jun 4 2024 12:41:42 on schedir\n",
"[Seed = 2017523455]\n",
"Total time: 5.650 seconds, Total memory usage: 64.12MB"
],
[664376138496,112896,5630688,2016,2688,2688,2016,2016,36,5647152,115248,14406,
7203,4802,49,2688,2688,2688,2688,64,64,48,48,2352,2352,98,98,48,48,48,48,57,57
,57,2058,147,147,147,42,48,48,48,48,56,56,42,42,43,43,43,43,43,43,43,48,48,48,
48,48,48,48,48,56,56,56,56,57,57,57,57,57,57],
[,[1,1,3,4,2,2,3,4,4,10,11,12,13,14,15,6,6,5,5,6,5,7,8,10,11,14,12,19,18,16,17
,33,34,32,35,37,36,38,39,22,22,23,23,24,25,35,39,49,51,48,52,54,50,53,41,40,40
,41,42,43,43,42,44,44,45,45,68,69,67,71,72,70],[1,2,1,1,5,6,2,2,2,10,11,12,13,
14,15,17,16,19,18,20,21,6,5,24,25,26,27,29,28,31,30,33,34,32,10,13,13,12,11,16
,17,19,18,44,45,24,25,50,48,53,49,51,54,52,31,30,30,31,28,29,29,28,64,63,66,65
,32,33,34,33,34,32],,,,[1,2,3,4,5,6,7,8,9,1,1,1,1,1,1,16,17,18,19,20,21,22,23,
2,2,2,2,28,29,30,31,32,33,34,3,3,3,3,4,40,41,42,43,5,6,7,8,48,49,50,51,52,53,
54,55,56,57,58,59,60,61,62,19,18,16,17,67,68,69,70,71,72],,,,,,,,,,,,[1,2,3,4,
5,6,7,8,9,10,11,12,13,14,15,17,16,19,18,20,21,22,23,24,25,26,27,29,28,31,30,1,
1,1,35,36,37,38,39,41,40,43,42,44,45,46,47,51,52,49,54,53,48,50,57,55,58,56,61
,59,62,60,64,63,66,65,3,3,3,3,3,3],,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,17,16,19,18,20,21,22,23,24,25,26,27,29,28,31,30,33,34,32,35,
36,37,38,39,41,40,43,42,44,45,46,47,1,1,1,1,1,1,1,56,58,55,57,60,62,59,61,64,
63,66,65,68,69,67,71,72,70]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[344,8,56
,-1,8,0,8,-1,-1,1,8,15,-6,1,1,0,0,8,8,0,0,0,-1,1,8,1,1,2,2,0,0,2,2,2,7,0,0,0,-
1,0,0,-1,-1,1,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,0,0,-1,-1,-1,-1,-1,
-1],[1806,-18,96,0,6,6,0,0,0,91,-21,14,7,-7,0,6,6,6,6,-2,-2,0,0,3,3,3,-4,0,0,0
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,-1,1,1,1,1,1,1],[2451,-13,57,9,-5,-5,-7,-7,-1,50,50,1,1,1,1,7,7,7,7,-1,-1,1,1
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-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],[4256,32,152,8,0,0,8,8,2,140,28,14,7,-7,0,
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1,-1,-1],
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1],[14706,-30,342,0,-6,-14,6,0,0,-43,-36,20,-1,6,-1,2,2,6,6,2,-2,-2,0,5,12,-2,
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[GALOIS,[7,2]],[13832,0,-19,8,8,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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[GALOIS,[9,9]],
[GALOIS,[9,3]],
[GALOIS,[9,6]],
[GALOIS,[9,2]],
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[GALOIS,[16,2]],
[GALOIS,[16,3]],[18981,-27,27,0,0,0,0,-3,0,0,0,1,1,1,1,1,1,1,1,1,0,0,0,-1,-1,
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-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1],[19684,28,1,1,1,1,1,0,1,1,1,
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[GALOIS,[21,4]],
[GALOIS,[21,3]],
[GALOIS,[21,5]],
[GALOIS,[21,6]],
[GALOIS,[21,2]],[19684,-28,1,1,1,-1,-1,0,1,1,1,E(13)+E(13)^12,E(13)^3+E(13)^10
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[GALOIS,[27,4]],
[GALOIS,[27,3]],
[GALOIS,[27,5]],
[GALOIS,[27,6]],
[GALOIS,[27,2]],[26936,0,-37,-10,-10,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,
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[GALOIS,[33,4]],
[GALOIS,[33,2]]],
[(30,32,31)(33,35,34),(30,33)(31,34)(32,35),(30,35,31,33,32,34),(21,22,23),
(21,23,22),(18,19,20),(18,20,19),(12,16,14,15,13,17)(24,28,26,27,25,29),
( 4, 5)( 6, 7)(10,11)]);
ARC("R(27)","isSimple",true);
ARC("R(27)","extInfo",["","3"]);
ALF("R(27)","R(27).3",[1,2,3,4,5,6,7,8,9,10,11,12,12,12,13,13,13,14,14,14,
15,15,15,16,16,16,17,17,17,18,18,18,19,19,19],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALN("R(27)",["2G2(27)","R(27).3M1"]);
MOT("R(27).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: Aut(R(27))"
],
[30220333416,58968,59049,4374,4374,162,162,84,243,243,243,26,26,28,19,26,26,
37,37,4536,4536,72,72,81,81,54,54,54,54,18,18,18,18,21,21,27,27,27,27,27,27],
[,[1,1,3,5,4,5,4,8,9,11,10,13,12,8,15,13,12,19,18,21,20,21,20,25,24,27,26,29,
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1,9,10,11,13,12,2,15,17,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,20,
21,40,41,36,37,38,39],,,,,,[1,2,3,4,5,6,7,8,9,10,11,1,1,14,15,2,2,19,18,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,38,39,40,41,36,37],,,,,,[1,2,3,4,5,
6,7,8,9,10,11,13,12,14,1,17,16,19,18,20,21,22,23,24,25,26,27,28,29,30,31,32,
33,34,35,36,37,38,39,40,41],,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,13,12,
14,15,17,16,1,1,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,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,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,E(3),E(3)^2],
[TENSOR,[2,2]],[703,-1,-26,1,1,-1,-1,3,1,1,1,1,1,-1,0,-1,-1,0,0,7,7,-1,-1,-2,
-2,1,1,1,1,-1,-1,-1,-1,0,0,1,1,1,1,1,1],
[TENSOR,[4,2]],
[TENSOR,[4,3]],[741,13,12,6*E(3)-3*E(3)^2,-3*E(3)+6*E(3)^2,2*E(3)-E(3)^2,
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-2*E(3)-E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2,E(3),E(3)^2,1,1,-1,-1,0,0,0,0,0,0],
[TENSOR,[7,2]],
[TENSOR,[7,3]],
[GALOIS,[7,2]],
[TENSOR,[10,2]],
[TENSOR,[10,3]],[1443,-13,-15,6*E(3)-3*E(3)^2,-3*E(3)+6*E(3)^2,-2*E(3)+E(3)^2,
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[TENSOR,[13,2]],
[TENSOR,[13,3]],
[GALOIS,[13,2]],
[TENSOR,[16,2]],
[TENSOR,[16,3]],[2184,0,-3,12*E(3)-6*E(3)^2,-6*E(3)+12*E(3)^2,0,0,0,-3,
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-2*E(9)^4-E(9)^7],
[TENSOR,[19,2]],
[TENSOR,[19,3]],
[GALOIS,[19,8]],
[TENSOR,[22,2]],
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[GALOIS,[25,2]],[18278,78,53,-1,-1,-3,-3,1,-1,-1,-1,0,0,1,0,0,0,0,0,8,8,0,0,
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[TENSOR,[27,2]],
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[TENSOR,[31,2]],
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[TENSOR,[34,2]],
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(28,29)(30,31)(32,33)(34,35)(36,41,38,37,40,39),(36,40,38)(37,41,39)]);
MOT("Sz(32)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[32537600,1024,64,64,25,25,25,25,25,25,31,31,31,31,31,31,31,31,31,31,31,31,31,
31,31,41,41,41,41,41,41,41,41,41,41],
[,[1,1,2,2,5,8,9,10,6,7,12,13,14,15,11,17,18,19,20,16,22,23,24,25,21,27,28,29,
30,26,32,33,34,35,31],,,[1,2,3,4,1,5,5,5,5,5,16,17,18,19,20,21,22,23,24,25,11,
12,13,14,15,28,29,30,26,27,33,34,35,31,32],,,,,,,,,,,,,,,,,,,,,,,,,,[1,2,4,3,
5,7,8,9,10,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,29,30,26,27,28,34,35,31,32,
33],,,,,,,,,,[1,2,3,4,5,9,10,6,7,8,17,18,19,20,16,22,23,24,25,21,12,13,14,15,
11,1,1,1,1,1,1,1,1,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[124,
-4,4*E(4),-4*E(4),-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,
1,1,1,1],
[GALOIS,[2,3]],[775,7,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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-E(41)^16-E(41)^20-E(41)^21-E(41)^25,-E(41)^3-E(41)^14-E(41)^27-E(41)^38,
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-E(41)^11-E(41)^17-E(41)^24-E(41)^30,-E(41)^7-E(41)^19-E(41)^22-E(41)^34],
[GALOIS,[4,16]],
[GALOIS,[4,8]],
[GALOIS,[4,4]],
[GALOIS,[4,2]],
[GALOIS,[4,3]],
[GALOIS,[4,7]],
[GALOIS,[4,11]],
[GALOIS,[4,12]],
[GALOIS,[4,6]],[1024,0,0,0,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1],[1025,1,1,1,0,0,0,0,0,0,E(31)+E(31)^30,
E(31)^2+E(31)^29,E(31)^4+E(31)^27,E(31)^8+E(31)^23,E(31)^15+E(31)^16,
E(31)^5+E(31)^26,E(31)^10+E(31)^21,E(31)^11+E(31)^20,E(31)^9+E(31)^22,
E(31)^13+E(31)^18,E(31)^6+E(31)^25,E(31)^12+E(31)^19,E(31)^7+E(31)^24,
E(31)^14+E(31)^17,E(31)^3+E(31)^28,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[15,15]],
[GALOIS,[15,8]],
[GALOIS,[15,4]],
[GALOIS,[15,2]],
[GALOIS,[15,6]],
[GALOIS,[15,3]],
[GALOIS,[15,14]],
[GALOIS,[15,7]],
[GALOIS,[15,12]],
[GALOIS,[15,5]],
[GALOIS,[15,13]],
[GALOIS,[15,9]],
[GALOIS,[15,11]],
[GALOIS,[15,10]],[1271,-9,-1,-1,-4,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[1271,-9,-1,-1,1,E(25)^4+E(25)^6-E(25)^7+E(25)^9+E(25)^11
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-E(25)^19,E(25)^3+E(25)^7+E(25)^8-E(25)^11+E(25)^12+E(25)^13-E(25)^14
+E(25)^17+E(25)^18+E(25)^22,-E(25)^9-E(25)^12-E(25)^13-E(25)^16,
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0,0,0,0],
[GALOIS,[31,3]],
[GALOIS,[31,9]],
[GALOIS,[31,2]],
[GALOIS,[31,6]]],
[(26,30,29,28,27)(31,35,34,33,32),(26,31)(27,32)(28,33)(29,34)(30,35),
(26,32,28,34,30,31,27,33,29,35),(11,25,19,13,22,16,15,24,18,12,21,20,14,23,17
),( 6, 8,10, 7, 9),( 6,10, 9, 8, 7),(3,4),(11,15,14,13,12)(16,20,19,18,17)
(21,25,24,23,22),(11,21,16)(12,22,17)(13,23,18)(14,24,19)(15,25,20)]);
ARC("Sz(32)","maxes",["2^(5+5):31","41:4","25:4","D62"]);
ARC("Sz(32)","isSimple",true);
ARC("Sz(32)","extInfo",["","5"]);
ARC("Sz(32)","tomfusion",rec(name:="Sz(32)",map:=[1,2,8,8,9,68,68,68,68,68,69,
69,69,69,69,69,69,69,69,69,69,69,69,69,69,96,96,96,96,96,96,96,96,96,96],
text:=[
"fusion map is unique"
]));
ALF("Sz(32)","Sz(32).5",[1,2,3,4,5,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,9,9,9,9,
9,10,10,10,10,10,11,11,11,11,11],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
MOT("Sz(32).5",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: Aut(Sz(32))"
],
[162688000,5120,320,320,125,25,31,31,31,41,41,100,100,100,100,20,20,20,20,20,
20,20,20,20,20,20,20,25,25,25,25],
[,[1,1,2,2,5,6,7,8,9,10,11,13,15,12,14,13,15,12,14,17,19,16,18,17,19,16,18,29,
31,28,30],,,[1,2,3,4,1,5,8,9,7,10,11,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,
5],,,,,,,,,,,,,,,,,,,,,,,,,,[1,2,4,3,5,6,1,1,1,10,11,12,13,14,15,16,17,18,19,
24,25,26,27,20,21,22,23,28,29,30,31],,,,,,,,,,[1,2,3,4,5,6,8,9,7,1,1,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,
1,1,1,1,1,E(5),E(5)^2,E(5)^3,E(5)^4,E(5),E(5)^2,E(5)^3,E(5)^4,E(5),E(5)^2,
E(5)^3,E(5)^4,E(5),E(5)^2,E(5)^3,E(5)^4,E(5),E(5)^2,E(5)^3,E(5)^4],
[TENSOR,[2,2]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],[124,-4,4*E(4),-4*E(4),-1,-1,0,0,0,1,1,-1,-1,-1,-1,1,1,1,1,
-E(4),-E(4),-E(4),-E(4),E(4),E(4),E(4),E(4),-1,-1,-1,-1],
[TENSOR,[6,2]],
[TENSOR,[6,3]],
[TENSOR,[6,4]],
[TENSOR,[6,5]],
[GALOIS,[6,3]],
[TENSOR,[11,2]],
[TENSOR,[11,3]],
[TENSOR,[11,4]],
[TENSOR,[11,5]],[3875,35,-5,-5,0,0,0,0,0,-E(41)-E(41)^2-E(41)^4-E(41)^5
-E(41)^8-E(41)^9-E(41)^10-E(41)^16-E(41)^18-E(41)^20-E(41)^21-E(41)^23
-E(41)^25-E(41)^31-E(41)^32-E(41)^33-E(41)^36-E(41)^37-E(41)^39-E(41)^40,
-E(41)^3-E(41)^6-E(41)^7-E(41)^11-E(41)^12-E(41)^13-E(41)^14-E(41)^15-E(41)^17
-E(41)^19-E(41)^22-E(41)^24-E(41)^26-E(41)^27-E(41)^28-E(41)^29-E(41)^30
-E(41)^34-E(41)^35-E(41)^38,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[16,3]],[1024,0,0,0,-1,-1,1,1,1,-1,-1,4,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,
-1,-1,-1,-1],
[TENSOR,[18,2]],
[TENSOR,[18,3]],
[TENSOR,[18,4]],
[TENSOR,[18,5]],[5125,5,5,5,0,0,E(31)+E(31)^2+E(31)^4+E(31)^8+E(31)^15
+E(31)^16+E(31)^23+E(31)^27+E(31)^29+E(31)^30,E(31)^5+E(31)^9+E(31)^10
+E(31)^11+E(31)^13+E(31)^18+E(31)^20+E(31)^21+E(31)^22+E(31)^26,
E(31)^3+E(31)^6+E(31)^7+E(31)^12+E(31)^14+E(31)^17+E(31)^19+E(31)^24+E(31)^25
+E(31)^28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[23,3]],
[GALOIS,[23,5]],[1271,-9,-1,-1,-4,1,0,0,0,0,0,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,
-1,-1,-1,1,1,1,1],
[TENSOR,[26,2]],
[TENSOR,[26,3]],
[TENSOR,[26,4]],
[TENSOR,[26,5]],[6355,-45,-5,-5,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0]],
[(12,13,15,14)(16,17,19,18)(20,21,23,22)(24,25,27,26)(28,29,31,30),(10,11),
(7,9,8),( 3, 4)(20,24)(21,25)(22,26)(23,27),(12,14,15,13)(16,18,19,17)
(20,22,23,21)(24,26,27,25)(28,30,31,29)]);
MOT("Sz(8)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[29120,64,16,16,5,7,7,7,13,13,13],
[,[1,1,2,2,5,7,8,6,10,11,9],,,[1,2,3,4,1,7,8,6,9,10,11],,[1,2,4,3,5,1,1,1,11,
9,10],,,,,,[1,2,3,4,5,6,7,8,1,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1],[14,-2,2*E(4),-2*E(4),-1,0,0,0,1,1,1],
[GALOIS,[2,3]],[35,3,-1,-1,0,0,0,0,-E(13)-E(13)^5-E(13)^8-E(13)^12,
-E(13)^2-E(13)^3-E(13)^10-E(13)^11,-E(13)^4-E(13)^6-E(13)^7-E(13)^9],
[GALOIS,[4,4]],
[GALOIS,[4,2]],[64,0,0,0,-1,1,1,1,-1,-1,-1],[65,1,1,1,0,E(7)+E(7)^6,
E(7)^2+E(7)^5,E(7)^3+E(7)^4,0,0,0],
[GALOIS,[8,3]],
[GALOIS,[8,2]],[91,-5,-1,-1,1,0,0,0,0,0,0]],
[( 9,10,11),( 9,11,10),(6,8,7),(3,4)]);
ARC("Sz(8)","CAS",[rec(name:="sz8",
permchars:=(),
permclasses:=(),
text:=[
"names:=sz[8]\n",
" 2b2[8] [lie-not.]\n",
" order: 2^6.5.7.13 = 29,120\n",
" number of classes: 11\n",
" source:mckay, john\n",
" the non-abelian simple groups g,\n",
" ord[g]<10^6 - character tables\n",
" comm.algebra 7\n",
" [1979],1407-1445\n",
" comments: -\n",
""])]);
ARC("Sz(8)","projectives",["2.Sz(8)",[[40,0,0,0,0,-E(7)-E(7)^6,-E(7)^2-E(7)^5,
-E(7)^3-E(7)^4,1,1,1],
[GALOIS,[1,3]],
[GALOIS,[1,2]],[56,0,0,0,1,0,0,0,E(13)+E(13)^5+E(13)^8+E(13)^12,
E(13)^2+E(13)^3+E(13)^10+E(13)^11,E(13)^4+E(13)^6+E(13)^7+E(13)^9],
[GALOIS,[4,4]],
[GALOIS,[4,2]],[64,0,0,0,-1,1,1,1,-1,-1,-1],[104,0,0,0,-1,-1,-1,-1,0,0,0]],]);
ARC("Sz(8)","maxes",["2^(3+3):7","13:4","5:4","D14"]);
ARC("Sz(8)","isSimple",true);
ARC("Sz(8)","extInfo",["2^2","3"]);
ARC("Sz(8)","tomfusion",rec(name:="Sz(8)",map:=[1,2,3,3,5,6,6,6,12,12,12],
text:=[
"fusion map is unique"
]));
ALF("Sz(8)","Sz(8).3",[1,2,3,4,5,6,6,6,7,7,7]);
ALN("Sz(8)",["sz8"]);
MOT("Sz(8).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: Aut(Sz(8))"
],
[87360,192,48,48,15,7,13,60,60,12,12,12,12,12,12,15,15],
[,[1,1,2,2,5,6,7,9,8,9,8,11,10,11,10,17,16],[1,2,4,3,5,6,7,1,1,2,2,4,4,3,3,5,
5],,[1,2,3,4,1,6,7,9,8,11,10,13,12,15,14,9,8],,[1,2,4,3,5,1,7,8,9,10,11,14,15,
12,13,16,17],,,,,,[1,2,3,4,5,6,1,8,9,10,11,12,13,14,15,16,17]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,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],
[TENSOR,[2,2]],[14,-2,2*E(4),-2*E(4),-1,0,1,-1,-1,1,1,-E(4),-E(4),E(4),E(4),
-1,-1],
[TENSOR,[4,2]],
[TENSOR,[4,3]],
[GALOIS,[4,3]],
[TENSOR,[7,2]],
[TENSOR,[7,3]],[105,9,-3,-3,0,0,1,0,0,0,0,0,0,0,0,0,0],[64,0,0,0,-1,1,-1,4,4,
0,0,0,0,0,0,-1,-1],
[TENSOR,[11,2]],
[TENSOR,[11,3]],[195,3,3,3,0,-1,0,0,0,0,0,0,0,0,0,0,0],[91,-5,-1,-1,1,0,0,1,1,
1,1,-1,-1,-1,-1,1,1],
[TENSOR,[15,2]],
[TENSOR,[15,3]]],
[( 8, 9)(10,11)(12,13)(14,15)(16,17),( 3, 4)(12,14)(13,15)]);
ARC("Sz(8).3","maxes",["Sz(8)","2^(3+3):7:3","13:12","5:4x3","7:6"]);
ARC("Sz(8).3","tomfusion",rec(name:="Sz(8).3",map:=[1,2,3,3,5,6,10,21,
21,22,22,23,23,23,23,25,25],text:=[
"fusion map is unique"
],perm:=(1,2,3,4,5)));
LIBTABLE.LOADSTATUS.ctoatres:="userloaded";
#############################################################################
##
#E
