| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/ctbllib/data/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 1.2.2023 mit Größe 1 MB |
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Quelle ctomax10.tbl Sprache: unbekannt |
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Spracherkennung für: .tbl vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen] #############################################################################
## #W ctomax10.tbl GAP table library Thomas Breuer ## ## This file contains the ordinary character tables of some maximal ## subgroups of $Fi_{24}^{\prime}$ and $Fi_{24}$. ## #H ctbllib history #H --------------- #H $Log: ctomax10.tbl,v $ #H Revision 4.8 2012/01/30 08:31:45 gap #H removed #H entries from the headers #H TB #H #H Revision 4.7 2011/09/28 14:32:14 gap #H removed revision entry and SET_TABLEFILENAME call #H TB #H #H Revision 4.6 2010/11/15 16:35:30 gap #H added a comment to the fusion 3^7.O7(3):2 -> F3+.2 #H (finally resolved the ambiguity) #H TB #H #H Revision 4.5 2010/05/05 13:20:03 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 4.4 2009/04/30 16:21:42 gap #H added a missing table #H TB #H #H Revision 4.3 2009/04/22 12:39:03 gap #H added missing maxes of He.2, ON.2, HN.2, Fi24, and B #H TB #H #H Revision 4.2 2002/03/25 18:14:15 gap #H added the three missing tables of maxes of F3+ (computed by Alexander) #H TB #H #H Revision 4.1 2001/10/22 15:51:04 gap #H added two new tables (contributed by Faryad Ali) #H TB #H ## MOT("3^7.O7(3):2", [ "non-split extension of 3^7 by O7(3).2,\n", "origin: computed by Faryad Ali using Clifford matrices,\n", "maximal subgroup of F3+.2,\n", "tests: 1.o.r., pow[2,3,5,7,13]" ], [20056328248320,26529534720,27549901440,28570268160,78382080,39191040, 100776960,1119744,1399680,1259712,746496,124416,93312,62208,306110016,25509168 ,1417176,51018336,76527504,76527504,14171760,5668704,1417176,524880,68024448, 2125764,419904,2834352,2834352,472392,59049,52488,52488,52488,13122,13122, 78732,13122,13122,13122,26244,26244,39366,17280,8640,62208,10368,7776,5184, 2304,1152,10368,1728,1296,864,6480,1080,810,540,139968,69984,7776,23328,11664, 139968,69984,5832,10368,5184,46656,11664,11664,2592,46656,11664,11664,7776, 3888,23328,11664,11664,5832,1296,23328,5832,5832,3888,1944,23328,3888,2916, 1944,648,648,648,648,324,162,324,324,324,84,42,96,48,96,48,2916,1458,1944,8748 ,4374,4374,486,8748,8748,4374,81,81,81,240,120,120,60,864,432,7776,1944,1944, 1296,648,432,216,432,216,288,144,108,108,108,144,72,78,39,78,39,84,42,90,45, 108,324,324,324,216,108,120,60,17686356480,75582720,75582720,68024448,1866240, 933120,933120,466560,2799360,139968,93312,93312,207360,24192,373248,15552, 15552,11664,6912,1728,1728,3456,1728,1728,864,1889568,944784,944784,26244, 1889568,1889568,944784,629856,52488,11664,104976,157464,157464,629856,104976, 78732,52488,11664,58320,23328,5832,23328,23328,23328,11664,11664,11664,7776, 3888,3888,1944,2592,1296,7776,3888,1296,3888,1944,1944,972,2916,2916,2916,1458 ,1458,1458,324,162,972,486,324,324,192,576,144,144,240,720,180,180,360,180,180 ,90,2592,864,432,432,2592,324,1296,648,216,1296,648,216,864,216,216,432,432, 432,216,216,216,36,972,486,324,324,972,972,972,162,324,324,324,162,162,162,40, 24,26,26,28,28,30,36], [,[1,2,3,4,1,4,1,4,2,3,1,4,3,2,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30 ,31,32,33,34,35,36,37,38,39,40,41,42,43,7,9,11,12,13,14,11,12,7,9,10,8,56,57, 58,59,15,18,22,25,29,15,18,17,25,27,25,28,29,27,15,19,20,18,16,22,21,22,23,24, 22,23,21,22,23,25,29,26,28,34,30,33,32,34,36,42,41,37,102,103,46,49,50,51,108, 109,110,111,112,113,114,115,116,117,118,119,120,56,57,56,59,68,69,74,75,76,77, 78,70,71,79,80,74,77,94,95,96,79,83,145,146,143,144,102,103,149,150,110,116, 111,115,110,108,121,122,1,2,4,3,1,2,4,3,1,3,2,4,7,5,7,9,8,10,7,9,8,11,14,12,13 ,18,16,20,17,15,18,19,22,23,24,22,23,21,25,28,26,29,27,21,22,23,18,15,18,19,20 ,16,22,21,22,23,22,24,25,28,27,25,28,29,26,37,42,41,40,39,38,34,35,37,43,42,41 ,46,46,49,47,56,56,57,59,56,57,59,58,65,70,60,79,65,67,70,72,73,79,80,83,70,71 ,72,77,74,77,75,76,78,93,108,109,110,108,116,115,111,114,111,116,115,117,112, 113,121,125,145,143,147,147,149,155],[1,1,1,1,5,5,7,7,7,7,11,11,11,11,1,1,1,1, 1,1,1,1,1,3,1,1,3,1,1,3,3,3,1,1,3,3,3,3,3,3,1,3,3,44,44,46,46,46,46,50,50,52, 52,52,52,56,56,56,56,5,5,5,5,5,7,7,7,11,13,7,7,7,10,11,11,11,11,11,7,7,7,7,10, 11,11,11,11,11,11,11,11,11,5,13,11,13,11,13,13,11,13,102,102,104,104,106,106, 18,18,15,18,18,18,19,18,18,18,31,31,30,121,121,123,123,46,48,46,46,46,46,46,44 ,44,44,44,50,50,48,46,48,52,54,143,143,145,145,147,147,56,58,60,61,61,61,65,66 ,157,157,159,159,159,159,163,163,163,163,167,167,167,167,171,172,173,173,173, 173,177,177,177,180,180,180,180,159,159,159,159,159,159,159,159,159,162,159, 159,159,159,159,159,159,162,167,167,167,163,163,163,163,163,163,163,163,163, 163,167,168,167,167,168,163,163,163,163,162,162,159,162,162,162,167,168,168, 168,168,167,236,237,237,237,240,241,241,241,244,244,244,244,171,171,172,171, 173,173,173,173,176,173,173,176,177,177,177,180,180,180,180,180,180,172,184, 184,188,189,184,184,184,190,207,207,207,207,207,207,284,236,286,287,288,289, 240,248],,[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, 52,53,54,55,1,2,3,4,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78, 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 ,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,7,9,5,6, 125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,145, 146,143,144,147,148,21,24,151,152,153,154,155,156,44,45,159,160,161,162,163, 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, 221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239, 167,159,160,161,163,164,165,166,248,249,250,251,252,253,254,255,256,257,258, 259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277, 278,279,280,281,282,283,171,285,287,286,289,288,202,291],,[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, 88,89,90,91,92,93,94,95,96,97,98,99,100,101,1,4,104,105,106,107,108,109,110, 111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129, 130,131,132,133,134,135,136,137,138,139,140,141,142,145,146,143,144,5,6,149, 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, 226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244, 245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263, 264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282, 283,284,285,287,286,172,172,290,291],,,,,,[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 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5,6,7,30,4,7,31,6,7,29,32,31,8,8,32,33,29,31,33,30,7,33,32,10,41,9,42,39, 38,11,47,10,41,44,48,12,53,54,55,20,17,21,16,22,19,15,19,16,58,13,18,19, 59,22,22,16,17,21,18,15,18,19,61,14,20,17,21,22,16,20,22,21,23,60,23,58, 23,62,62,22,60,25,69,26,73,28,77,30,33,34,33,31,32,34,31,29,33,80,80,79, 35,83,36,84,40,88,43,43,38,39,42,41,48,48,44,49,45,89,46,88,48,90,50,91, 50,92,52,95,54,96,64,60,62,58,63,61,65,97,98,104,107,105,99,108,111,106, 99,109,108,112,101,103,100,120,124,122,101,125,130,102,126,131,127,105, 107,104,110,110,105,110,107,110,139,107,110,105,104,107,110,110,140,106, 111,113,106,113,109,113,108,111,112,109,111,113,112,143,108,112,144,108, 112,113,113,138,142,110,139,142,140,114,145,141,145,146,113,115,116,152, 154,119,118,161,163,119,162,164,165,129,125,132,130,128,128,121,128,167, 124,122,168,125,130,129,127,133,123,133,126,131,134,139,142,147,139,138, 140,142,147,146,141,144,146,144,145,149,153,157,156,159,160,165,170],[ "fusion determined up to table automorphisms using the subgroup 3^6:L4(3)\n", "in the intersection of 3^7.O7(3):2 and S3xO8+(3):S3" ]); ALF("3^7.O7(3):2","O7(3).2",[1,1,1,1,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,6,6, 6,6,7,7,7,7,7,8,8,8,8,9,9,9,10,10,10,10,10,10,10,11,11,12,12,12,12,13,13, 14,14,14,14,15,15,15,15,16,16,17,18,18,19,19,19,20,20,21,21,21,21,22,22, 22,22,22,23,23,23,23,23,24,24,24,24,24,25,25,25,25,26,27,27,27,28,28,29, 29,29,30,30,31,31,32,32,33,33,33,34,34,34,34,34,34,34,35,35,35,36,36,37, 37,38,38,39,39,39,39,39,40,40,41,41,42,42,43,43,43,44,44,45,45,46,46,47, 47,48,48,49,50,50,50,51,51,52,52,53,53,53,53,54,54,54,54,55,55,55,55,56, 57,58,58,58,58,59,59,59,60,60,60,60,61,61,61,61,61,61,61,62,62,62,62,62, 62,63,63,63,63,63,64,64,64,65,65,65,65,65,65,66,66,66,66,67,67,68,68,68, 69,69,69,69,70,70,70,70,70,70,71,71,72,72,72,72,73,74,74,74,75,76,76,76, 77,77,77,77,78,79,80,81,82,82,83,83,83,84,84,84,85,85,85,86,86,86,86,86, 86,87,88,88,88,88,89,89,89,89,90,90,90,90,90,90,91,92,93,94,95,96,97,98]); MOT("2^(3+12).(L3(2)xA6)", [ "origin: Computed by A. Hulpke, using Dixon's Algorithm" ], [1981808640,283115520,4718592,4718592,393216,294912,98304,491520,491520,147456 ,34560,245760,147456,24576,8192,7680,7680,6144,34560,2304,2304,2520,2520,2304, 688128,98304,8192,774144,12096,864,864,24576,24576,8192,8192,8192,6144,5376, 2048,2048,2048,2048,2048,2048,1024,512,512,512,256,128,6720,6720,110592,9216, 9216,2304,1728,1536,1536,864,864,288,288,192,192,144,48,768,512,256,256,256, 256,128,128,128,128,128,64,64,960,960,160,160,160,160,4608,4608,2304,768,288, 288,192,192,192,192,144,144,144,96,96,48,48,48,48,56,56,30,30,32,80,80,40,40, 40,40,63,63,63,63,288,288,72,72,48,48,28,28,30,30,35,35,35,35], [,[1,1,1,1,1,2,2,1,1,1,11,2,2,3,3,9,8,4,11,11,11,22,23,13,1,1,1,28,29,30,31,3, 3,2,3,3,4,25,5,5,5,4,5,3,4,5,9,8,26,27,52,51,28,28,28,28,29,28,28,30,31,30,30, 11,11,29,31,32,7,6,7,32,13,33,15,14,15,36,39,43,52,51,52,51,52,51,53,53,53,53, 57,57,54,55,20,20,60,61,61,59,58,21,60,64,64,22,23,109,108,69,82,81,84,83,86, 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11,10,11,11,12,12,16,13,16,16,23,13,16,22,23,19,20,18,21,23,23,28,27,26, 28,28,26,26,27,26,28,28,28,28,36,36,36,36,35,35,40,38,40,40,46,47,41,40, 42,48,43,46,47,40,41,49,50,49,49,52,52,56,56,57,68,68,68,68,67,67,69,69, 70,70,76,77,78,79,81,82,87,87,91,91,94,94,94,94],[ "fusion map is unique up to table automorphisms" ]); MOT("2^(6+8).(S3xA8)", [ "origin: Computed by A. Hulpke, using Dixon's Algorithm" ], [1981808640,70778880,56623104,5505024,786432,294912,294912,3870720,138240, 110592,5160960,737280,43008,138240,17280,6912,864,589824,589824,147456,49152, 32768,12288,147456,98304,49152,32768,18432,16384,12288,12288,12288,12288,6144, 6144,6144,4096,4096,4096,4096,3072,3072,2048,2048,2048,1024,1024,1024,768,768, 256,256,256,360,27648,13824,9216,9216,9216,9216,6912,6912,6912,5760,4608,3456, 1728,1536,1152,864,864,864,576,576,384,384,288,288,288,288,288,288,288,288,288 ,96,168,168,1536,768,768,768,256,256,256,256,256,256,256,256,128,128,128,128, 64,120,120,40,4608,1536,1152,1152,768,576,576,576,576,288,288,192,192,192,192, 144,144,144,96,96,96,96,96,48,48,48,48,48,48,56,56,28,28,180,90,90,45,45,32,21 ,21,96,96,48,48,48,28,28,60,30,30], [,[1,1,1,1,1,3,3,8,8,8,1,1,4,14,15,16,17,1,1,1,1,1,1,3,3,3,3,2,3,3,3,5,5,2,4,2 ,5,5,5,5,19,18,4,4,5,5,18,19,21,20,21,20,22,54,14,14,8,8,8,8,16,16,16,15,8,15, 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28,27,26,26,27,27,26,28,35,36,35,38,40,45,39,40,41,39,48,42,44,42,41,41, 40,40,49,43,50,40,41,48,42,48,49,49,49,49,50,50,52,52,52,52,54,56,56,55, 55,57,69,69,76,77,80,81,82,87,87,90,91,91],[ "fusion map is unique up to table automorphisms" ]); MOT("3^2.3^4.3^8.(A5x2A4).2", [ "origin: Computed by A. Hulpke, using Dixon's Algorithm" ], [13774950720,1721868840,153055008,76527504,76527504,51018336,6377292,4251528, 4251528,4251528,3188646,2125764,2125764,2125764,1062882,708588,472392,354294, 354294,236196,39366,26244,118098,59049,26244,19683,13122,13122,1259712,944784, 118098,104976,104976,39366,19683,13122,13122,1080,157464,69984,69984,34992, 17496,17496,17496,5832,2916,2916,2916,2916,2916,52488,52488,52488,6561,6561, 6561,4374,4374,4374,2187,2187,2187,486,486,135,324,233280,139968,69984,69984, 34992,23328,11664,11664,7776,2916,1458,1296,1296,1296,972,324,120,648,648,648, 38880,288,3888,1944,1944,1296,216,216,216,144,144,72,20,108,108,108,7085880, 3542940,1417176,1417176,708588,708588,708588,708588,354294,354294,354294, 236196,177147,118098,8748,4374,4374,4374,2187,29160,5832,5832,5832,5832,5832, 2916,2916,2916,2916,2916,2916,2916,2916,1944,1944,1944,1458,1458,1458,1458,972 ,972,972,972,324,162,162,162,13122,13122,13122,13122,8748,8748,6561,6561,6561, 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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,108,108,0,-54, -54,-162,0,-54,81,-108,27,54,0,0,0,0,0,0,0,0,-12,0,12,0,0,-12,6,0,0,-6,-6,0,0, 0,0,6,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]], [(275,276),(249,250)(271,272)(273,274),(237,238),(208,210),(205,206), (189,190)(191,192)(211,212),(187,188),( 64, 65)(261,262), (244,245)(246,247)(263,264)(265,266)(267,268)(269,270)(271,273)(272,274), ( 32, 33)( 36, 37)( 52, 53)( 55, 56)( 80, 81)( 85, 86)( 95, 96)(101,102) (120,121)(149,150)(153,154)(159,160)(165,167)(170,173)(171,175)(172,176) (177,185)(178,183)(179,184)(198,203)(201,202)(239,240)(241,242)(267,269) (268,270) ]); ALF("3^2.3^4.3^8.(A5x2A4).2","F3+",[1,5,7,4,5,6,4,4,5,6,7,5,7,6,6,7,6,7,7, 7,7,8,29,32,30,32,33,31,2,4,7,8,8,6,7,8,8,12,15,19,18,15,18,13,15,18,19, 15,18,19,19,31,31,29,31,31,32,31,29,33,33,31,32,34,34,55,62,3,3,20,14,17, 22,16,17,21,16,22,16,23,23,21,23,36,59,59,61,9,11,43,38,39,42,40,46,47,48, 50,45,68,96,95,97,6,5,4,7,7,7,7,5,6,7,7,6,7,7,7,7,8,8,8,14,16,22,13,18,19, 17,20,19,19,18,15,19,15,20,16,21,22,18,19,19,21,17,22,21,19,23,23,22,29, 29,29,33,30,31,32,32,32,33,33,31,30,33,31,33,33,30,31,33,32,31,32,33,32, 33,32,31,31,33,29,32,31,33,34,34,34,56,56,55,55,60,62,61,59,63,61,59,63, 63,63,61,64,65,66,62,85,84,86,91,91,3,10,17,14,20,17,16,16,22,22,21,17,22, 21,22,20,17,21,16,16,16,21,22,22,23,23,23,23,23,23,21,26,26,28,28,44,49, 49,49,41,44,49,63,59,61,59,63,61,65,66,76,76,77,77,78,78,79,79,81,82,81, 82,98,98],[ "fusion map is unique up to table automorphisms" ]); MOT("S3xO8+(3):S3", [ "4th maximal subgroup of Fi24" ], 0, 0, 0, [(45,46)(72,73)(120,121)(170,171)(197,198)(245,246)(295,296)(322,323)(370, 371)], ["ConstructDirectProduct",[["Dihedral",6],["O8+(3).S3"]]]); ALF("S3xO8+(3):S3","F3+.2",[1,2,3,5,6,4,5,7,6,7,9,10,9,12,15,17,18,13,21, 16,18,17,22,14,21,20,24,26,26,30,31,29,33,30,34,35,39,42,38,39,39,43,48, 41,50,50,51,55,53,61,59,65,4,7,16,22,29,33,33,31,40,38,43,60,62,58,67,74, 73,79,89,91,92,98,99,100,100,101,102,105,104,107,111,105,110,109,107,112, 106,113,110,108,111,113,116,115,118,119,122,120,122,124,125,123,131,124, 130,127,133,135,140,139,144,139,147,141,146,148,152,157,156,158,161,164, 168,4,13,16,4,5,6,7,6,7,7,38,41,40,53,13,16,15,18,17,21,19,22,21,22,20,22, 67,73,74,30,31,32,33,33,34,83,38,39,42,40,43,42,44,48,92,91,94,54,55,61, 59,97,8,8,23,23,31,29,32,33,46,46,46,58,60,62,68,75,75,79,88,93,93,104, 108,120,121,125,126,104,107,105,106,110,107,108,110,109,113,111,110,112, 113,113,152,153,161,162,120,124,121,122,130,126,127,128,129,133,131,172, 140,139,144,142,147,145,146,177,154,182,181,183,163,165,168,98,99,99,105, 107,104,105,110,107,110,102,101,102,118,109,106,112,108,111,108,112,109, 113,111,112,113,135,115,116,139,140,138,142,139,147,119,127,131,126,127, 123,133,130,125,156,157,136,163,161,143,144,149,104,110,108,113,138,142, 142,140,126,126,133,141,146,144,172,153,152,176,169,181,182,2,3,10,10,10, 11,15,13,18,14,15,19,17,18,21,17,20,19,16,21,22,26,26,35,36,44,41,44,48, 41,45,47,48,48,45,49,51,59,61,58,61,63,60,62,65,73,78,78,81,83,84,90],[ "fusion map is unique up to table automorphisms" ]); ALN("S3xO8+(3):S3",["F3+.2N3A"]); MOT("3^(1+10):(2xU5(2):2)", [ "7th maximal subgroup of Fi24" ], [9697565306880,4848782653440,2448880128,1147912560,255091680,76527504,40310784 ,8957952,113374080,113374080,113374080,17006112,8503056,5668704,5668704, 5668704,2834352,472392,314928,236196,236196,157464,104976,26244,124416,10368, 4608,1620,20155392,4478976,559872,373248,104976,69984,69984,69984,69984,46656, 46656,46656,34992,31104,31104,31104,23328,11664,7776,7776,7776,7776,7776,7776, 3888,3888,2916,1944,1944,1944,1944,1944,1296,192,944784,524880,419904,118098, 78732,52488,39366,26244,26244,26244,26244,13122,13122,13122,2916,2916,2916, 1944,1458,1458,1458,486,243,66,62208,20736,6912,5184,3888,2592,2592,2592,2304, 1944,1296,1296,1296,648,432,432,432,432,216,144,144,144,810,270,270,270,270,90 ,5184,2592,1296,1296,648,324,324,324,324,324,216,54,96,162,81,66,66,432,216,72 ,45,699840,5184,349920,34992,23328,17496,11664,7776,1944,972,648,324,324,1152, 1152,192,60,864,648,432,72,32,32,324,324,324,108,576,576,144,144,96,72,72,30, 36,6530347008,164229120,4478976,699840,93312,41472,13824,5184,3265173504, 82114560,7558272,4251528,2239488,1889568,839808,839808,839808,472392,466560, 466560,466560,209952,209952,209952,209952,209952,209952,209952,104976,93312, 58320,34992,23328,23328,23328,23328,23328,23328,23328,23328,23328,23328,23328, 17496,17496,17496,15552,15552,15552,11664,8748,8748,8748,5832,3888,3888,1944, 1944,1944,972,972,648,324,324,324,1152,1152,192,192,180,60,46656,20736,15552, 6912,5184,3888,1944,1728,1296,1296,1296,864,864,864,864,648,648,432,432,432, 432,432,432,432,432,216,108,72,32,32,34992,11664,11664,3888,2916,2916,2916, 2916,2916,2916,2916,1458,1458,1296,1296,972,486,486,324,324,324,324,324,324, 324,324,324,324,324,162,162,162,162,66,576,576,144,144,96,96,72,72,90,90,90,90 ,30,216,216,72,36,54,66,66], [,[1,2,3,4,5,6,1,1,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,8,7,8,28,2,2 ,3,3,4,5,14,16,15,9,11,10,6,9,11,10,12,13,16,14,15,16,14,15,17,19,20,18,22,19, 22,22,23,27,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84, 85,86,30,32,32,29,45,42,44,43,30,46,47,49,48,53,34,40,38,39,61,47,49,48,109, 110,111,112,113,114,65,65,64,63,68,70,78,77,79,71,80,84,95,128,129,130,131,115 ,118,117,135,1,7,5,6,3,4,6,5,12,21,19,24,23,25,25,25,28,31,33,34,54,62,62,73, 72,67,80,89,89,91,91,88,105,105,110,119,1,1,1,1,7,8,8,7,2,2,3,4,2,5,11,10,9,6, 11,9,10,12,16,15,14,15,16,14,13,3,4,4,5,16,14,15,12,5,3,5,16,14,15,19,22,22,11 ,10,9,13,18,21,20,6,19,19,22,12,22,17,20,19,24,21,24,25,25,25,27,28,28,29,30, 31,30,31,34,33,32,39,40,38,31,44,43,42,41,41,34,45,48,47,49,48,47,49,46,56,54, 62,62,63,64,65,63,67,73,72,70,68,71,71,75,76,64,65,67,69,66,68,72,73,80,70,79, 78,77,79,77,78,82,83,81,74,86,88,88,91,91,89,95,100,100,109,111,112,113,114, 117,116,118,125,128,131,130],[1,1,1,1,1,1,7,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 25,26,27,28,7,8,7,8,7,7,8,8,8,7,7,7,7,8,8,8,8,8,8,8,8,7,7,7,8,7,8,7,8,8,8,7,8, 62,2,2,2,2,4,4,4,2,4,4,4,4,4,4,14,14,14,6,14,14,14,16,16,86,25,25,25,26,25,25, 25,25,27,25,25,25,25,25,26,26,26,26,25,27,27,27,28,28,28,28,28,28,30,29,29,30, 33,30,35,35,35,33,41,36,62,63,66,86,86,87,87,90,109,136,137,136,136,136,136, 136,136,136,136,136,136,136,149,150,151,152,137,137,137,137,157,158,141,141, 141,139,149,150,149,150,151,149,150,152,154,172,173,174,175,176,177,178,179, 172,173,172,172,174,172,172,172,172,172,173,173,173,172,172,172,172,172,172, 172,172,174,175,175,174,173,173,173,173,175,175,175,174,174,174,172,172,172, 174,174,174,173,172,172,172,175,173,174,173,175,174,175,174,175,175,175,174, 237,238,239,240,241,242,176,177,176,178,176,176,176,177,176,176,176,179,178, 178,178,179,176,179,178,178,178,178,177,177,177,178,176,179,271,272,180,180, 180,184,183,183,183,180,183,183,183,183,183,184,184,203,203,184,203,203,203, 189,184,196,196,196,206,206,206,206,206,206,203,306,237,238,237,238,239,240, 237,238,241,241,241,241,242,243,243,244,258,273,306,306],,[1,2,3,4,5,6,7,8,9, 10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,1,29,30,31,32,33,34,35, 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, 88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,2,5,11 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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, 74,75,76,77,78,79,80,81,82,83,84,85,1,87,88,89,90,91,92,93,94,95,96,97,98,99, 100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118, 119,120,121,122,123,124,125,126,127,128,129,2,2,132,133,134,135,136,137,138, 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, 234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252, 253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271, 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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, 0,0,0,2,0,0,27,-9,0,-9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,-1, 0,0,0,0,0,0,0,0,0,0,0,0, -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)^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 ], [GALOIS,[323,5]], [TENSOR,[324,2]], [TENSOR,[323,2]]], [(130,131)(325,326), (149,150)(157,158)(163,164)(165,166)(168,169)(237,238)(271,272)(307,308) (309,310)(313,314) ]); ALF("3^(1+10):(2xU5(2):2)","F3+.2",[1,5,4,5,6,7,2,3,5,4,6,4,7,5,6,7,6,7,6, 7,7,7,8,8,9,10,11,12,15,17,13,16,15,18,17,20,14,15,18,13,19,17,21,16,16, 22,22,17,21,19,15,18,21,18,22,19,22,21,20,19,23,27,29,30,31,32,29,30,32, 33,30,31,33,32,31,33,33,31,29,34,32,33,31,34,34,37,39,38,40,44,38,39,38, 42,45,43,43,42,39,42,48,41,44,48,46,49,47,45,54,55,55,53,54,54,58,59,61, 60,61,62,58,62,60,61,63,64,76,79,80,85,86,88,89,90,96,3,10,14,20,16,17,22, 21,16,22,21,23,23,26,26,26,36,41,44,48,48,56,56,62,58,60,64,74,74,73,73, 73,75,75,84,90,98,99,99,99,100,102,102,101,105,106,104,105,109,107,107, 104,105,110,111,106,108,104,110,107,105,107,110,105,110,108,106,109,112, 113,109,111,108,112,108,111,113,106,111,107,110,110,112,108,109,113,110, 110,110,113,112,111,113,108,113,112,113,112,114,113,114,116,116,115,117, 119,119,122,123,120,127,121,124,122,126,124,120,122,125,126,131,127,129, 128,130,126,123,133,131,127,133,131,133,128,130,137,137,138,139,140,141, 138,142,140,142,139,139,139,140,142,143,144,141,145,145,143,144,146,147, 146,138,140,142,141,146,144,146,144,145,145,150,152,152,152,152,153,155, 154,154,165,164,162,165,165,168,167,169,170,176,179,178],[ "fusion map is unique up to table automorphisms" ]); MOT("2^2.U6(2):S3x2", [ "9th maximal subgroup of Fi24\n", "(the subgroup is really a direct product, the ATLAS does not state this)" ], 0, 0, 0, [(146,147)(295,296),(140,141)(289,290),(96,97)(245,246),(99,248)(100,249)(101, 250)(102,251)(103,252)(104,253)(105,254)(106,255)(107,256)(108,257)(109,258) (110,259)(111,260)(112,261)(113,262)(114,263)(115,264)(116,265)(117,266)(118, 267)(119,268)(120,269)(121,270)(122,271)(123,272)(124,273)(125,274)(126,275) (127,276)(128,277)(129,278)(130,279)(131,280)(132,281)(133,282)(134,283)(135, 284)(136,285)(137,286)(138,287)(139,288)(140,289)(141,290)(142,291)(143,292) (144,293)(145,294)(146,295)(147,296)(148,297)(149,298)], ["ConstructDirectProduct",[["Cyclic",2],["2^2.U6(2).3.2"]]]); ALF("2^2.U6(2):S3x2","F3+.2",[1,2,3,2,2,3,3,4,13,5,15,6,18,9,11,9,11,10, 10,10,12,35,17,15,16,13,15,17,13,16,21,18,18,21,14,21,24,51,27,26,26,31, 59,30,61,36,35,37,70,39,38,40,45,39,45,41,41,53,83,58,59,5,6,7,8,17,14,15, 21,20,18,18,22,21,19,23,29,32,33,39,45,42,44,47,43,48,49,48,55,54,60,62, 68,76,84,85,86,89,2,10,3,10,10,9,10,9,10,11,13,41,15,44,16,41,18,48,21,48, 26,26,27,26,26,35,65,36,65,41,38,44,39,41,40,48,42,48,47,51,81,56,56,61, 90,73,74,76,76,83,97,99,98,98,99,99,99,99,108,104,109,105,112,107,102,102, 102,102,100,101,101,119,118,105,109,104,108,106,109,108,108,107,112,111, 112,112,111,136,135,117,115,116,144,140,143,139,118,119,150,151,123,126, 126,127,127,123,120,125,162,161,140,144,106,111,113,114,105,107,109,107, 110,111,112,110,112,113,114,141,145,146,127,123,131,122,131,133,124,133, 130,164,165,138,142,173,155,163,178,179,169,99,100,99,101,100,102,101,102, 101,102,108,120,109,122,108,125,112,124,112,130,116,115,117,116,115,119, 148,119,149,120,126,122,127,125,126,124,131,130,131,136,158,137,137,143, 168,152,153,155,155,162,177],[ "fusion map is unique up to table automorphisms" ]); MOT("2^(1+12)_+.3_1.U4(3).2^2_{122}", [ "10th maximal subgroup of Fi24" ], [321052999680,321052999680,424673280,94371840,79626240,39191040,39191040, 7077888,7077888,393216,589824,98304,36864,32768,13824,13824,139968,139968, 4478976,4478976,82944,62208,5971968,5971968,55296,36864,248832,27648,46656, 46656,7776,124416,124416,6912,10368,10368,10368,576,864,36864,36864,2048,3072, 1152,1152,3072,1024,512,512,96,1920,1920,320,160,160,60,60,1728,1728,13824, 13824,2304,576,13824,13824,1152,768,1728,1728,288,13824,13824,768,1152,1728, 1728,288,84,84,42,42,384,128,48,1296,1296,216,324,324,5184,5184,288,432,108, 108,288,288,576,576,96,637009920,637009920,2359296,2654208,2654208,491520, 311040,311040,442368,24576,24576,16384,3456,18432,2048,3072,576,73728,73728, 6144,4096,3072,1024,576,576,7776,7776,497664,497664,9216,6912,124416,124416, 20736,5184,10368,10368,1728,20736,20736,1152,1728,82944,82944,4608,13824,6912, 2304,1536,2592,2592,432,1152,1152,192,144,48,384,128,48,480,480,80,60,60,144, 576,576,96,576,576,96,288,288,48,432,432,72,108,108,432,432,72,1548288,24576, 184320,368640,368640,12288,12288,15360,9216,73728,73728,12288,3072,4096,4096, 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2026-05-26