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SSL ctomisc7.tbl Sprache: unbekannt |
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Spracherkennung für: .tbl vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen] #############################################################################
## #W ctomisc7.tbl GAP table library Thomas Breuer ## ## This file contains the ordinary character tables of some ## solvable subgroups of maximal order in sporadic simple groups. ## #H ctbllib history #H --------------- #H $Log: ctomisc7.tbl,v $ #H Revision 1.8 2012/06/20 14:45:32 gap #H added tables and fusions, as documented in ctbldiff.dat #H TB #H #H Revision 1.7 2012/04/23 16:16:15 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 1.6 2012/01/30 08:31:58 gap #H removed #H entries from the headers #H TB #H #H Revision 1.5 2011/09/28 13:28:47 gap #H - removed revision entry and SET_TABLEFILENAME call, #H - added fusions 2^6:3^(1+2).D8 -> 3^(1+2):D8, 2^6:3^(1+2).D8 -> M24, #H 2^6:3^(1+2).D8 -> He #H TB #H #H Revision 1.4 2010/05/05 13:20:07 gap #H - added many class fusions, #H - changed several class fusions according to consistency conditions, #H after systematic checks of consistency #H - with Brauer tables w.r.t. the restriction of characters, #H - of subgroup fusions with the corresponding subgroup fusions between #H proper factors where the factor fusions are stored, #H - of subgroup fusions from maximal subgroups with subgroup fusions of #H extensions inside automorphic extensions #H #H TB #H #H Revision 1.3 2009/05/11 15:37:12 gap #H added some missing `tomfusion' mappings #H TB #H #H Revision 1.2 2009/04/22 12:39:06 gap #H added missing maxes of He.2, ON.2, HN.2, Fi24, and B #H TB #H #H Revision 1.1 2008/11/14 17:27:18 gap #H some tables #H TB #H ## MOT("2^4:3^2:4", [ "origin: Dixon's Algorithm,\n", "solvable subgroup of maximal order in M22" ], [576,96,64,36,9,12,16,16,8,8,8,8,8], [,[1,1,1,4,5,4,1,3,2,7,8,7,8],[1,2,3,1,1,2,7,8,9,12,13,10,11]], [[1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,-1,-1,-1,E(4),E(4),-E(4),-E(4)], [TENSOR,[2,2]], [TENSOR,[2,3]],[4,4,4,-2,1,-2,0,0,0,0,0,0,0],[6,2,-2,3,0,-1,-2,2,0,0,0,0,0],[ 4,4,4,1,-2,1,0,0,0,0,0,0,0], [TENSOR,[6,2]],[12,4,-4,-3,0,1,0,0,0,0,0,0,0],[9,-3,1,0,0,0,1,1,-1,1,-1,1,-1] , [TENSOR,[10,2]], [TENSOR,[10,3]], [TENSOR,[10,4]]], [(10,12)(11,13)]); ALF("2^4:3^2:4","2^4:a6",[1,2,2,6,8,7,3,4,5,9,10,9,10],[ "fusion map is unique" ]); ALF("2^4:3^2:4","M22",[1,2,2,3,3,7,2,4,5,4,10,4,10],[ "fusion map uniquely determined by Brauer tables" ]); MOT("2^6:3^(1+2).D8", [ "origin: Dixon's Algorithm,\n", "solvable subgroup of maximal order in M24 and He" ], [13824,768,768,512,108,72,24,72,24,384,128,64,64,12,48,16,12,12,96,96,32,32,12 ,12,96,96,32,32,12,12], [,[1,1,1,1,5,6,6,8,8,1,1,4,4,5,10,11,14,14,1,2,2,4,6,7,1,3,3,4,8,9],[1,2,3,4,1 ,1,2,1,3,10,11,12,13,10,15,16,15,15,19,20,21,22,19,20,25,26,27,28,25,26]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1, 1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1], [TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0],[4,4,4,4,4,1,1,-2,-2,0,0,0,0,0,0,0,0,0,2,2,2,2,-1,-1,0,0,0,0,0,0], [TENSOR,[6,2]],[4,4,4,4,4,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,-1, -1], [TENSOR,[8,2]],[6,6,6,6,-3,0,0,0,0,-2,-2,-2,-2,1,2,2,-1,-1,0,0,0,0,0,0,0,0,0, 0,0,0], [TENSOR,[10,3]],[6,6,6,6,-3,0,0,0,0,2,2,2,2,-1,0,0,-E(12)^7+E(12)^11, E(12)^7-E(12)^11,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[12,3]],[18,2,-6,2,0,3,-1,0,0,6,-2,2,-2,0,0,0,0,0,4,-4,0,0,1,-1,0,0,0 ,0,0,0], [TENSOR,[14,2]],[18,2,-6,2,0,3,-1,0,0,-6,2,-2,2,0,0,0,0,0,2,-2,2,-2,-1,1,0,0, 0,0,0,0], [TENSOR,[16,2]],[18,-6,2,2,0,0,0,3,-1,6,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,4,-4,0, 0,1,-1], [TENSOR,[18,2]],[18,-6,2,2,0,0,0,3,-1,-6,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,2,-2,2, -2,-1,1], [TENSOR,[20,2]],[27,3,3,-5,0,0,0,0,0,3,3,-1,-1,0,3,-1,0,0,3,3,-1,-1,0,0,3,3, -1,-1,0,0], [TENSOR,[22,2]], [TENSOR,[22,3]], [TENSOR,[22,4]],[36,4,-12,4,0,-3,1,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,2,-1,1,0,0,0 ,0,0,0], [TENSOR,[26,2]],[36,-12,4,4,0,0,0,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2, 2,-1,1], [TENSOR,[28,2]],[54,6,6,-10,0,0,0,0,0,-6,-6,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,0,0]], [(17,18), ( 2, 3)( 6, 8)( 7, 9)(12,13)(19,25)(20,26)(21,27)(22,28)(23,29)(24,30)]); ALF("2^6:3^(1+2).D8","3^(1+2):D8",[1,1,1,1,5,6,6,7,7,2,2,2,2,9,8,8,12,13, 3,3,3,3,10,10,4,4,4,4,11,11]); ALF("2^6:3^(1+2).D8","M24",[1,2,3,2,4,4,10,5,11,2,3,7,6,10,6,8,17,17,2,6, 7,7,10,17,3,8,8,6,11,18],[ "fusion map is unique up to table automorphisms" ]); ALF("2^6:3^(1+2).D8","He",[1,2,3,3,4,4,10,5,11,2,3,7,8,10,6,8,19,19,2,6,6, 7,10,19,3,7,8,8,11,20],[ "fusion map is unique up to table automorphisms" ]); MOT("3^(1+4):4S4", [ "origin: Dixon's Algorithm,\n", "solvable subgroup of maximal order in McL.2" ], [23328,11664,243,162,288,144,48,144,48,18,24,324,162,36,18,27,27,12,12,24,8,24 ,8,12,24,24], [,[1,2,3,4,1,2,5,1,5,4,6,12,13,12,13,17,16,14,14,5,5,9,9,6,11,11],[1,1,1,1,5,5 ,7,8,9,8,9,1,1,5,5,2,2,7,7,20,21,22,23,20,22,22]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1],[2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1 ,-1,-1,0,0,0,0,0,0,0],[3,3,3,3,3,3,3,-1,-1,-1,-1,0,0,0,0,0,0,0,0,-1,-1,1,1,-1, 1,1], [TENSOR,[4,2]],[1,1,1,1,1,1,-1,-1,1,-1,1,1,1,1,1,1,1,-1,-1,1,-1,1,-1,1,1,1], [TENSOR,[2,6]], [TENSOR,[3,6]], [TENSOR,[4,7]], [TENSOR,[4,6]],[4,4,4,4,-4,-4,0,0,0,0,0,-2,-2,2,2,-2,-2,0,0,0,0,0,0,0,0,0],[4 ,4,4,4,-4,-4,0,0,0,0,0,1,1,-1,-1,1,1,-E(12)^7+E(12)^11,E(12)^7-E(12)^11,0,0,0, 0,0,0,0], [TENSOR,[12,6]],[32,32,5,-4,0,0,0,0,0,0,0,8,8,0,0,-1,-1,0,0,0,0,0,0,0,0,0],[ 32,32,5,-4,0,0,0,0,0,0,0,-4,-4,0,0,-2*E(3)+E(3)^2,E(3)-2*E(3)^2,0,0,0,0,0,0,0, 0,0], [GALOIS,[15,2]],[48,48,-6,3,0,0,0,-8,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[17,6]],[18,-9,0,0,2,-1,0,0,2,0,-1,-6,3,2,-1,0,0,0,0,-2,0,2,0,1,-1,-1 ], [TENSOR,[19,2]],[36,-18,0,0,4,-2,0,0,4,0,-2,6,-3,-2,1,0,0,0,0,0,0,0,0,0,0,0], [36,-18,0,0,-4,2,0,0,0,0,0,6,-3,2,-1,0,0,0,0,0,0,0,0,0, E(24)+E(24)^11-E(24)^17-E(24)^19,-E(24)-E(24)^11+E(24)^17+E(24)^19], [TENSOR,[22,2]],[54,-27,0,0,6,-3,0,0,-2,0,1,0,0,0,0,0,0,0,0,-2,0,-2,0,1,1,1], [TENSOR,[24,2]],[72,-36,0,0,-8,4,0,0,0,0,0,-6,3,-2,1,0,0,0,0,0,0,0,0,0,0,0]], [(25,26),(18,19),(16,17)]); ARC("3^(1+4):4S4","tomfusion",rec(name:="3^(1+4)+.(2S4x2)",map:=[1,4,6,7, 2,15,9,3,10,20,44,5,8,16,18,41,41,49,49,11,13,23,28,46,78,78],text:=[ "fusion map is unique" ])); ALF("3^(1+4):4S4","U4(3).2_3",[1,3,4,5,2,9,17,16,6,18,15,3,4,9,10,13,14, 23,23,17,7,19,12,23,24,25],[ "fusion map is unique up to table automorphisms" ]); ALF("3^(1+4):4S4","McL.2",[1,3,4,4,2,8,21,20,5,22,16,3,4,8,9,12,12,26,26, 21,5,23,11,26,32,33],[ "fusion map is unique up to table aut." ]); MOT("2^(4+4).(S3xS3).2", [ "origin: Dixon's Algorithm,\n", "maximal subgroup in He.2,\n", "solvable subgroup of maximal order in He.2" ], [18432,3072,2048,768,256,256,256,72,72,24,24,128,128,64,32,32,32,16,16,16,16, 384,128,128,128,96,64,32,12,12,96,96,12,64,64,32,12], [,[1,1,1,1,1,3,3,8,9,8,9,1,3,2,4,5,6,12,13,17,17,1,1,3,3,4,3,5,8,10,1,2,9,7,7, 7,11],[1,2,3,4,5,6,7,1,1,4,2,12,13,14,15,16,17,18,19,21,20,22,23,24,25,26,27, 28,22,26,31,32,31,35,34,36,32]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[ 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, -1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1, -1,-1,-1,-1,-1,-1,-1], [TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0 ,0,0,0,0,0,0,0,0,0],[4,4,4,4,4,4,4,1,-2,1,-2,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,2,2 ,-1,-1,0,0,0,0,0,0,0], [TENSOR,[6,2]],[4,4,4,4,4,4,4,-2,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,2,2,-1,2,2,2,-1], [TENSOR,[8,2]],[6,6,6,2,2,-2,-2,3,0,-1,0,2,2,2,0,0,-2,0,0,0,0,4,0,4,0,2,0,-2, 1,-1,0,0,0,0,0,0,0], [TENSOR,[10,2]],[6,6,6,2,2,-2,-2,3,0,-1,0,-2,-2,-2,0,0,2,0,0,0,0,2,-2,2,-2,4, -2,0,-1,1,0,0,0,0,0,0,0], [TENSOR,[12,2]],[9,9,9,-3,-3,1,1,0,0,0,0,1,1,1,-1,-1,1,1,1,-1,-1,-3,1,-3,1,3, 1,-1,0,0,-3,-3,0,1,1,1,0], [TENSOR,[14,2]], [TENSOR,[14,3]], [TENSOR,[14,4]],[12,12,12,4,4,-4,-4,-3,0,1,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,-2,2 ,-2,-1,1,0,0,0,0,0,0,0], [TENSOR,[18,2]],[18,18,18,-6,-6,2,2,0,0,0,0,-2,-2,-2,2,2,-2,0,0,0,0,0,0,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0],[18,-6,2,6,-2,-2,2,0,0,0,0,2,2,-2,0,0,0,0,0, E(8)-E(8)^3,-E(8)+E(8)^3,6,2,-2,2,0,-2,0,0,0,0,0,0,2*E(8)-2*E(8)^3, -2*E(8)+2*E(8)^3,0,0], [TENSOR,[21,3]], [TENSOR,[21,2]], [TENSOR,[21,4]],[24,8,-8,0,0,0,0,0,3,0,-1,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,2,-2,-1,2,2,-2,1], [TENSOR,[25,2]],[24,8,-8,0,0,0,0,0,3,0,-1,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,2,-2,-1,-2,-2,2,1], [TENSOR,[27,2]],[36,-12,4,12,-4,-4,4,0,0,0,0,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0],[36,-12,4,-12,4,-4,4,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[30,3]],[36,-12,4,0,0,4,-4,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,6,2,-2,-6,0,2 ,0,0,0,0,0,0,0,0,0,0], [TENSOR,[32,2]],[36,-12,4,0,0,4,-4,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,6,-6,-2,2,0,2 ,0,0,0,0,0,0,0,0,0,0], [TENSOR,[34,2]],[48,16,-16,0,0,0,0,0,-3,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,0,0,4,-4,1,0,0,0,-1], [TENSOR,[36,2]]], [(20,21)(34,35)]); ALF("2^(4+4).(S3xS3).2","He.2",[1,2,3,2,3,8,7,4,4,10,10,2,7,6,6,7,15,28, 34,38,39,2,3,7,7,6,8,8,10,17,27,28,30,33,32,34,36],[ "fusion map is unique up to table automorphisms" ]); MOT("2.2^(2+2).2^(1+1+2+2):S4", [ "origin: Dixon's Algorithm,\n", "one type of solvable subgroups of maximal order in Ru" ], [49152,49152,8192,2048,1536,768,1024,1024,512,512,512,64,64,512,256,256,512, 512,512,256,256,256,256,256,256,128,128,128,32,32,24,24,12,12,12,128,128,64,64 ,64,64,64,32,32,32,32,32,32,32,16,16,16], [,[1,1,1,1,2,2,1,2,3,3,3,7,8,1,1,1,2,3,3,2,3,3,3,3,3,4,4,4,9,10,31,31,32,32,32 ,1,3,4,7,7,14,14,15,15,5,11,19,17,18,28,13,13],[1,2,3,4,5,6,7,8,9,10,11,12,13, 14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,1,2,5,6,6,36,37,38,39,40,41 ,42,43,44,45,46,47,48,49,50,52,51]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2,2 ,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1, -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,1,1,1,1, -1,-1], [TENSOR,[4,2]],[3,3,3,3,3,3,3,3,3,3,3,-1,-1,3,-1,3,3,3,3,-1,3,3,3,3,3,-1,-1, -1,-1,-1,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,1,1,1], [TENSOR,[6,2]],[3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,3,-1,-1,-1,-1,3,-1,-1,-1,-1,-1 ,3,3,3,-1,-1,0,0,0,0,0,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,1,-1,1,1], [TENSOR,[8,2]],[6,6,6,6,6,6,6,6,6,6,6,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2, -2,-2,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[12,12,12,12,12, 12,-4,-4,-4,-4,-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,-2,-2,-2,2,2 ,0,0,0,0,-2,2,0,0,0,0,0,0], [TENSOR,[11,2]],[4,4,4,4,4,-4,4,4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,0,1,1,1,-1,-1,-2,-2,-2,2,2,0,0,0,0,2,-2,0,0,0,0,0,0], [TENSOR,[13,2]],[6,6,6,6,6,-6,-2,-2,2,2,-2,2,-2,2,2,-2,2,2,2,2,2,2,-2,-2,-2, -2,-2,2,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,0,0,0,0,2,2,0,0,0,0,0,0], [TENSOR,[15,2]],[6,6,6,6,6,-6,-2,-2,2,2,-2,-2,2,-2,2,2,-2,-2,-2,2,-2,-2,2,2,2 ,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,0,0,0,0,0,2,0,0], [TENSOR,[17,2]],[6,6,6,6,6,-6,-2,-2,2,2,-2,-2,2,2,-2,-2,2,2,2,-2,2,2,-2,-2,-2 ,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,0,0,0,0,-2,2,2,0,0,0], [TENSOR,[19,2]],[6,6,6,6,6,-6,-2,-2,2,2,-2,2,-2,-2,-2,2,-2,-2,-2,-2,-2,-2,2,2 ,2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(4),2*E(4)], [TENSOR,[21,2]],[8,8,8,8,8,-8,8,8,-8,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,0,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,-8,0,-8,-8,0,0,8,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0],[8,8,8,8,-8,0,-8,-8,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1, -E(3)+E(3)^2,E(3)-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[25,2]],[12,12,12,12,-12,0,4,4,0,0,-4,0,0,-4,4,0,4,4,-4,4,4,-4,0,0,0, 0,0,-4,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[12,12,12,12,-12,0,4, 4,0,0,-4,0,0,4,-4,0,-4,-4,4,-4,-4,4,0,0,0,0,0,4,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0 ,0,0,0,0,0,0,0,0,0],[12,12,12,12,-12,0,4,4,0,0,-4,0,0,4,4,0,-4,-4,4,4,-4,4,0,0 ,0,0,0,-4,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[12,12,12,12,-12,0 ,4,4,0,0,-4,0,0,-4,-4,0,4,4,-4,-4,4,-4,0,0,0,0,0,4,2,-2,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0],[12,12,12,-4,0,0,4,-4,-4,4,0,0,0,4,0,-4,0,8,-4,0,-4,0,0 ,0,4,0,0,0,0,0,0,0,0,0,0,-2,-2,2,-2,2,-2,-2,0,0,0,0,2,0,0,0,0,0], [TENSOR,[31,2]],[12,12,12,-4,0,0,4,-4,4,-4,0,0,0,8,0,0,4,-4,0,0,0,-4,4,-4,0,0 ,0,0,0,0,0,0,0,0,0,-2,-2,2,2,-2,0,0,0,0,0,0,0,-2,2,0,0,0], [TENSOR,[33,2]],[12,12,12,-4,0,0,4,-4,-4,4,0,0,0,-4,0,4,8,0,4,0,-4,0,0,0,-4,0 ,0,0,0,0,0,0,0,0,0,-2,-2,2,-2,2,2,2,0,0,0,0,-2,0,0,0,0,0], [TENSOR,[35,2]],[12,12,12,-4,0,0,4,-4,4,-4,0,0,0,0,0,0,-4,4,8,0,0,-4,-4,4,0,0 ,0,0,0,0,0,0,0,0,0,-2,-2,2,2,-2,0,0,0,0,0,0,0,2,-2,0,0,0], [TENSOR,[37,2]],[24,24,24,-8,0,0,-8,8,0,0,0,0,0,8,0,0,0,0,-8,0,0,0,0,8,-8,0,0 ,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],[24,24,24,-8,0,0,-8,8,0,0, 0,0,0,-8,0,-8,0,0,8,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0],[24,24,24,-8,0,0,-8,8,0,0,0,0,0,0,0,8,-8,8,0,0,0,0,0,-8,0,0,0,0,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,24,-8,0,0,-8,8,0,0,0,0,0,0, 0,0,8,-8,0,0,0,0,-8,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] ,[24,24,24,-8,0,0,8,-8,-8,8,0,0,0,0,0,0,-8,-8,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,24,-8,0,0,8,-8,8,-8,0,0,0,-8,0,0,0 ,0,-8,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[48, 48,-16,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,-4,0,0,0,0,0,-4,4,0,0,0,0,0,0,0,0,-4,4, 0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0], [TENSOR,[45,2]],[48,48,-16,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,-4,0,0,0,0,0,4,-4, 0,0,0,0,0,0,0,0,-4,4,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0], [TENSOR,[47,2]],[96,96,-32,0,0,0,0,0,0,0,0,0,0,0,-8,0,0,0,0,8,0,0,0,0,0,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[64,-64,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,-4,4,0,0,0,0,0,0,0,0, 0,0], [TENSOR,[50,2]],[128,-128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]], [(51,52),(41,42),(34,35),(26,27)(43,44)]); ALF("2.2^(2+2).2^(1+1+2+2):S4","Ru",[1,2,2,2,5,6,2,7,8,5,8,7,14,2,2,3,8,5, 7,7,6,8,7,6,8,5,8,8,15,13,4,11,18,19,19,2,7,7,8,7,5,8,8,7,13,15,14,15,13, 15,25,26],[ "fusion map is unique up to table aut." ]); MOT("2^(2+1+2).2^(1+1+2).2^2.S4", [ "origin: Dixon's Algorithm,\n", "one type of solvable subgroups of maximal order in Ru" ], [49152,16384,12288,2048,1536,768,1024,1024,512,512,512,128,128,64,512,256,256, 512,512,512,256,256,256,256,256,256,128,64,32,32,24,24,12,12,12,128,128,128, 128,128,128,64,32,32,32,32,32,32,32,32,16,16,16], [,[1,1,1,1,3,3,1,2,3,2,2,7,7,8,1,1,1,2,3,3,2,3,3,2,3,2,4,4,10,11,31,31,32,32, 32,1,2,4,4,7,7,7,16,16,15,9,5,18,20,19,27,14,14],[1,2,3,4,5,6,7,8,9,10,11,12, 13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,1,3,5,6,6,36,37,38,39,40 ,41,42,43,44,45,46,47,48,49,50,51,53,52]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1] ,[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1, -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1 ,1,1,1,1,-1,-1], [TENSOR,[4,2]],[3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,3,-1,3,3,3,3,-1,3,3,3,3,3,-1, -1,-1,-1,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,1,1,1], [TENSOR,[6,2]],[3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,3,-1,-1,-1,-1,3,-1,-1,-1,-1 ,-1,3,3,-1,-1,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,-1,1,1], [TENSOR,[8,2]],[6,6,6,6,6,6,6,6,6,6,6,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2, -2,-2,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[12,12,12,12,12 ,12,-4,-4,-4,-4,-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,-2,-2,-2,-2 ,2,2,2,0,0,0,2,-2,0,0,0,0,0,0], [TENSOR,[11,2]],[4,4,4,4,4,-4,4,4,4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 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38,34,38,34,35,40,40,4,8,9,10,7,8,9,10,9,12,12,9,12,8,12,11,12,12,11,12, 13,27,24,26,25,27,24,23,25,24,27,23,26,25,27,28,23,27,49,48,2,3,4,2,4,3,4, 4,4,3,4,4,9,8,8,8,9,10,9,12,9,8,12,11,9,12,12,11,8,9,8,12,9,12,8,12,11,10, 12,12,12,8,12,9,11,12,13,12,11,13,12,11,11,13,18,21,21,20,20,18,21,23,27, 24,24,27,23,27,26,27,24,27,28,28,39,37,37,41,41,39,39,39,55],[ "fusion map is unique up to table aut." ]); MOT("5^(1+4):4.3^2:D8", [ "origin: Dixon's Algorithm,\n", "solvable subgroup of maximal order in Ly" ], [900000,225000,3750,1250,1250,625,1440,360,288,288,9000,360,360,360,72,72,72, 72,2250,90,75,90,90,400,80,50,50,50,40,40,24,24,24,24,24,24,80,80,24,24,16,16, 24,24,24,24,40,40,40,40], [,[1,2,3,4,5,6,1,2,7,7,11,12,11,12,13,13,14,14,19,20,21,19,20,1,7,4,5,3,8,8,9, 10,15,15,16,16,25,25,10,9,25,25,18,18,17,17,29,30,29,30],[1,2,3,4,5,6,7,8,10,9 ,1,1,7,7,10,9,10,9,2,2,3,8,8,24,25,26,27,28,29,30,32,31,32,32,31,31,37,38,40, 39,42,41,40,40,39,39,47,48,49,50],,[1,1,1,1,1,1,7,7,9,10,11,12,13,14,15,16,17, 18,11,12,11,13,14,24,25,24,24,24,25,25,31,32,33,34,35,36,38,37,39,40,42,41,43, 44,45,46,38,38,37,37]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1, -1,-1,-1,-1,1,1,1,1], [TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2, -2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[4,4,4,4,4,4,4,4,4,4,-2,1,-2,1, -2,-2,1,1,-2,1,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,0,0,-1,-1,-1,-1,0,0,0 ,0], [TENSOR,[6,2]],[4,4,4,4,4,4,4,4,4,4,1,-2,1,-2,1,1,-2,-2,1,-2,1,1,-2,0,0,0,0,0 ,0,0,-2,-2,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[8,3]],[1,1,1,1,1,1,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,-1,1,-1, -1,-1,1,1,-E(4),E(4),-E(4),-E(4),E(4),E(4),1,1,-E(4),E(4),-1,-1,-E(4),-E(4), E(4),E(4),1,1,1,1], [TENSOR,[3,10]], [TENSOR,[2,10]], [TENSOR,[2,11]], [TENSOR,[5,10]], [TENSOR,[6,11]], [TENSOR,[6,10]], [TENSOR,[8,11]], [TENSOR,[8,10]],[2,2,2,2,2,2,-2,-2,-2*E(4),2*E(4),2,2,-2,-2,-2*E(4),2*E(4), -2*E(4),2*E(4),2,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,E(8)+E(8)^3,-E(8)-E(8)^3, 0,0,-E(8)+E(8)^3,E(8)-E(8)^3,0,0,0,0,E(8)+E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3, -E(8)-E(8)^3], [TENSOR,[19,2]], [TENSOR,[19,12]], [TENSOR,[19,10]],[4,4,4,4,4,4,-4,-4,-4*E(4),4*E(4),-2,1,2,-1,2*E(4),-2*E(4), -E(4),E(4),-2,1,-2,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, -E(24)^11+E(24)^19,E(24)^11-E(24)^19,-E(24)+E(24)^17,E(24)-E(24)^17,0,0,0,0], [TENSOR,[23,2]], [TENSOR,[23,10]], [TENSOR,[23,11]],[4,4,4,4,4,4,-4,-4,-4*E(4),4*E(4),1,-2,-1,2,-E(4),E(4), 2*E(4),-2*E(4),1,-2,1,-1,2,0,0,0,0,0,0,0,0,0,-E(24)+E(24)^17,E(24)-E(24)^17, E(24)^11-E(24)^19,-E(24)^11+E(24)^19,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[27,3]], [TENSOR,[27,11]], [TENSOR,[27,10]],[48,48,23,-2,-2,-2,0,0,0,0,24,0,0,0,0,0,0,0,24,0,-1,0,0,8,0, -2,-2,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[31,10]],[96,96,46,-4,-4,-4,0,0,0,0,-24,0,0,0,0,0,0,0,-24,0,1,0,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[144,144,-6,-6,19,-6,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,-2,3,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,0,0,0], [TENSOR,[34,10]],[144,144,-6,19,-6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-8,0, -3,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[36,10]],[288,288,-12,-12,-12,13,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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],[100,-25,0,0,0,0,4,-1,0,0 ,-20,4,4,4,0,0,0,0,5,-1,0,-1,-1,0,4,0,0,0,-1,-1,0,0,0,0,0,0,-4,-4,0,0,0,0,0,0, 0,0,1,1,1,1], [TENSOR,[39,2]],[100,-25,0,0,0,0,-4,1,0,0,-20,4,-4,-4,0,0,0,0,5,-1,0,1,1,0,0, 0,0,0,-E(20)-E(20)^9+E(20)^13+E(20)^17,E(20)+E(20)^9-E(20)^13-E(20)^17,0,0,0,0 ,0,0,-2*E(8)-2*E(8)^3,2*E(8)+2*E(8)^3,0,0,0,0,0,0,0,0, -E(40)^13-E(40)^31-E(40)^37-E(40)^39,-E(40)^7-E(40)^21-E(40)^23-E(40)^29, E(40)^13+E(40)^31+E(40)^37+E(40)^39,E(40)^7+E(40)^21+E(40)^23+E(40)^29], [TENSOR,[41,2]], [GALOIS,[41,11]], [TENSOR,[43,2]],[100,-25,0,0,0,0,4,-1,0,0,-20,4,4,4,0,0,0,0,5,-1,0,-1,-1,0,-4 ,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(20)-E(20)^9+E(20)^13+E(20)^17, E(20)+E(20)^9-E(20)^13-E(20)^17,-E(20)-E(20)^9+E(20)^13+E(20)^17, E(20)+E(20)^9-E(20)^13-E(20)^17], [TENSOR,[45,2]],[400,-100,0,0,0,0,-16,4,0,0,40,4,8,-4,0,0,0,0,-10,-1,0,-2,1,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[400,-100,0,0,0,0,-16,4, 0,0,-20,-8,-4,8,0,0,0,0,5,2,0,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,0,0,0,0,0],[400,-100,0,0,0,0,16,-4,0,0,40,4,-8,4,0,0,0,0,-10,-1,0,2,-1,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[400,-100,0,0,0,0,16,-4,0,0, -20,-8,4,-8,0,0,0,0,5,2,0,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,0,0,0]], [(43,44)(45,46),(33,34)(35,36),(29,30)(47,48)(49,50),( 4, 5)(26,27), ( 9,10)(15,16)(17,18)(31,32)(33,35)(34,36)(39,40)(41,42)(43,45)(44,46), (37,38)(41,42)(47,49)(48,50)]); ALF("5^(1+4):4.3^2:D8","5^(1+4):4S6",[1,2,4,3,4,4,5,6,7,8,14,21,15,22,17, 16,24,23,18,25,19,20,26,9,10,11,12,12,13,13,40,41,49,51,50,48,27,27,42,43, 28,28,53,54,55,52,29,30,30,29],[ "fusion map is unique up to table automorphisms" ]); ALF("5^(1+4):4.3^2:D8","Ly",[1,6,7,6,7,7,2,15,5,5,3,4,8,9,19,19,20,20,22, 23,24,36,37,2,5,15,16,16,26,26,12,12,31,31,31,31,12,12,13,13,13,13,32,33, 33,32,47,48,48,47],[ "fusion map is unique up to table automorphisms" ]); MOT("2^11.2^6.3^(1+2).D8", [ "origin: Dixon's Algorithm,\n", "solvable subgroup of maximal order in J4,\n", "sorted w.r.t. normal series 2.2^6.2^4.2^6.3.3^2.D8" ], [28311552,28311552,786432,786432,524288,294912,294912,196608,196608,49152, 32768,98304,65536,65536,49152,49152,32768,32768,24576,16384,98304,32768,24576, 24576,16384,16384,8192,8192,8192,8192,8192,8192,6144,4096,4096,4096,2048,2048, 2048,2048,2048,3456,3456,576,576,384,384,2304,576,2304,2304,2304,576,384,384, 288,288,192,192,96,96,96,192,192,48,48,49152,49152,8192,8192,8192,4096,4096, 4096,4096,4096,3072,3072,2048,2048,1536,1536,1024,1024,1024,1024,1024,1024,512 ,512,256,256,96,96,256,256,256,128,96,96,48,48,768,768,128,128,128,192,192,128 ,128,32,48,48,48,48,48,48,48,48,12288,12288,6144,6144,2048,6144,4096,4096,3072 ,3072,3072,2048,2048,2048,2048,1536,1536,1536,1024,1024,1024,1024,1024,1024, 768,768,512,512,512,512,512,512,512,512,512,512,512,512,512,512,512,256,256, 256,256,256,256,96,96,48,48,768,256,256,256,256,256,256,256,256,256,128,128, 128,128,128,128,64,96,96,48,48,48,48,24,24,24,48,48], [,[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5,5,5,5,5,5,3,4,5,4,3,4 ,3,3,5,42,42,42,42,42,42,48,49,48,48,48,49,48,48,48,48,48,48,49,49,49,50,50,53 ,54,1,1,1,1,1,5,5,5,5,2,9,9,5,5,6,6,14,14,13,13,14,14,13,11,20,10,42,42,26,31, 31,32,46,46,45,45,68,68,69,71,70,77,77,76,76,90,93,93,93,93,99,99,99,99,1,1,1, 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67,4,7,6,5,7,13,11,11,10,12,11,13,11,13,13,15,16,13,14,14,13,12,12,11,22, 21,15,16,14,14,19,19,17,17,18,18,20,19,19,20,13,21,22,20,14,20,20,29,28, 31,30,34,36,36,36,36,35,36,34,36,35,37,37,35,36,34,34,37,45,46,50,49,47, 47,51,48,52,67,68],[ "fusion map is unique up to table aut." ]); ALF("2^11.2^6.3^(1+2).D8","J4",[1,2,3,2,2,3,2,3,2,2,2,2,3,2,2,3,3,3,3,3,5, 5,5,6,5,6,5,6,5,6,5,6,7,5,6,6,7,6,7,7,6,4,9,10,11,10,11,4,4,10,11,9,10,11, 10,11,10,10,11,10,11,10,21,22,21,23,3,2,3,3,2,5,5,6,6,6,6,5,6,6,7,7,6,5,7, 7,6,6,7,6,7,6,10,11,16,14,14,15,22,21,23,23,5,6,7,6,7,15,15,16,16,16,21, 21,22,22,37,38,38,37,2,3,2,3,3,7,5,5,5,6,5,7,5,7,7,6,5,7,6,6,7,6,6,5,7,6, 6,5,6,6,7,7,6,6,6,6,7,7,7,7,7,6,7,7,6,7,7,11,10,10,11,15,14,14,14,14,16, 14,15,14,16,16,16,16,14,15,15,16,21,22,22,21,23,23,22,21,23,37,38],[ "fusion map determined by factorization through 2^11:M24" ]); MOT("2^(4+12).(S3x3^(1+2)_+:D8)", [ "origin: Dixon's Algorithm,\n", "solvable subgroup of maximal order in Co1" ], 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93,94,96,100,97,75,76,82,83,84,89,88,99,46,37,41,49,44,45,38,43,50,36,42, 51,56,57,34,35,31,32,53,52,55,33,54,69,67,60,63,73,39,40,29,30,47,48,48, 70,68,66,65,58,62,59,61,72,74,64,71,112,102,107,110,106,111,103,108,109, 105,104,101,120,120,121,121,118,118,113,116,116,119,119,122,122,117,117, 114,115,115,138,169,139,180,156,137,137,152,154,168,153,152,145,144,155, 179,164,178,141,140,141,140,159,158,158,159,165,166,177,176,167,173,164, 178,143,173,170,170,160,201,213,182,215,161,206,217,218,151,150,142,148, 147,148,147,171,172,142,146,149,149,157,146,163,163,175,174,174,146,174, 162,202,212,162,204,203,208,207,205,181,214,219,216,220,210,209,211],[ "fusion map is unique" ]); ALF("2^(4+12).(S3x3^(1+2)_+:D8)","Co1",[1,2,2,4,2,3,2,4,4,4,4,10,9,9,10, 11,10,10,11,12,10,12,11,12,6,22,22,4,2,4,11,12,11,12,14,5,6,18,18,24,22, 22,19,20,24,45,46,45,46,6,7,8,8,22,20,21,23,24,20,22,24,22,25,26,25,26,26, 49,51,48,55,52,53,54,57,2,3,4,4,9,12,12,10,10,10,12,11,11,12,12,11,12,10, 12,10,14,14,14,18,19,22,22,24,31,29,32,30,32,33,33,45,47,47,46,49,49,54, 54,51,53,81,80,12,10,13,14,14,29,30,34,32,32,32,34,47,47,54,54,50,50,54, 51,51,80,80,82,82,83,83,82,84,84,2,4,4,3,4,11,11,11,9,10,10,11,12,10,12, 12,14,14,12,11,12,11,12,11,11,12,12,10,12,10,14,13,14,14,14,13,14,14,20, 22,23,24,26,24,24,26,25,30,29,33,32,31,32,31,30,29,33,33,30,30,32,33,32, 32,32,34,34,33,34,53,53,52,53,54,51,49,53,54,51,57,57,57,56,84,82,85],[ "fusion map is unique" ]); MOT("3^(1+10)_+:2^(1+6)_-:3^(1+2)_+:2S4", [ "origin: Dixon's Algorithm,\n", "solvable subgroup of maximal order in Fi24'" ], [29386561536,14693280768,34012224,19131876,8503056,2125764,1224440064,9565938, 4251528,4251528,3188646,1417176,1062882,354294,4478976,2239488,186624,6718464, 62208,3359232,139968,34992,31104,279936,17496,17496,5832,10368,3456,944784, 944784,944784,34992,34992,34992,157464,13122,39366,1458,19683,6561,2187,944784 ,472392,39366,11664,5832,13122,13122,13122,1944,972,157464,104976,104976,19683 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(248,249)(251,252)(253,254)(260,261)(271,272)(273,274)(275,276)(277,278) (280,281)(282,283) , ( 54, 55)( 57, 58)( 60, 61)( 62, 63)( 64, 68)( 69, 71)( 70, 72)( 74, 75) (173,174)(176,177)(219,220)(242,244)(245,247)(262,268)(263,270)(264,269) (273,278)(274,277) ]); ALF("3^(1+10)_+:2^(1+6)_-:3^(1+2)_+:2S4","3^(1+10):U5(2):2",[1,2,3,4,5,6, 3,3,4,5,6,6,5,6,7,8,9,10,48,11,15,12,49,15,12,13,14,51,50,24,22,23,66,67, 68,29,25,26,69,28,25,27,30,31,33,80,81,36,35,32,124,125,39,37,38,33,37,38, 84,83,82,36,36,34,34,35,32,34,32,35,32,35,128,126,127,10,7,54,52,11,15,8, 13,12,14,9,86,87,85,72,70,71,55,53,56,73,88,48,52,97,49,51,50,53,122,120, 121,134,135,133,98,123,16,17,18,22,23,24,41,40,41,26,19,19,45,64,62,63,74, 75,76,74,75,76,72,70,71,67,68,66,86,87,85,62,63,64,91,89,90,93,94,94,78, 78,90,89,91,69,20,29,21,20,21,20,28,25,46,47,46,27,43,43,44,44,25,27,27, 42,100,101,99,42,103,104,116,117,115,120,121,122,131,129,130,134,135,133, 65,79,79,77,73,79,77,77,65,92,142,143,141,88,96,92,95,144,145,102,102,102, 118,119,123,132,146,153,152,147,148,150,149,151,149,147,150,151,147,148, 148,148,149,150,150,159,157,158,159,163,158,168,170,172,172,172,168,170, 155,154,155,154,156,180,181,160,161,162,161,162,160,160,162,161,169,171, 183,186,182,185,187,184,173,173,173,169,171],[ "fusion map is unique up to table automorphisms" ]); ALF("3^(1+10)_+:2^(1+6)_-:3^(1+2)_+:2S4","F3+",[1,5,4,5,6,7,4,4,5,6,7,7,6, 7,3,17,16,2,9,15,13,18,39,13,18,15,19,38,40,7,5,6,17,14,20,29,30,7,22,32, 30,33,4,7,7,16,22,29,33,31,38,43,6,8,8,7,8,8,21,23,23,29,29,32,32,33,31, 32,31,33,31,33,42,46,47,2,3,10,11,15,13,17,15,18,19,16,18,19,15,22,17,21, 44,45,49,61,62,9,11,27,39,38,40,45,43,39,42,48,50,45,80,97,4,5,6,5,6,7,7, 6,7,7,7,7,8,21,16,17,13,15,18,13,15,18,22,17,21,14,20,17,18,19,15,16,17, 21,20,21,22,18,19,19,19,19,22,21,20,22,31,29,30,31,30,31,32,30,33,30,33, 33,31,31,32,32,30,33,33,34,29,33,31,34,34,34,39,42,38,39,42,43,49,41,44, 48,50,45,59,60,60,62,61,60,62,62,59,63,61,63,59,62,62,63,64,65,66,84,84, 84,96,95,97,98,3,10,14,16,22,21,17,20,17,16,21,20,16,22,22,22,17,21,21,23, 16,23,23,22,23,26,26,26,26,26,26,26,41,49,41,49,44,57,57,59,63,61,63,61, 59,59,61,63,77,77,79,79,76,76,78,78,76,76,76,77,77],[ "fusion map determined by factorization through 3^(1+10):U5(2):2" ]); MOT("3^(1+10)_+:(2x2^(1+6)_-:3^(1+2)_+:2S4)", [ "origin: Dixon's Algorithm,\n", "solvable subgroup of maximal order in Fi24'.2" ], [58773123072,29386561536,4251528,38263752,68024448,17006112,8957952,4478976, 124416,62208,69984,279936,6718464,13436928,1889568,1889568,1889568,26244, 314928,69984,69984,69984,78732,26244,26244,26244,944784,1889568,11664,23328, 1944,3888,181398528,90699264,314928,157464,472392,2519424,93312,2239488, 1119744,3888,93312,46656,41472,20736,69984,69984,69984,2916,3888,23328,23328, 23328,4374,13122,4374,13122,6561,104976,1296,216,39366,13122,13122,13122, 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2026-05-26