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Quelle ctomisc7.tbl Sprache: unbekannt |
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## #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, --> -------------------- --> maximum size reached --> -------------------- [ Dauer der Verarbeitung: 0.14 Sekunden (vorverarbeitet) ] |
2026-04-02