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## #W ctoline5.tbl GAP table library Thomas Breuer ## ## This file contains the ordinary character tables related to the ## linear groups $L_3(9)$, $L_4(3)$, $L_5(2)$ and $L_6(2)$ of the ATLAS. ## #H ctbllib history #H --------------- #H $Log: ctoline5.tbl,v $ #H Revision 4.20 2012/04/23 16:16:07 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 4.19 2012/01/30 08:31:44 gap #H removed #H entries from the headers #H TB #H #H Revision 4.18 2012/01/26 11:20:46 gap #H fixed revision entry #H TB #H #H Revision 4.17 2012/01/26 11:20:01 gap #H fusion from "L6(2)" to "2^6:L6(2)" not to "P1L72" (name change) #H TB #H #H Revision 4.16 2011/09/28 14:32:13 gap #H removed revision entry and SET_TABLEFILENAME call #H TB #H #H Revision 4.15 2010/05/05 13:20:01 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 4.14 2010/01/19 17:05:31 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 4.13 2009/07/29 13:59:41 gap #H added maxes of L4(3) #H TB #H #H Revision 4.12 2008/06/24 16:23:05 gap #H added several fusions and names #H TB #H #H Revision 4.11 2005/08/10 14:33:20 gap #H corrected InfoText values concerning GV4 constructions, #H added table of 2^2.L3(4).2_1 and related fusions #H TB #H #H Revision 4.10 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 4.9 2003/05/15 17:38:05 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 4.8 2003/01/24 15:57:30 gap #H replaced several fusions by ones that are compatible with Brauer tables #H TB #H #H Revision 4.7 2002/07/12 06:45:55 gap #H further tidying up: removed `irredinfo' stuff, rearranged constructions #H TB #H #H Revision 4.6 2001/05/04 16:47:45 gap #H first revision for ctbllib #H #H #H tbl history (GAP 4) #H ------------------- #H (Rev. 4.6 of ctbllib coincides with Rev. 4.5 of tbl in GAP 4) #H #H RCS file: /gap/CVS/GAP/4.0/tbl/ctoline5.tbl,v #H Working file: ctoline5.tbl #H head: 4.5 #H branch: #H locks: strict #H access list: #H symbolic names: #H GAP4R2: 4.5.0.8 #H GAP4R2PRE2: 4.5.0.6 #H GAP4R2PRE1: 4.5.0.4 #H GAP4R1: 4.5.0.2 #H keyword substitution: kv #H total revisions: 6; selected revisions: 6 #H description: #H ---------------------------- #H revision 4.5 #H date: 1999/07/14 11:39:38; author: gap; state: Exp; lines: +4 -3 #H cosmetic changes for the release ... #H #H TB #H ---------------------------- #H revision 4.4 #H date: 1999/06/23 11:59:17; author: gap; state: Exp; lines: +103 -2 #H added admissible name L4(3).2^2 to the table of this group, #H added fusions from index 2 subgroups #H #H TB #H ---------------------------- #H revision 4.3 #H date: 1998/03/11 08:05:25; author: gap; state: Exp; lines: +14 -2 #H mainly new fusions to tables of marks added #H #H TB #H ---------------------------- #H revision 4.2 #H date: 1997/11/25 15:44:52; author: gap; state: Exp; lines: +5 -2 #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 15:40:35; author: fceller; state: Exp; lines: +2 -2 #H for version 4 #H ---------------------------- #H revision 1.1 #H date: 1996/10/21 15:59:37; author: sam; state: Exp; #H first proposal of the table library #H ========================================================================== ## MOT("2.L4(3)", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]" ], [12130560,12130560,2880,1152,11664,11664,3888,3888,3888,3888,162,162,2880, 2880,192,192,32,40,40,72,72,144,144,36,36,16,16,54,54,54,54,40,40,72,72,72,72, 24,24,26,26,26,26,26,26,26,26,40,40,40,40], [,[1,1,2,1,5,5,7,7,9,9,11,11,3,3,4,4,3,18,18,8,10,5,5,7,9,15,15,28,28,30,30, 19,19,20,20,21,21,22,22,44,44,46,46,42,42,40,40,33,33,32,32],[1,2,3,4,1,2,1,2, 1,2,1,2,13,14,15,16,17,18,19,3,3,4,4,4,4,26,27,5,6,5,6,32,33,13,14,13,14,15, 16,40,41,42,43,44,45,46,47,48,49,50,51],,[1,2,3,4,5,6,7,8,9,10,11,12,14,13,15, 16,17,1,2,20,21,22,23,24,25,27,26,28,29,30,31,3,3,35,34,37,36,38,39,44,45,46, 47,42,43,40,41,14,13,14,13],,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,14,13,15,16,17, 18,19,20,21,22,23,24,25,27,26,28,29,30,31,33,32,35,34,37,36,38,39,1,2,1,2,1,2, 1,2,51,50,49,48]], 0, [(40,44,42,46)(41,45,43,47),(32,33)(48,50)(49,51),(13,14)(26,27)(34,35)(36,37) (48,49)(50,51),(13,14)(26,27)(32,33)(34,35)(36,37)(48,51)(49,50),( 7, 9) ( 8,10)(20,21)(24,25)(28,30)(29,31)(34,36)(35,37),(40,42)(41,43)(44,46) (45,47),(40,46,42,44)(41,47,43,45)], ["ConstructProj",[["L4(3)",[]],["2.L4(3)",[]]]]); ALF("2.L4(3)","L4(3)",[1,1,2,3,4,4,5,5,6,6,7,7,8,8,9,9,10,11,11,12,13,14, 14,15,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27, 27,28,28,29,29]); ALF("2.L4(3)","2.L4(3).2_1",[1,2,3,4,5,6,7,8,7,8,9,10,11,12,13,14,15,16, 17,18,18,19,20,21,21,22,23,24,25,24,25,26,27,28,29,28,29,30,31,32,33,34, 35,36,37,38,39,40,41,42,43],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables and factors" ]); ALF("2.L4(3)","2.L4(3).2_2",[1,2,3,4,5,6,7,8,9,10,11,12,13,13,14,15,16,17, 18,19,20,21,22,23,24,25,25,26,27,28,29,30,30,31,31,32,32,33,34,35,36,35, 36,37,38,37,38,39,40,40,39],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables and factors" ]); ALF("2.L4(3)","2.L4(3).2_3",[1,2,3,4,5,6,7,8,7,8,9,10,11,11,12,13,14,15, 16,17,17,18,19,20,20,21,21,22,23,22,23,24,24,25,26,26,25,27,28,29,30,29, 30,31,32,31,32,33,34,34,33],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); MOT("2.L4(3).2_1", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13],\n", "constructions: GL(4,3)" ], [24261120,24261120,5760,2304,23328,23328,3888,3888,324,324,5760,5760,384,384, 64,80,80,72,288,288,36,32,32,54,54,80,80,72,72,48,48,52,52,52,52,52,52,52,52, 80,80,80,80,22464,22464,32,216,216,36,36,384,384,384,384,80,80,64,64,48,48,48, 48,52,52,52,52,52,52,52,52,80,80,80,80,80,80,80,80], [,[1,1,2,1,5,5,7,7,9,9,3,3,4,4,3,16,16,8,5,5,7,13,13,24,24,17,17,18,18,19,19, 36,36,38,38,34,34,32,32,27,27,26,26,1,1,4,5,5,9,9,13,13,13,13,11,12,14,14,30, 30,30,30,36,36,38,38,34,34,32,32,42,42,41,41,43,43,40,40],[1,2,3,4,1,2,1,2,1, 2,11,12,13,14,15,16,17,3,4,4,4,22,23,5,6,26,27,11,12,13,14,32,33,34,35,36,37, 38,39,40,41,42,43,44,45,46,44,45,44,45,51,52,53,54,55,56,57,58,51,52,53,54,63, 64,65,66,67,68,69,70,71,72,73,74,75,76,77,78],,[1,2,3,4,5,6,7,8,9,10,12,11,13, 14,15,1,2,18,19,20,21,23,22,24,25,3,3,29,28,30,31,36,37,38,39,34,35,32,33,12, 11,12,11,44,45,46,47,48,49,50,53,54,51,52,56,55,58,57,61,62,59,60,67,68,69,70, 65,66,63,64,56,56,55,55,55,55,56,56],,,,,,,,[1,2,3,4,5,6,7,8,9,10,12,11,13,14, 15,16,17,18,19,20,21,23,22,24,25,27,26,29,28,30,31,1,2,1,2,1,2,1,2,43,42,41, 40,44,45,46,47,48,49,50,53,54,51,52,56,55,58,57,61,62,59,60,44,45,44,45,44,45, 44,45,74,73,72,71,78,77,76,75]], 0, [(32,34)(33,35)(36,38)(37,39)(63,65)(64,66)(67,69)(68,70),(32,36,34,38) (33,37,35,39)(63,67,65,69)(64,68,66,70),(32,38,34,36)(33,39,35,37) (63,69,65,67)(64,70,66,68),(26,27)(40,42)(41,43)(71,77,72,78)(73,75,74,76), (26,27)(40,42)(41,43)(71,78,72,77)(73,76,74,75),(11,12)(22,23)(26,27)(28,29) (40,43)(41,42)(51,53)(52,54)(55,56)(57,58)(59,61)(60,62)(71,74)(72,73)(75,78) (76,77),(11,12)(22,23)(28,29)(40,41)(42,43)(51,53)(52,54)(55,56)(57,58)(59,61) (60,62)(71,76,72,75)(73,78,74,77),(71,72)(73,74)(75,76)(77,78),(44,45)(47,48) (49,50)(51,52)(53,54)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)], ["ConstructProj",[["L4(3).2_1",[]],["2.L4(3).2_1",[]]]]); ALF("2.L4(3).2_1","L4(3).2_1",[1,1,2,3,4,4,5,5,6,6,7,7,8,8,9,10,10,11,12, 12,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24, 25,25,26,27,27,28,28,29,29,30,30,31,32,33,33,34,34,35,35,36,36,37,37,38, 38,39,39,40,40,41,41,42,42,43,43]); MOT("Isoclinic(2.L4(3).2_1)", [ "isoclinic group of the 2.L4(3).2_1 given in the ATLAS" ], 0, 0, 0, [(32,36,34,38)(33,37,35,39)(63,67,65,69)(64,68,66,70),(26,27)(40,42)(41,43) (71,77,72,78)(73,75,74,76),(11,12)(22,23)(28,29)(40,41)(42,43)(51,53)(52,54) (55,56)(57,58)(59,61)(60,62)(71,75,72,76)(73,77,74,78),(44,45)(47,48)(49,50) (51,52)(53,54)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)], ["ConstructIsoclinic",[["2.L4(3).2_1"]]]); ALF("Isoclinic(2.L4(3).2_1)","L4(3).2_1",[1,1,2,3,4,4,5,5,6,6,7,7,8,8,9, 10,10,11,12,12,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22, 23,23,24,24,25,25,26,27,27,28,28,29,29,30,30,31,32,33,33,34,34,35,35,36, 36,37,37,38,38,39,39,40,40,41,41,42,42,43,43]); MOT("2.L4(3).2_2", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]" ], [24261120,24261120,5760,2304,23328,23328,7776,7776,7776,7776,324,324,2880,384, 384,64,80,80,144,144,288,288,72,72,16,108,108,108,108,40,72,72,48,48,26,26,26, 26,40,40,103680,103680,1152,192,192,192,2592,2592,2592,2592,432,432,216,216, 144,144,36,36,16,20,20,48,48,24,24,36,36,36,36], [,[1,1,2,1,5,5,7,7,9,9,11,11,3,4,4,3,17,17,8,10,5,5,7,9,14,26,26,28,28,18,19, 20,21,21,37,37,35,35,30,30,2,2,1,4,3,3,6,6,6,6,10,8,8,10,7,9,11,11,14,18,18, 22,22,19,20,29,29,27,27],[1,2,3,4,1,2,1,2,1,2,1,2,13,14,15,16,17,18,3,3,4,4,4, 4,25,5,6,5,6,30,13,13,14,15,35,36,37,38,39,40,41,42,43,44,45,46,41,41,42,42, 41,42,41,42,43,43,43,43,59,60,61,44,44,45,46,48,47,50,49],,[1,2,3,4,5,6,7,8,9, 10,11,12,13,14,15,16,1,2,19,20,21,22,23,24,25,26,27,28,29,3,31,32,33,34,37,38, 35,36,13,13,41,42,43,44,45,46,48,47,50,49,51,52,53,54,55,56,57,58,59,41,42,63, 62,64,65,67,66,69,68],,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19, 20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,1,2,1,2,39,40,41,42,43,44,45,46, 47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69]], 0, [(57,58),(47,48)(49,50)(62,63)(66,67)(68,69),(39,40),(39,40)(47,48)(49,50) (62,63)(66,67)(68,69),(35,37)(36,38),( 7, 9)( 8,10)(19,20)(23,24)(26,28) (27,29)(31,32)(41,42)(45,46)(47,49)(48,50)(51,52)(53,54)(55,56)(60,61)(64,65) (66,68)(67,69)], ["ConstructProj",[["L4(3).2_2",[]],["2.L4(3).2_2",[]]]]); ALF("2.L4(3).2_2","L4(3).2_2",[1,1,2,3,4,4,5,5,6,6,7,7,8,9,9,10,11,11,12, 13,14,14,15,16,17,18,18,19,19,20,21,22,23,23,24,24,25,25,26,26,27,28,29, 30,31,32,33,33,34,34,35,36,37,38,39,40,41,41,42,43,44,45,45,46,47,48,48, 49,49]); ALF("2.L4(3).2_2","2.O7(3)",[1,2,4,5,6,7,8,9,10,11,18,19,20,21,22,24,25, 26,35,32,34,33,36,37,49,54,55,52,53,60,67,66,64,65,76,77,74,75,88,87,4,3, 5,23,24,20,30,30,27,27,32,28,35,29,36,31,45,46,49,60,61,68,68,73,66,86,86, 85,84],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables and factors" ]); MOT("Isoclinic(2.L4(3).2_2)", [ "isoclinic group of the 2.L4(3).2_2 given in the ATLAS" ], 0, 0, 0, [(57,58),(47,48)(49,50)(62,63)(66,67)(68,69),(39,40),(35,37)(36,38),(7,9)(8, 10)(19,20)(23,24)(26,28)(27,29)(31,32)(41,42)(45,46)(47,49)(48,50)(51,52)(53, 54)(55,56)(60,61)(64,65)(66,68)(67,69)], ["ConstructIsoclinic",[["2.L4(3).2_2"]]]); ALF("Isoclinic(2.L4(3).2_2)","L4(3).2_2",[1,1,2,3,4,4,5,5,6,6,7,7,8,9,9, 10,11,11,12,13,14,14,15,16,17,18,18,19,19,20,21,22,23,23,24,24,25,25,26, 26,27,28,29,30,31,32,33,33,34,34,35,36,37,38,39,40,41,41,42,43,44,45,45, 46,47,48,48,49,49]); MOT("2.L4(3).2_3", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]" ], [24261120,24261120,5760,2304,23328,23328,3888,3888,324,324,2880,384,384,64,80, 80,72,288,288,36,16,54,54,40,72,72,48,48,26,26,26,26,40,40,1440,96,36,36,192, 192,32,16,16,20,20,24,24,48,48,48,48], [,[1,1,2,1,5,5,7,7,9,9,3,4,4,3,15,15,8,5,5,7,12,22,22,16,17,17,18,18,31,31,29, 29,24,24,1,4,9,9,13,13,12,14,14,15,15,19,19,28,28,28,28],[1,2,3,4,1,2,1,2,1,2, 11,12,13,14,15,16,3,4,4,4,21,5,6,24,11,11,12,13,29,30,31,32,33,34,35,36,35,35, 40,39,41,43,42,45,44,36,36,40,40,39,39],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1, 2,17,18,19,20,21,22,23,3,26,25,27,28,31,32,29,30,11,11,35,36,37,38,40,39,41, 43,42,35,35,47,46,50,51,48,49],,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16, 17,18,19,20,21,22,23,24,26,25,27,28,1,2,1,2,33,34,35,36,37,38,40,39,41,43,42, 45,44,46,47,51,50,49,48]], 0, [(46,47)(48,49)(50,51),(44,45),(37,38),(33,34),(33,34)(44,45),(33,34)(39,40) (42,43)(46,47)(48,50)(49,51),(29,31)(30,32),(25,26),(25,26)(46,47)(48,49) (50,51),(39,40)(42,43)(48,51)(49,50)], ["ConstructProj",[["L4(3).2_3",[]],["2.L4(3).2_3",[]]]]); ALF("2.L4(3).2_3","L4(3).2_3",[1,1,2,3,4,4,5,5,6,6,7,8,8,9,10,10,11,12,12, 13,14,15,15,16,17,17,18,18,19,19,20,20,21,21,22,23,24,24,25,26,27,28,29, 30,31,32,32,33,33,34,34]); MOT("Isoclinic(2.L4(3).2_3)", [ "isoclinic group of the 2.L4(3).2_3 given in the ATLAS" ], 0, 0, 0, [(46,47)(48,49)(50,51),(44,45),(39,40)(42,43)(46,47)(48,50)(49,51),(37,38), (33,34),(29,31)(30,32),(25,26)], ["ConstructIsoclinic",[["2.L4(3).2_3"]]]); ALF("Isoclinic(2.L4(3).2_3)","L4(3).2_3",[1,1,2,3,4,4,5,5,6,6,7,8,8,9,10, 10,11,12,12,13,14,15,15,16,17,17,18,18,19,19,20,20,21,21,22,23,24,24,25, 26,27,28,29,30,31,32,32,33,33,34,34]); MOT("L3(9)", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]" ], [42456960,5760,5832,81,5760,5760,64,80,80,72,91,91,5760,5760,5760,5760,64,64, 64,64,64,64,80,80,72,72,91,91,91,91,80,80,80,80,80,80,80,80,72,72,72,72,80,80, 80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,91,91,91,91, 91,91,91,91,91,91,91,91,91,91,91,91,91,91,91,91,91,91,91,91], [,[1,1,3,4,2,2,2,9,8,3,11,12,5,6,6,5,5,6,7,7,7,7,9,8,10,10,30,29,27,28,13,14, 15,16,24,24,23,23,25,26,26,25,38,37,36,35,38,37,36,35,50,49,48,47,46,45,44,43, 50,49,48,47,46,45,44,43,90,89,88,87,83,84,85,86,74,73,72,71,67,68,69,70,82,81, 80,79,75,76,77,78],[1,2,1,1,6,5,7,9,8,2,12,11,15,16,13,14,18,17,20,19,21,22, 24,23,6,5,27,28,29,30,33,34,31,32,37,38,35,36,15,16,13,14,45,46,43,44,49,50, 47,48,53,54,51,52,57,58,55,56,61,62,59,60,65,66,63,64,69,70,67,68,73,74,71,72, 77,78,75,76,81,82,79,80,85,86,83,84,89,90,87,88],,[1,2,3,4,5,6,7,1,1,10,12,11, 16,15,14,13,17,18,20,19,22,21,2,2,25,26,30,29,27,28,34,33,32,31,5,6,6,5,42,41, 40,39,16,15,14,13,13,14,15,16,34,33,32,31,31,32,33,34,34,33,32,31,31,32,33,34, 80,79,82,81,77,78,75,76,88,87,90,89,85,86,83,84,72,71,74,73,69,70,67,68],,[1, 2,3,4,6,5,7,9,8,10,1,1,14,13,16,15,18,17,19,20,22,21,24,23,26,25,29,30,28,27, 32,31,34,33,37,38,35,36,40,39,42,41,49,50,47,48,45,46,43,44,57,58,55,56,61,62, 59,60,65,66,63,64,53,54,51,52,29,30,29,30,28,27,28,27,29,30,29,30,28,27,28,27, 29,30,29,30,28,27,28,27],,,,,,[1,2,3,4,5,6,7,9,8,10,12,11,16,15,14,13,17,18, 20,19,22,21,24,23,25,26,1,1,1,1,34,33,32,31,38,37,36,35,42,41,40,39,46,45,44, 43,50,49,48,47,62,61,60,59,66,65,64,63,54,53,52,51,58,57,56,55,12,11,11,12,12, 11,11,12,12,11,11,12,12,11,11,12,12,11,11,12,12,11,11,12]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1],[90,10,9,0,10,10,2,0,0,1,-1,-1,10,10,10,10,2,2,2,2, 2,2,0,0,1,1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, -1,-1,-1,-1],[91,11,10,1,11,11,3,1,1,2,0,0,-9,-9,-9,-9,-1,-1,-1,-1,-1,-1,1,1, 2,2,0,0,0,0,-1,-1,-1,-1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1, -1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[ 91,11,10,1,-9,-9,-1,1,1,2,0,0,-1+10*E(4),-1-10*E(4),-1-10*E(4),-1+10*E(4), -1+2*E(4),-1-2*E(4),1,1,1,1,1,1,0,0,0,0,0,0,-E(4),E(4),E(4),-E(4),1,1,1,1, -1+E(4),-1-E(4),-1-E(4),-1+E(4),-1,-1,-1,-1,-1,-1,-1,-1,-E(4),E(4),E(4),-E(4), -E(4),E(4),E(4),-E(4),-E(4),E(4),E(4),-E(4),-E(4),E(4),E(4),-E(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], [GALOIS,[4,3]],[91,-9,10,1,-1+10*E(4),-1-10*E(4),1,1,1,0,0,0,10*E(8)-E(8)^2, E(8)^2-10*E(8)^3,E(8)^2+10*E(8)^3,-10*E(8)-E(8)^2,E(4),-E(4),1+E(8)-E(8)^3, 1-E(8)+E(8)^3,-1+E(8)+E(8)^3,-1-E(8)-E(8)^3,1,1,-1+E(4),-1-E(4),0,0,0,0, E(8)^3,-E(8),E(8),-E(8)^3,-1,-1,-1,-1,E(8)-E(8)^2,E(8)^2-E(8)^3,E(8)^2+E(8)^3, -E(8)-E(8)^2,-E(4),E(4),E(4),-E(4),-E(4),E(4),E(4),-E(4),E(8)^3,-E(8),E(8), -E(8)^3,-E(8)^3,E(8),-E(8),E(8)^3,E(8)^3,-E(8),E(8),-E(8)^3,-E(8)^3,E(8), -E(8),E(8)^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], [GALOIS,[6,7]], [GALOIS,[6,3]], [GALOIS,[6,5]],[640,0,-8,1,0,0,0,0,0,0,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6, E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4, E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4, E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6, E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6, E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4, E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4, E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6, E(7)+E(7)^2+E(7)^4], [GALOIS,[10,3]],[640,0,-8,1,0,0,0,0,0,0,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0, E(13)+E(13)^3+E(13)^9,E(13)^4+E(13)^10+E(13)^12,E(13)^7+E(13)^8+E(13)^11, E(13)^2+E(13)^5+E(13)^6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,E(13)+E(13)^3+E(13)^9,E(13)^4+E(13)^10+E(13)^12, E(13)+E(13)^3+E(13)^9,E(13)^4+E(13)^10+E(13)^12,E(13)^7+E(13)^8+E(13)^11, E(13)^2+E(13)^5+E(13)^6,E(13)^7+E(13)^8+E(13)^11,E(13)^2+E(13)^5+E(13)^6, E(13)+E(13)^3+E(13)^9,E(13)^4+E(13)^10+E(13)^12,E(13)+E(13)^3+E(13)^9, E(13)^4+E(13)^10+E(13)^12,E(13)^7+E(13)^8+E(13)^11,E(13)^2+E(13)^5+E(13)^6, E(13)^7+E(13)^8+E(13)^11,E(13)^2+E(13)^5+E(13)^6,E(13)+E(13)^3+E(13)^9, E(13)^4+E(13)^10+E(13)^12,E(13)+E(13)^3+E(13)^9,E(13)^4+E(13)^10+E(13)^12, E(13)^7+E(13)^8+E(13)^11,E(13)^2+E(13)^5+E(13)^6,E(13)^7+E(13)^8+E(13)^11, E(13)^2+E(13)^5+E(13)^6], [GALOIS,[12,4]], [GALOIS,[12,2]], [GALOIS,[12,7]],[640,0,-8,1,0,0,0,0,0,0,E(7)+E(7)^2+E(7)^4, E(7)^3+E(7)^5+E(7)^6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(13)+E(13)^3+E(13)^9, E(13)^4+E(13)^10+E(13)^12,E(13)^7+E(13)^8+E(13)^11,E(13)^2+E(13)^5+E(13)^6,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, E(91)^20+E(91)^73+E(91)^89,E(91)^2+E(91)^18+E(91)^71,E(91)^37+E(91)^60 +E(91)^85,E(91)^6+E(91)^31+E(91)^54,E(91)^38+E(91)^69+E(91)^75, E(91)^16+E(91)^22+E(91)^53,E(91)^23+E(91)^25+E(91)^43,E(91)^48+E(91)^66 +E(91)^68,E(91)^24+E(91)^33+E(91)^34,E(91)^57+E(91)^58+E(91)^67, E(91)^8+E(91)^11+E(91)^72,E(91)^19+E(91)^80+E(91)^83,E(91)^10+E(91)^82 +E(91)^90,E(91)+E(91)^9+E(91)^81,E(91)^30+E(91)^64+E(91)^88,E(91)^3+E(91)^27 +E(91)^61,E(91)^47+E(91)^59+E(91)^76,E(91)^15+E(91)^32+E(91)^44, E(91)^46+E(91)^50+E(91)^86,E(91)^5+E(91)^41+E(91)^45,E(91)^12+E(91)^17 +E(91)^62,E(91)^29+E(91)^74+E(91)^79,E(91)^4+E(91)^36+E(91)^51, E(91)^40+E(91)^55+E(91)^87], [GALOIS,[16,10]], [GALOIS,[16,3]], [GALOIS,[16,30]], [GALOIS,[16,57]], [GALOIS,[16,24]], [GALOIS,[16,19]], [GALOIS,[16,8]], [GALOIS,[16,16]], [GALOIS,[16,38]], [GALOIS,[16,48]], [GALOIS,[16,23]], [GALOIS,[16,2]], [GALOIS,[16,20]], [GALOIS,[16,6]], [GALOIS,[16,37]], [GALOIS,[16,29]], [GALOIS,[16,12]], [GALOIS,[16,40]], [GALOIS,[16,4]], [GALOIS,[16,15]], [GALOIS,[16,47]], [GALOIS,[16,5]], [GALOIS,[16,46]],[728,8,-1,-1,8,8,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,0,0,8,8,8, 8,0,0,0,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,-1,0,0,0,0,2,2,2,2,-E(5)-E(5)^4, -E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-1,-1,-1,-1,-E(5)-E(5)^4, 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[GALOIS,[42,2]],[728,-8,-1,-1,8*E(4),-8*E(4),0,-2,-2,1,0,0,8*E(8),-8*E(8)^3, 8*E(8)^3,-8*E(8),0,0,0,0,0,0,2,2,-E(4),E(4),0,0,0,0,0,0,0,0,-2*E(4),2*E(4), 2*E(4),-2*E(4),-E(8),E(8)^3,-E(8)^3,E(8),-2*E(8),2*E(8)^3,-2*E(8)^3,2*E(8), 2*E(8),-2*E(8)^3,2*E(8)^3,-2*E(8),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[44,7]], [GALOIS,[44,3]], [GALOIS,[44,5]],[728,8,-1,-1,8,8,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,0,0,-8,-8, -8,-8,0,0,0,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,-1,0,0,0,0,2*E(4),-2*E(4), -2*E(4),2*E(4),-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,1,1,1, 1,E(5)+E(5)^4,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)+E(5)^4, E(5)^2+E(5)^3,E(5)^2+E(5)^3,E(20)+E(20)^9,-E(20)-E(20)^9,-E(20)^13-E(20)^17, E(20)^13+E(20)^17,E(20)+E(20)^9,-E(20)-E(20)^9,-E(20)^13-E(20)^17, E(20)^13+E(20)^17,E(20)+E(20)^9,-E(20)-E(20)^9,-E(20)^13-E(20)^17, E(20)^13+E(20)^17,E(20)+E(20)^9,-E(20)-E(20)^9,-E(20)^13-E(20)^17, 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(67,85,75,69,83,77)(68,86,76,70,84,78)(71,89,79,73,87,81)(72,90,80,74,88,82), ( 8, 9)(23,24)(35,38)(36,37)(43,50)(44,49)(45,48)(46,47)(51,58,59,66) (52,57,60,65)(53,56,61,64)(54,55,62,63),( 5, 6)(13,14)(15,16)(17,18)(21,22) (25,26)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50) (51,60)(52,59)(53,62)(54,61)(55,64)(56,63)(57,66)(58,65),(67,83,75)(68,84,76) (69,85,77)(70,86,78)(71,87,79)(72,88,80)(73,89,81)(74,90,82)]); ARC("L3(9)","isSimple",true); ARC("L3(9)","extInfo",["","2^2"]); ARC("L3(9)","maxes",["3^4:GL2(9)","3^4:GL2(9)","U3(3)","L3(3)","A6.2_2", "8^2:S3","91:3"]); ARC("L3(9)","tomfusion",rec(name:="L3(9)",map:=[1,2,3,4,5,5,6,8,8,12,13,13,14, 14,14,14,17,17,16,16,15,15,30,30,32,32,36,36,36,36,39,39,39,39,59,59,59,59,63, 63,63,63,96,96,96,96,96,96,96,96,148,148,148,148,148,148,148,148,148,148,148, 148,148,148,148,148,157,157,157,157,157,157,157,157,157,157,157,157,157,157, 157,157,157,157,157,157,157,157,157,157],text:=[ "fusion map is unique" ])); ALF("L3(9)","L3(9).2_1",[1,2,3,4,5,5,6,7,8,9,10,10,11,11,12,12,13,13,14, 15,16,16,17,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,28, 28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,39,40, 40,41,41,42,42,43,43,44,44,45,45,46,46,47,47,48,48,49,49,50,50,51,51],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); ALF("L3(9)","L3(9).2_2",[1,2,3,4,5,5,6,7,7,8,9,9,10,11,10,11,12,12,13,13, 14,15,16,16,17,17,18,19,20,21,22,23,22,23,24,25,24,25,26,27,26,27,28,29, 28,29,30,31,30,31,32,33,32,33,34,35,34,35,36,37,36,37,38,39,38,39,40,41, 40,41,42,43,42,43,44,45,44,45,46,47,46,47,48,49,48,49,50,51,50,51],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); ALF("L3(9)","L3(9).2_3",[1,2,3,4,5,6,7,8,8,9,10,11,12,13,13,12,14,15,16, 16,17,17,18,18,19,20,21,21,22,22,23,24,24,23,25,26,26,25,27,28,28,27,29, 30,30,29,31,32,32,31,33,34,34,33,35,36,36,35,37,38,38,37,39,40,40,39,41, 42,42,41,43,44,44,43,45,46,46,45,47,48,48,47,49,50,50,49,51,52,52,51],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); MOT("L3(9).2_1", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13],\n", "constructions: SL(3,9) extended by transpose-inverse" ], [84913920,11520,11664,162,5760,128,160,160,144,91,5760,5760,64,128,128,64,160, 160,72,91,91,80,80,80,80,72,72,80,80,80,80,80,80,80,80,80,80,80,80,91,91,91, 91,91,91,91,91,91,91,91,91,1440,1440,18,16,20,20,36,36,16,16,20,20], [,[1,1,3,4,2,2,8,7,3,10,5,5,5,6,6,6,8,7,9,21,20,11,12,18,17,19,19,25,24,25,24, 31,30,29,28,31,30,29,28,51,50,48,49,43,42,40,41,47,46,44,45,1,2,4,6,8,7,9,9, 14,15,18,17],[1,2,1,1,5,6,8,7,2,10,12,11,13,15,14,16,18,17,5,20,21,23,22,25, 24,12,11,29,28,31,30,33,32,35,34,37,36,39,38,41,40,43,42,45,44,47,46,49,48,51, 50,52,53,52,55,57,56,53,53,61,60,63,62],,[1,2,3,4,5,6,1,1,9,10,12,11,13,15,14, 16,2,2,19,21,20,23,22,5,5,27,26,12,11,11,12,23,22,22,23,23,22,22,23,46,47,45, 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[TENSOR,[60,2]],[1820,-20,38,2,-20,4,0,0,-2,0,0,0,0,-4,-4,4,0,0,-2,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0],[1820,-20,38,2,20,-4,0,0,-2,0,-20,-20,4,0,0,0,0,0,2,0,0,0,0,0,0,-2,-2,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]], [(58,59),(40,49,44,41,48,45)(42,51,46,43,50,47),(32,36)(33,37)(34,38)(35,39), (20,21)(40,47,49,42,44,51,41,46,48,43,45,50),(11,12)(14,15)(22,23)(26,27) (28,30)(29,31)(32,34,36,38)(33,35,37,39)(60,61),( 7, 8)(17,18)(24,25)(28,31) (29,30)(32,35,36,39)(33,34,37,38)(56,57)(62,63)]); ALF("L3(9).2_1","L3(9).2^2",[1,2,3,4,5,6,7,7,8,9,10,10,11,12,12,13,14,14, 15,16,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,28, 28,29,29,30,30,31,31,32,32,33,34,35,36,37,37,38,39,40,40,41,41],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); MOT("L3(9).2_2", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13],\n", "constructions: PGammaL(3,9), SigmaL(3,9), PSigmaL(3,9)", ], [84913920,11520,11664,162,5760,128,80,144,91,5760,5760,64,64,128,128,80,72, 182,182,182,182,80,80,80,80,72,72,80,80,80,80,80,80,80,80,80,80,80,80,91,91, 91,91,91,91,91,91,91,91,91,91,11232,96,108,18,16,12,16,16,26,26,26,26], [,[1,1,3,4,2,2,7,3,9,5,5,5,6,6,6,7,8,21,20,18,19,10,11,16,16,17,17,25,24,25, 24,31,30,29,28,31,30,29,28,51,50,48,49,43,42,40,41,47,46,44,45,1,2,3,4,6,8,14, 15,21,20,18,19],[1,2,1,1,5,6,7,2,9,10,11,12,13,14,15,16,5,18,19,20,21,22,23, 24,25,10,11,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49, 50,51,52,53,52,52,56,53,58,59,60,61,62,63],,[1,2,3,4,5,6,1,8,9,11,10,12,13,15, 14,2,17,21,20,18,19,23,22,5,5,27,26,11,10,10,11,23,22,22,23,23,22,22,23,47,46, 44,45,51,50,48,49,43,42,40,41,52,53,54,55,56,57,59,58,63,62,60,61],,[1,2,3,4, 5,6,7,8,1,11,10,12,13,15,14,16,17,20,21,19,18,23,22,24,25,27,26,30,31,28,29, 34,35,36,37,38,39,32,33,20,21,19,18,20,21,19,18,20,21,19,18,52,53,54,55,56,57, 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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],[910,-10,19, 1,10,-2,0,-1,0,-10+10*E(8)+10*E(8)^3,-10-10*E(8)-10*E(8)^3,2,0, -2*E(8)-2*E(8)^3,2*E(8)+2*E(8)^3,0,1,0,0,0,0,0,0,0,0,-1+E(8)+E(8)^3, -1-E(8)-E(8)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,26,-2,-1,-1,0, 1,-E(8)-E(8)^3,E(8)+E(8)^3,0,0,0,0], [TENSOR,[60,2]], [GALOIS,[60,5]], [TENSOR,[62,2]]], [(40,48,44)(41,49,45)(42,50,46)(43,51,47),(32,36)(33,37)(34,38)(35,39),(24,25) (28,31)(29,30)(32,35,36,39)(33,34,37,38),(18,21,19,20)(40,47,49,42,44,51,41, 46,48,43,45,50)(60,63,61,62),(10,11)(14,15)(22,23)(26,27)(28,30)(29,31) (32,34,36,38)(33,35,37,39)(58,59),(10,11)(14,15)(22,23)(24,25)(26,27)(28,29) (30,31)(32,37)(33,36)(34,39)(35,38)(58,59)]); ALF("L3(9).2_2","L3(9).2^2",[1,2,3,4,5,6,7,8,9,10,10,11,12,13,13,14,15,16, 16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,28, 28,29,29,30,30,31,31,32,32,42,43,44,45,46,47,48,48,49,49,50,50],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); MOT("L3(9).2_3", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]" ], [84913920,11520,11664,162,11520,11520,128,80,144,182,182,5760,5760,128,128,64, 64,80,144,144,91,91,80,80,80,80,72,72,80,80,80,80,80,80,80,80,80,80,80,80,91, 91,91,91,91,91,91,91,91,91,91,91,12096,192,216,18,192,192,32,24,14,14,16,16, 24,24], [,[1,1,3,4,2,2,2,8,3,10,11,5,6,5,6,7,7,8,9,9,22,21,12,13,18,18,19,20,25,26,25, 26,31,32,29,30,31,32,29,30,51,52,49,50,43,44,41,42,47,48,45,46,1,2,3,4,5,6,7, 9,10,11,14,15,19,20],[1,2,1,1,6,5,7,8,2,11,10,13,12,15,14,16,17,18,6,5,21,22, 24,23,26,25,13,12,30,29,32,31,34,33,36,35,38,37,40,39,42,41,44,43,46,45,48,47, 50,49,52,51,53,54,53,53,58,57,59,54,62,61,64,63,58,57],,[1,2,3,4,5,6,7,1,9,11, 10,12,13,14,15,16,17,2,19,20,22,21,23,24,5,6,27,28,12,13,12,13,23,24,23,24,23, 24,23,24,48,47,46,45,52,51,50,49,44,43,42,41,53,54,55,56,57,58,59,60,62,61,63, 64,65,66],,[1,2,3,4,6,5,7,8,9,1,1,13,12,15,14,16,17,18,20,19,22,21,24,23,26, 25,28,27,32,31,30,29,36,35,38,37,40,39,34,33,22,22,21,21,22,22,21,21,22,22,21, 21,53,54,55,56,58,57,59,60,53,53,64,63,66,65],,,,,,[1,2,3,4,5,6,7,8,9,11,10, 12,13,14,15,16,17,18,19,20,1,1,23,24,25,26,27,28,29,30,31,32,37,38,39,40,33, 34,35,36,11,10,11,10,11,10,11,10,11,10,11,10,53,54,55,56,57,58,59,60,62,61,63, 64,65,66]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[90,10,9,0,10,10,2,0,1,-1,-1, 10,10,2,2,2,2,0,1,1,-1,-1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1, -1,-1,-1,-1,-1,-1,-1,6,-2,-3,0,-2,-2,2,1,-1,-1,0,0,1,1], [TENSOR,[3,2]],[91,11,10,1,11,11,3,1,2,0,0,-9,-9,-1,-1,-1,-1,1,2,2,0,0,-1,-1, 1,1,0,0,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,7,-1,-2,1,3,3, -1,2,0,0,-1,-1,0,0], [TENSOR,[5,2]],[91,11,10,1,-9,-9,-1,1,2,0,0,-1+10*E(4),-1-10*E(4),-1+2*E(4), -1-2*E(4),1,1,1,0,0,0,0,-E(4),E(4),1,1,-1+E(4),-1-E(4),-1,-1,-1,-1,-E(4),E(4), -E(4),E(4),-E(4),E(4),-E(4),E(4),0,0,0,0,0,0,0,0,0,0,0,0,7,3,-2,1,-1+2*E(4), -1-2*E(4),1,0,0,0,-E(4),E(4),-1-E(4),-1+E(4)], [TENSOR,[7,2]], [GALOIS,[7,3]], [TENSOR,[9,2]],[182,-18,20,2,-2+20*E(4),-2-20*E(4),2,2,0,0,0,-2*E(4),2*E(4), 2*E(4),-2*E(4),2,-2,2,-2+2*E(4),-2-2*E(4),0,0,0,0,-2,-2,-2*E(4),2*E(4), -2*E(4),2*E(4),-2*E(4),2*E(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, 0,0,0,0,0,0,0,0,0,0], [GALOIS,[11,3]],[640,0,-8,1,0,0,0,0,0,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6, 0,0,0,0,0,0,0,0,0,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(7)+E(7)^2+E(7)^4, E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6, E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4, E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6, E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,32,0,-4,-1,0,0,0,0,-E(7)-E(7)^2-E(7)^4 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[GALOIS,[19,12]], [GALOIS,[19,15]], [GALOIS,[19,5]],[1456,16,-2,-2,16,16,0,1,-2,0,0,16,16,0,0,0,0,1,-2,-2,0,0,4,4, 1,1,-2,-2,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0],[1456,16,-2,-2,16,16,0,1,-2,0,0,16,16,0,0,0,0,1,-2,-2,0,0,-4, -4,1,1,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0],[1456,-16,-2,-2,16*E(4),-16*E(4),0,-4,2,0,0,0,0,0,0,0,0,4, -2*E(4),2*E(4),0,0,0,0,-4*E(4),4*E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[33,3]],[1456,16,-2,-2,16,16,0,1,-2,0,0,-16,-16,0,0,0,0,1,-2,-2,0,0, 4*E(4),-4*E(4),1,1,2,2,-1,-1,-1,-1,-E(4),E(4),-E(4),E(4),-E(4),E(4),-E(4), E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[35,3]],[1456,16,-2,-2,-16,-16,0,1,-2,0,0,16*E(4),-16*E(4),0,0,0,0,1, 2,2,0,0,0,0,-1,-1,-2*E(4),2*E(4),E(4),-E(4),E(4),-E(4),E(40)^13-E(40)^21 -E(40)^29+E(40)^37,-E(40)^7-E(40)^23+E(40)^31+E(40)^39,-E(40)^13+E(40)^21 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[GALOIS,[41,17]], [GALOIS,[41,7]],[729,9,0,0,9,9,1,-1,0,1,1,9,9,1,1,1,1,-1,0,0,1,1,-1,-1,-1,-1, 0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,27,3,0,0,3,3, -1,0,-1,-1,1,1,0,0], [TENSOR,[49,2]],[819,19,9,0,19,19,3,-1,1,0,0,-1,-1,-1,-1,-1,-1,-1,1,1,0,0,1,1, -1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,21,5,3,0,1,1, 1,-1,0,0,-1,-1,1,1], [TENSOR,[51,2]],[819,19,9,0,-1,-1,-1,-1,1,0,0,-9+10*E(4),-9-10*E(4),-1+2*E(4), -1-2*E(4),1,1,-1,-1,-1,0,0,E(4),-E(4),-1,-1,E(4),-E(4),1,1,1,1,E(4),-E(4), E(4),-E(4),E(4),-E(4),E(4),-E(4),0,0,0,0,0,0,0,0,0,0,0,0,21,1,3,0,-3-2*E(4), -3+2*E(4),-1,1,0,0,-E(4),E(4),E(4),-E(4)], [TENSOR,[53,2]], [GALOIS,[53,3]], [TENSOR,[55,2]],[1638,-2,18,0,-18+20*E(4),-18-20*E(4),2,-2,-2,0,0,-18*E(4), 18*E(4),2*E(4),-2*E(4),2,-2,-2,2*E(4),-2*E(4),0,0,0,0,2,2,0,0,2*E(4),-2*E(4), 2*E(4),-2*E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0], [GALOIS,[57,3]],[910,30,19,1,-10,-10,-2,0,3,0,0,10,10,2,2,-2,-2,0,-1,-1,0,0,0, 0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,14,-2,5,-1,2,2,2,1, 0,0,0,0,-1,-1], [TENSOR,[59,2]],[1820,-20,38,2,20,20,-4,0,-2,0,0,20,20,-4,-4,0,0,0,2,2,0,0,0, 0,0,0,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0],[910,-10,19,1,-10+20*E(4),-10-20*E(4),2,0,-1,0,0,10*E(4),-10*E(4), -2*E(4),2*E(4),-2,2,0,-1+2*E(4),-1-2*E(4),0,0,0,0,0,0,E(4),-E(4),0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,28,-4,1,1,-4*E(4),4*E(4),0,-1,0,0,0,0, -E(4),E(4)], [TENSOR,[62,2]], [GALOIS,[62,3]], [TENSOR,[64,2]],[1820,-20,38,2,20,20,-4,0,-2,0,0,-20,-20,4,4,0,0,0,2,2,0,0,0, 0,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0]], [(33,37)(34,38)(35,39)(36,40),(29,31)(30,32)(33,35,37,39)(34,36,38,40),(21,22) (41,47,49,43,45,51)(42,48,50,44,46,52),(10,11)(41,50,45,42,49,46) (43,52,47,44,51,48)(61,62),( 5, 6)(12,13)(14,15)(19,20)(23,24)(25,26)(27,28) (29,30)(31,32)(33,38)(34,37)(35,40)(36,39)(57,58)(63,64)(65,66),(41,45,49) (42,46,50)(43,47,51)(44,48,52)]); ALF("L3(9).2_3","L3(9).2^2",[1,2,3,4,5,5,6,7,8,9,9,10,10,11,11,12,13,14, 15,15,16,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27, 28,28,29,29,30,30,31,31,32,32,51,52,53,54,55,55,56,57,58,58,59,59,60,60],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); MOT("L3(9).2^2", [ "constructed using `PossibleCharacterTablesOfTypeGV4',\n", "constructions: Aut(L3(9)), SigmaL(3,9) extended by transpose-inverse", ], [169827840,23040,23328,324,11520,256,160,288,182,5760,128,128,128,160,144,182, 182,80,80,72,80,80,80,80,80,80,91,91,91,91,91,91,2880,2880,36,32,20,72,72,16, 20,22464,192,216,36,32,24,16,26,26,24192,384,432,36,192,64,48,14,16,24], [,[1,1,3,4,2,2,7,3,9,5,5,6,6,7,8,17,16,10,14,15,19,19,22,21,22,21,32,31,28,27, 30,29,1,2,4,6,7,8,8,12,14,1,2,3,4,6,8,13,17,16,1,2,3,4,5,6,8,9,11,15],[1,2,1,1 ,5,6,7,2,9,10,11,12,13,14,5,16,17,18,19,10,21,22,23,24,25,26,27,28,29,30,31,32 ,33,34,33,36,37,34,34,40,41,42,43,42,42,46,43,48,49,50,51,52,51,51,55,56,52,58 ,59,55],,[1,2,3,4,5,6,1,8,9,10,11,12,13,2,15,17,16,18,5,20,10,10,18,18,18,18, 30,29,32,31,28,27,33,34,35,36,33,38,39,40,34,42,43,44,45,46,47,48,50,49,51,52, 53,54,55,56,57,58,59,60],,[1,2,3,4,5,6,7,8,1,10,11,12,13,14,15,17,16,18,19,20, 22,21,24,25,26,23,17,16,17,16,17,16,33,34,35,36,37,38,39,40,41,42,43,44,45,46, 47,48,50,49,51,52,53,54,55,56,57,51,59,60],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13 ,14,15,1,1,18,19,20,21,22,25,26,23,24,9,9,9,9,9,9,33,34,35,36,37,38,39,40,41, 42,43,44,45,46,47,48,42,42,51,52,53,54,55,56,57,58,59,60]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1, -1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-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]],[90,10,9,0,10,2,0,1,-1,10,2,2,2,0,1,-1,-1,0,0,1,0,0,0,0,0,0,-1 ,-1,-1,-1,-1,-1,0,0,0,0,0,3,-3,0,0,12,4,3,0,0,1,0,-1,-1,6,-2,-3,0,-2,2,1,-1,0, 1], [TENSOR,[5,2]], [TENSOR,[5,3]], [TENSOR,[5,4]],[91,11,10,1,11,3,1,2,0,-9,-1,-1,-1,1,2,0,0,-1,1,0,1,1,-1,-1,-1 ,-1,0,0,0,0,0,0,1,9,1,1,1,0,0,-1,-1,13,-3,4,1,1,0,-1,0,0,7,-1,-2,1,3,-1,2,0,-1 ,0], [TENSOR,[9,2]], [TENSOR,[9,3]], [TENSOR,[9,4]],[182,22,20,2,-18,-2,2,4,0,-2,-2,2,2,2,0,0,0,0,2,-2,-2,-2,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,14,6,-4,2,-2,2,0,0,0,-2], [TENSOR,[13,2]],[364,-36,40,4,-4,4,4,0,0,0,0,4,-4,4,-4,0,0,0,-4,0,0,0,0,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1280,0, -16,2,0,0,0,0,-1,0,0,0,0,0,0,6,6,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,0,0,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,64,0,-8,-2,0,0,0,1,0,0], [TENSOR,[16,2]],[1280,0,-16,2,0,0,0,0,6,0,0,0,0,0,0, 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)^11,0,0,0,0,0,0,0,0,0, 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, 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, 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)^11,0,0,0,0,0,0,0,0,0,32,0,-4,2,0 ,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)^11,0,0,0,0,0,0,0,0,0,0], [TENSOR,[18,2]], [GALOIS,[18,2]], [TENSOR,[20,2]],[2560,0,-32,4,0,0,0,0,-2,0,0,0,0,0,0, 2*E(13)+2*E(13)^3+2*E(13)^4+2*E(13)^9+2*E(13)^10+2*E(13)^12, 2*E(13)^2+2*E(13)^5+2*E(13)^6+2*E(13)^7+2*E(13)^8+2*E(13)^11,0,0,0,0,0,0,0,0,0 , E(91)^2+E(91)^6+E(91)^18+E(91)^20+E(91)^31+E(91)^37+E(91)^54+E(91)^60+E(91)^71 +E(91)^73+E(91)^85+E(91)^89 , E(91)^16+E(91)^22+E(91)^23+E(91)^25+E(91)^38+E(91)^43+E(91)^48+E(91)^53 +E(91)^66+E(91)^68+E(91)^69+E(91)^75 , E(91)^8+E(91)^11+E(91)^19+E(91)^24+E(91)^33+E(91)^34+E(91)^57+E(91)^58 +E(91)^67+E(91)^72+E(91)^80+E(91)^83 , E(91)+E(91)^3+E(91)^9+E(91)^10+E(91)^27+E(91)^30+E(91)^61+E(91)^64+E(91)^81 +E(91)^82+E(91)^88+E(91)^90 , E(91)^5+E(91)^15+E(91)^32+E(91)^41+E(91)^44+E(91)^45+E(91)^46+E(91)^47 +E(91)^50+E(91)^59+E(91)^76+E(91)^86 , E(91)^4+E(91)^12+E(91)^17+E(91)^29+E(91)^36+E(91)^40+E(91)^51+E(91)^55 +E(91)^62+E(91)^74+E(91)^79+E(91)^87 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[22,8]], [GALOIS,[22,16]], [GALOIS,[22,2]], [GALOIS,[22,4]], [GALOIS,[22,5]],[1456,16,-2,-2,16,0,1,-2,0,16,0,0,0,1,-2,0,0,4,1,-2,1,1,-1,-1 ,-1,-1,0,0,0,0,0,0,16,-16,-2,0,1,2,2,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0], [TENSOR,[28,3]],[1456,16,-2,-2,16,0,1,-2,0,16,0,0,0,1,-2,0,0,-4,1,-2,1,1,1,1, 1,1,0,0,0,0,0,0,16,16,-2,0,1,-2,-2,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[30,3]],[2912,-32,-4,-4,0,0,-8,4,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2912,32, -4,-4,32,0,2,-4,0,-32,0,0,0,2,-4,0,0,0,2,4,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2912,32,-4,-4,-32,0,2,-4,0,0, 0,0,0,2,4,0,0,0,-2,0,0,0, -E(40)^7+E(40)^13-E(40)^21-E(40)^23-E(40)^29+E(40)^31+E(40)^37+E(40)^39, E(40)^7-E(40)^13+E(40)^21+E(40)^23+E(40)^29-E(40)^31-E(40)^37-E(40)^39, -E(40)^7+E(40)^13-E(40)^21-E(40)^23-E(40)^29+E(40)^31+E(40)^37+E(40)^39, E(40)^7-E(40)^13+E(40)^21+E(40)^23+E(40)^29-E(40)^31-E(40)^37-E(40)^39,0,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[34,7]],[2912,-32,-4,-4,0,0,2,4,0,0,0,0,0,-2,0,0,0,0,0,0, -E(40)^7+E(40)^13-E(40)^21-E(40)^23-E(40)^29+E(40)^31+E(40)^37+E(40)^39, E(40)^7-E(40)^13+E(40)^21+E(40)^23+E(40)^29-E(40)^31-E(40)^37-E(40)^39, E(80)^3+E(80)^9-E(80)^31-E(80)^37-E(80)^41+E(80)^53-E(80)^67+E(80)^79, -E(80)^19+E(80)^21-E(80)^47+E(80)^51-E(80)^57+E(80)^63-E(80)^69+E(80)^73, -E(80)^3-E(80)^9+E(80)^31+E(80)^37+E(80)^41-E(80)^53+E(80)^67-E(80)^79, E(80)^19-E(80)^21+E(80)^47-E(80)^51+E(80)^57-E(80)^63+E(80)^69-E(80)^73,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[36,11]], [GALOIS,[36,13]], [GALOIS,[36,7]],[729,9,0,0,9,1,-1,0,1,9,1,1,1,-1,0,1,1,-1,-1,0,-1,-1,-1,-1,-1 ,-1,1,1,1,1,1,1,9,9,0,1,-1,0,0,1,-1,27,3,0,0,-1,0,-1,1,1,27,3,0,0,3,-1,0,-1,1, 0], [TENSOR,[40,2]], [TENSOR,[40,3]], [TENSOR,[40,4]],[819,19,9,0,19,3,-1,1,0,-1,-1,-1,-1,-1,1,0,0,1,-1,-1,-1,-1,1, 1,1,1,0,0,0,0,0,0,9,1,0,1,-1,1,1,-1,1,39,-1,3,0,-1,-1,1,0,0,21,5,3,0,1,1,-1,0, -1,1], [TENSOR,[44,2]], [TENSOR,[44,3]], [TENSOR,[44,4]],[1638,38,18,0,-2,-2,-2,2,0,-18,-2,2,2,-2,-2,0,0,0,-2,0,2,2,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,42,2,6,0,-6,-2,2,0,0,0], [TENSOR,[48,2]],[3276,-4,36,0,-36,4,-4,-4,0,0,0,4,-4,-4,0,0,0,0,4,0,0,0,0,0,0 --> -------------------- --> maximum size reached --> -------------------- [ Dauer der Verarbeitung: 0.26 Sekunden (vorverarbeitet) ] |
2026-03-28