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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, 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-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 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[910, 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[,[1,1,1,4,5,6,7,2,3,2,11,5,6,4,5,6,9,18,19,11,12,13,14,26,27,25,24,20,20],[1, 2,3,1,1,1,1,8,9,10,11,2,2,3,3,3,17,4,4,20,8,8,9,24,25,26,27,28,29],,[1,2,3,4, 5,6,7,8,9,10,1,12,13,14,15,16,17,18,19,2,21,22,23,26,27,25,24,8,8],,,,,,,,[1, 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,1,1,1,1,29,28]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[26,6,2,-1,-1,8, -1,4,2,0,1,3,0,-1,-1,2,0,2,-1,1,1,-2,-1,0,0,0,0,-1,-1],[26,6,2,-1,8,-1,-1,4,2, 0,1,0,3,-1,2,-1,0,-1,2,1,-2,1,-1,0,0,0,0,-1,-1],[39,-1,7,12,3,3,3,-1,3,-1,-1, -1,-1,4,1,1,1,0,0,-1,-1,-1,0,0,0,0,0,-1,-1],[52,8,-4,-2,7,7,-2,-10,0,2,2,-1, -1,2,-1,-1,0,1,1,-2,-1,-1,0,0,0,0,0,0,0],[65,5,-7,11,2,11,2,-5,1,-1,0,2,-1,-1, 2,-1,-1,2,-1,0,-2,1,1,0,0,0,0,0,0],[65,5,-7,11,11,2,2,-5,1,-1,0,-1,2,-1,-1,2, -1,-1,2,0,1,-2,1,0,0,0,0,0,0],[90,10,10,9,9,9,0,10,-2,2,0,1,1,1,1,1,0,0,0,0,1, 1,1,-1,-1,-1,-1,0,0],[234,14,2,-9,18,-9,0,-4,2,0,-1,2,-1,-1,2,-1,0,0,0,-1,2, -1,-1,0,0,0,0,1,1],[234,14,2,-9,-9,18,0,-4,2,0,-1,-1,2,-1,-1,2,0,0,0,-1,-1,2, -1,0,0,0,0,1,1],[260,0,-4,-10,17,-1,-1,10,0,-2,0,-3,3,2,-1,-1,0,2,-1,0,1,1,0, 0,0,0,0,0,0],[260,0,-4,-10,-1,17,-1,10,0,-2,0,3,-3,2,-1,-1,0,-1,2,0,1,1,0,0,0, 0,0,0,0],[260,20,4,17,-10,-10,-1,0,4,0,0,2,2,1,-2,-2,0,-1,-1,0,0,0,1,0,0,0,0, 0,0],[351,-9,15,27,0,0,0,-9,-1,-1,1,0,0,3,0,0,-1,0,0,1,0,0,-1,0,0,0,0,1,1],[ 390,-10,-10,39,3,3,3,10,2,2,0,-1,-1,-1,-1,-1,0,0,0,0,1,1,-1,0,0,0,0,0,0],[416, 16,0,-16,2,2,2,16,0,0,1,-2,-2,0,0,0,0,-1,-1,1,-2,-2,0,0,0,0,0,1,1],[416,16,0, -16,2,2,2,-16,0,0,1,-2,-2,0,0,0,0,-1,-1,1,2,2,0,0,0,0,0,-1,-1],[416,-16,0,-16, 2,2,2,0,0,0,1,2,2,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,E(20)+E(20)^9-E(20)^13 -E(20)^17,-E(20)-E(20)^9+E(20)^13+E(20)^17], [GALOIS,[18,11]],[468,-8,-4,-18,9,9,0,-10,0,2,-2,1,1,2,-1,-1,0,0,0,2,-1,-1,0, 0,0,0,0,0,0],[585,5,1,18,-9,18,0,-5,-3,-1,0,-1,2,-2,1,-2,1,0,0,0,1,-2,0,0,0,0, 0,0,0],[585,5,1,18,18,-9,0,-5,-3,-1,0,2,-1,-2,-2,1,1,0,0,0,-2,1,0,0,0,0,0,0, 0],[640,0,0,-8,-8,-8,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,E(13)+E(13)^3+E(13)^9, E(13)^4+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], [GALOIS,[23,4]], [GALOIS,[23,7]], [GALOIS,[23,2]],[729,9,9,0,0,0,0,9,-3,1,-1,0,0,0,0,0,-1,0,0,-1,0,0,0,1,1,1,1, -1,-1],[780,-20,12,-3,6,6,-3,0,4,0,0,-2,-2,-3,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],[ 1040,0,-16,14,-4,-4,-4,0,0,0,0,0,0,2,2,2,0,-1,-1,0,0,0,0,0,0,0,0,0,0]], [(28,29),(24,26,25,27),( 5, 6)(12,13)(15,16)(18,19)(21,22),(24,25)(26,27), (24,27,25,26)]); ARC("L4(3)","CAS",[rec(name:="psl(4,3)", permchars:=( 2, 3)( 6, 7)(11,12,13)(21,22)(25,26), permclasses:=(12,13)(18,19)(21,22), text:=[ "names:=psl[4,3]; psl4[3], pom6[3,+]\n", " a3[3] d3[3] [lie-not.]\n", " order: 2^7.3^6.5.13 = 6,065,280\n", " number of classes: 29\n", " source:hunt, d.c.\n", " character tables of certain finite simple groups\n", " bull.austral.math.soc. 5\n", " [1971], 1-42\n", " comments: - \n", ""])]); ARC("L4(3)","projectives",["2.L4(3)",[[40,0,0,13,4,4,4,0,4,0,0,0,0,-3,0,0,0,1, 1,0,0,0,1,1,1,1,1,0,0],[208,0,0,-8,-8,10,1,-4*E(8)-4*E(8)^3,0,0,-2,0,0,0,0,0, 0,-2,1,0,2*E(8)+2*E(8)^3,-E(8)-E(8)^3,0,0,0,0,0,E(8)+E(8)^3,E(8)+E(8)^3], [GALOIS,[2,5]],[208,0,0,-8,10,-8,1,-4*E(8)-4*E(8)^3,0,0,-2,0,0,0,0,0,0,1,-2,0, -E(8)-E(8)^3,2*E(8)+2*E(8)^3,0,0,0,0,0,E(8)+E(8)^3,E(8)+E(8)^3], [GALOIS,[4,5]],[260,0,0,17,-10,-10,-1,10*E(8)+10*E(8)^3,2,0,0,0,0,-3,0,0, E(8)+E(8)^3,-1,-1,0,E(8)+E(8)^3,E(8)+E(8)^3,-1,0,0,0,0,0,0], [GALOIS,[6,5]],[416,0,0,-16,2,2,2,8*E(8)+8*E(8)^3,0,0,1,0,0,0,0,0,0,-1,-1, E(20)+E(20)^9-E(20)^13-E(20)^17,-E(8)-E(8)^3,-E(8)-E(8)^3,0,0,0,0,0, -E(40)^7-E(40)^21-E(40)^23-E(40)^29,-E(40)^13-E(40)^31-E(40)^37-E(40)^39], [GALOIS,[8,13]], [GALOIS,[8,7]], [GALOIS,[8,11]],[480,0,0,48,12,12,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1, -1,0,0],[520,0,0,-20,16,16,-2,0,4,0,0,0,0,0,0,0,0,1,1,0,0,0,-2,0,0,0,0,0,0],[ 520,0,0,7,-20,16,-2,0,4,0,0,0,0,3,0,0,0,1,-2,0,0,0,1,0,0,0,0,0,0],[520,0,0,7, 16,-20,-2,0,4,0,0,0,0,3,0,0,0,-2,1,0,0,0,1,0,0,0,0,0,0],[640,0,0,-8,-8,-8,1,0, 0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,E(13)+E(13)^3+E(13)^9,E(13)^4+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], [GALOIS,[16,4]], [GALOIS,[16,7]], [GALOIS,[16,2]],[780,0,0,-3,6,6,-3,10*E(8)+10*E(8)^3,-2,0,0,0,0,-3,0,0, -E(8)-E(8)^3,0,0,0,E(8)+E(8)^3,E(8)+E(8)^3,1,0,0,0,0,0,0], [GALOIS,[20,5]],[1080,0,0,27,0,0,0,0,-4,0,0,0,0,3,0,0,0,0,0,0,0,0,-1,1,1,1,1, 0,0]],]); ARC("L4(3)","isSimple",true); ARC("L4(3)","extInfo",["2","2^2"]); ARC("L4(3)","tomfusion",rec(name:="L4(3)",map:=[1,2,3,4,5,6,7,8,10,9,17,28, 27,26,29,30,49,61,62,65,82,83,84,91,91,91,91,152,152],text:=[ "fusion map is unique up to table automorphisms" ])); ARC("L4(3)","maxes",["3^3:L3(3)","3^3:L3(3)","U4(2).2","L4(3)M4", "3^4:2(A4xA4).2","(4xA6):2","A6.2_2","S4xS4"]); ALF("L4(3)","L4(3).2_1",[1,2,3,4,5,5,6,7,8,9,10,11,11,12,13,13,14,15,15, 16,17,17,18,19,20,21,22,23,24],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); ALF("L4(3)","L4(3).2_2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19, 20,21,22,23,24,24,25,25,26,26],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); ALF("L4(3)","L4(3).2_3",[1,2,3,4,5,5,6,7,8,9,10,11,11,12,13,13,14,15,15, 16,17,17,18,19,19,20,20,21,21],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); ALF("L4(3)","3^6:L4(3)",[1,5,9,18,23,29,35,44,45,50,53,56,59,63,73,78,83, 86,90,94,95,96,105,106,107,108,109,110,111],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); ALN("L4(3)",["O6+(3)","psl(4,3)"]); MOT("L4(3).2_1", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13],\n", "constructions: PGL(4,3)" ], [12130560,5760,2304,11664,1944,162,2880,192,64,40,72,144,36,16,27,40,36,24,26, 26,26,26,40,40,11232,32,108,18,192,192,80,80,32,24,24,26,26,26,26,40,40,40, 40], [,[1,1,1,4,5,6,2,3,2,10,5,4,5,8,15,10,11,12,21,22,20,19,16,16,1,3,4,6,8,8,7,7, 8,18,18,21,22,20,19,24,23,24,23],[1,2,3,1,1,1,7,8,9,10,2,3,3,14,4,16,7,8,19, 20,21,22,23,24,25,26,25,25,29,30,31,32,33,29,30,36,37,38,39,40,41,42,43],,[1, 2,3,4,5,6,7,8,9,1,11,12,13,14,15,2,17,18,21,22,20,19,7,7,25,26,27,28,30,29,32, 31,33,35,34,38,39,37,36,32,31,31,32],,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14, 15,16,17,18,1,1,1,1,24,23,25,26,27,28,30,29,32,31,33,35,34,25,25,25,25,41,40, 43,42]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1, -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[52,12,4,-2,7,-2,8,4,0,2,3,-2,1,0,1,2, -1,-2,0,0,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[39,-1,7,12,3,3,-1, 3,-1,-1,-1,4,1,1,0,-1,-1,0,0,0,0,0,-1,-1,13,1,4,1,3,3,-1,-1,-1,0,0,0,0,0,0,-1, -1,-1,-1], [TENSOR,[4,2]],[52,8,-4,-2,7,-2,-10,0,2,2,-1,2,-1,0,1,-2,-1,0,0,0,0,0,0,0,0,0, 0,0,2*E(8)+2*E(8)^3,-2*E(8)-2*E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,0,-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,[6,2]],[130,10,-14,22,13,4,-10,2,-2,0,1,-2,1,-2,1,0,-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],[90,10,10,9,9,0,10,-2,2,0,1,1,1,0,0,0, 1,1,-1,-1,-1,-1,0,0,12,0,3,0,-2,-2,0,0,2,1,1,-1,-1,-1,-1,0,0,0,0], [TENSOR,[9,2]],[468,28,4,-18,9,0,-8,4,0,-2,1,-2,1,0,0,-2,1,-2,0,0,0,0,2,2,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[520,0,-8,-20,16,-2,20,0,-4,0,0,4,-2,0,1,0, 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],[260,20,4,17,-10,-1,0, 4,0,0,2,1,-2,0,-1,0,0,1,0,0,0,0,0,0,26,2,-1,-1,2,2,0,0,2,-1,-1,0,0,0,0,0,0,0, 0], [TENSOR,[13,2]],[351,-9,15,27,0,0,-9,-1,-1,1,0,3,0,-1,0,1,0,-1,0,0,0,0,1,1,39, -1,3,0,-1,-1,1,1,-1,-1,-1,0,0,0,0,1,1,1,1], [TENSOR,[15,2]],[390,-10,-10,39,3,3,10,2,2,0,-1,-1,-1,0,0,0,1,-1,0,0,0,0,0,0, 26,-2,-1,-1,4,4,0,0,0,1,1,0,0,0,0,0,0,0,0], [TENSOR,[17,2]],[416,16,0,-16,2,2,16,0,0,1,-2,0,0,0,-1,1,-2,0,0,0,0,0,1,1,0,0, 0,0,0,0,4,4,0,0,0,0,0,0,0,-1,-1,-1,-1], [TENSOR,[19,2]],[416,16,0,-16,2,2,-16,0,0,1,-2,0,0,0,-1,1,2,0,0,0,0,0,-1,-1,0, 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,[21,2]],[416,-16,0,-16,2,2,0,0,0,1,2,0,0,0,-1,-1,0,0,0,0,0,0, E(20)+E(20)^9-E(20)^13-E(20)^17,-E(20)-E(20)^9+E(20)^13+E(20)^17,0,0,0,0,0,0, -2*E(8)-2*E(8)^3,2*E(8)+2*E(8)^3,0,0,0,0,0,0,0,-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,-E(40)^13-E(40)^31-E(40)^37-E(40)^39], [TENSOR,[23,2]], [GALOIS,[23,13]], [TENSOR,[25,2]],[468,-8,-4,-18,9,0,-10,0,2,-2,1,2,-1,0,0,2,-1,0,0,0,0,0,0,0,0, 0,0,0,2*E(8)+2*E(8)^3,-2*E(8)-2*E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,0, -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,[27,2]],[1170,10,2,36,9,0,-10,-6,-2,0,1,-4,-1,2,0,0,-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],[640,0,0,-8,-8,1,0,0,0,0,0,0,0,0,1,0,0, 0,E(13)+E(13)^3+E(13)^9,E(13)^4+E(13)^10+E(13)^12,E(13)^2+E(13)^5+E(13)^6, E(13)^7+E(13)^8+E(13)^11,0,0,16,0,-2,1,0,0,0,0,0,0,0,E(13)+E(13)^3+E(13)^9, E(13)^4+E(13)^10+E(13)^12,E(13)^2+E(13)^5+E(13)^6,E(13)^7+E(13)^8+E(13)^11,0, 0,0,0], [TENSOR,[30,2]], [GALOIS,[30,4]], [TENSOR,[32,2]], [GALOIS,[30,7]], [TENSOR,[34,2]], [GALOIS,[30,2]], [TENSOR,[36,2]],[729,9,9,0,0,0,9,-3,1,-1,0,0,0,-1,0,-1,0,0,1,1,1,1,-1,-1,27, -1,0,0,-3,-3,-1,-1,1,0,0,1,1,1,1,-1,-1,-1,-1], [TENSOR,[38,2]],[780,-20,12,-3,6,-3,0,4,0,0,-2,-3,0,0,0,0,0,1,0,0,0,0,0,0,26, 2,-1,-1,-2,-2,0,0,-2,1,1,0,0,0,0,0,0,0,0], [TENSOR,[40,2]],[1040,0,-16,14,-4,-4,0,0,0,0,0,2,2,0,-1,0,0,0,0,0,0,0,0,0,0,0, 0,0,4*E(8)+4*E(8)^3,-4*E(8)-4*E(8)^3,0,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,0,0,0,0,0, 0,0,0], [TENSOR,[42,2]]], [(29,30)(31,32)(34,35)(40,42)(41,43),(23,24)(40,43)(41,42),(23,24)(29,30) (31,32)(34,35)(40,41)(42,43),(19,21,20,22)(36,38,37,39)]); ARC("L4(3).2_1","CAS",[rec(name:="pgl(4,3)", permchars:=( 3, 5, 4)( 8,10, 9)(11,25,23,22,20,18,16,14,12,28,27,26,24,21,19, 17,15,13)(29,43,42,41,40,39,38,37,34,35,36,33,32,31,30), permclasses:=(), text:=[ "names:= pgl[4,3]\n", " order: 2^8.3^6.5.13 = 12,130,560\n", " number of classes: 43\n", " source:private communication of atlas compound table\n", " from cambridge 1980/81;\n", " blown up using cas\n", " comments: - \n", ""])]); ARC("L4(3).2_1","projectives",["2.L4(3).2_1",[[40,0,0,13,4,4,0,4,0,0,0,-3,0,0, 1,0,0,1,1,1,1,1,0,0,12,0,3,0,4,4,0,0,0,1,1,-1,-1,-1,-1,0,0,0,0],[416,0,0,-16, 2,2,-8*E(8)-8*E(8)^3,0,0,-4,0,0,0,0,-1,0,E(8)+E(8)^3,0,0,0,0,0, 2*E(8)+2*E(8)^3,2*E(8)+2*E(8)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[2,5]],[260,0,0,17,-10,-1,10*E(8)+10*E(8)^3,2,0,0,0,-3,0,E(8)+E(8)^3, -1,0,E(8)+E(8)^3,-1,0,0,0,0,0,0,26,0,-1,-1,2+E(8)+E(8)^3,2-E(8)-E(8)^3,0,0, E(8)+E(8)^3,-1+E(8)+E(8)^3,-1-E(8)-E(8)^3,0,0,0,0,0,0,0,0], 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an outer automorphisphm\n", " of order 2 \n", ""])]); ARC("L4(3).2_2","projectives",["2.L4(3).2_2",[[40,0,0,13,4,4,4,0,4,0,0,0,0,-3, 0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,-3*E(12)^7+3*E(12)^11, -3*E(12)^7+3*E(12)^11,0,0,0,0,0,0,0,0,0,0,-E(12)^7+E(12)^11,0,0, E(12)^7-E(12)^11,E(12)^7-E(12)^11],[416,0,0,-16,-16,20,2,0,0,0,-4,0,0,0,0,0,0, -4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[416,0,0, -16,20,-16,2,0,0,0,-4,0,0,0,0,0,0,2,-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],[520,0,0,34,-20,-20,-2,0,4,0,0,0,0,-6,0,0,0,-2,-2,0,0, 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],[832,0,0,-32,4,4,4, 0,0,0,2,0,0,0,0,0,0,-2,-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)^39,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0], [GALOIS,[5,7]],[480,0,0,48,12,12,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0],[520,0,0,-20,16,16,-2,0,4,0,0,0, 0,0,0,0,0,1,1,0,0,0,-2,0,0,0,0,0,0,0,0,0,-6*E(12)^7+6*E(12)^11, 6*E(12)^7-6*E(12)^11,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(12)^7+E(12)^11, E(12)^7-E(12)^11],[520,0,0,7,-20,16,-2,0,4,0,0,0,0,3,0,0,0,1,-2,0,0,0,1,0,0,0, 0,0,0,0,0,0,-9*E(12)^7+9*E(12)^11,3*E(12)^7-3*E(12)^11,0,0,0,0,0,0,0,0,0,0, -E(12)^7+E(12)^11,0,0,0,-E(12)^7+E(12)^11],[520,0,0,7,16,-20,-2,0,4,0,0,0,0,3, 0,0,0,-2,1,0,0,0,1,0,0,0,0,0,0,0,0,0,3*E(12)^7-3*E(12)^11, -9*E(12)^7+9*E(12)^11,0,0,0,0,0,0,0,0,0,0,-E(12)^7+E(12)^11,0,0, -E(12)^7+E(12)^11,0],[1280,0,0,-16,-16,-16,2,0,0,0,0,0,0,0,0,0,0,2,2,0,0,0,0, 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)^11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[11,2]],[1560,0,0,-6,12,12,-6,0,-4,0,0,0,0,-6,0,0,0,0,0,0,0,0,2,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1080,0,0,27,0,0,0,0,-4,0,0,0, 0,3,0,0,0,0,0,0,0,0,-1,1,1,0,0,0,0,0,0,0,-9*E(12)^7+9*E(12)^11, -9*E(12)^7+9*E(12)^11,0,0,0,0,0,0,0,0,0,0,E(12)^7-E(12)^11,0,0,0,0]],]); ALF("L4(3).2_2","O7(3)",[1,3,4,5,6,7,11,12,13,15,16,24,22,23,25,26,34,37, 36,40,45,44,43,51,50,58,3,2,4,14,15,12,20,17,22,18,24,19,25,21,32,34,40, 41,46,49,44,57,56],[ "fusion is unique up to table automorphisms,\n", "compatible with Brauer tables,\n", "the map on the CAS table was not compatible" ]); ALF("L4(3).2_2","L4(3).2^2",[1,2,3,4,5,5,6,7,8,9,10,11,11,12,13,13,14,15, 15,16,17,17,18,19,20,21,34,34,35,36,37,37,38,38,39,39,40,40,41,41,42,43, 44,44,45,46,46,47,47],[ "fusion map is unique up to table automorphisms" ]); ALF("L4(3).2_2","D8xL4(3).2_2",[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],[ "fusion map determined by the direct product construction,\n", "compatible with Brauer tables" ]); ALF("L4(3).2_2","F4(2)",[1,4,5,8,6,7,8,13,20,21,24,31,32,35,33,34,47,49, 50,53,58,59,68,71,71,84,3,2,5,20,18,19,30,29,26,25,27,28,33,34,35,47,52, 51,68,64,65,83,82],[ "fusion map is unique up to table automorphisms" ]); ALN("L4(3).2_2",["O6+(3).2_2","o6p3b"]); MOT("L4(3).2_3", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]" ], [12130560,5760,2304,11664,1944,162,2880,192,64,40,72,144,36,16,27,40,36,24,13, 13,20,1440,96,18,192,192,32,16,16,20,20,12,24,24], [,[1,1,1,4,5,6,2,3,2,10,5,4,5,8,15,10,11,12,20,19,16,1,3,6,8,8,8,9,9,10,10,12, 18,18],[1,2,3,1,1,1,7,8,9,10,2,3,3,14,4,16,7,8,19,20,21,22,23,22,26,25,27,29, 28,31,30,23,26,25],,[1,2,3,4,5,6,7,8,9,1,11,12,13,14,15,2,17,18,20,19,7,22,23, 24,26,25,27,29,28,22,22,32,34,33],,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15, 16,17,18,1,1,21,22,23,24,26,25,27,29,28,31,30,32,34,33]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[ 52,12,4,-2,7,-2,8,4,0,2,3,-2,1,0,1,2,-1,-2,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0],[ 39,-1,7,12,3,3,-1,3,-1,-1,-1,4,1,1,0,-1,-1,0,0,0,-1,-1,3,-1,-3,-3,1,1,1,-1,-1, 0,0,0], [TENSOR,[4,2]],[52,8,-4,-2,7,-2,-10,0,2,2,-1,2,-1,0,1,-2,-1,0,0,0,0,0,0,0, -2*E(8)+2*E(8)^3,2*E(8)-2*E(8)^3,0,E(8)-E(8)^3,-E(8)+E(8)^3,0,0,0,E(8)-E(8)^3, -E(8)+E(8)^3], [TENSOR,[6,2]],[130,10,-14,22,13,4,-10,2,-2,0,1,-2,1,-2,1,0,-1,2,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0],[90,10,10,9,9,0,10,-2,2,0,1,1,1,0,0,0,1,1,-1,-1,0,0,4,0, 2,2,-2,0,0,0,0,1,-1,-1], [TENSOR,[9,2]],[468,28,4,-18,9,0,-8,4,0,-2,1,-2,1,0,0,-2,1,-2,0,0,2,0,0,0,0,0, 0,0,0,0,0,0,0,0],[520,0,-8,-20,16,-2,20,0,-4,0,0,4,-2,0,1,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0],[260,20,4,17,-10,-1,0,4,0,0,2,1,-2,0,-1,0,0,1,0,0,0,10,2,1, 2,2,2,0,0,0,0,-1,-1,-1], [TENSOR,[13,2]],[351,-9,15,27,0,0,-9,-1,-1,1,0,3,0,-1,0,1,0,-1,0,0,1,9,1,0,1, 1,1,-1,-1,-1,-1,1,1,1], [TENSOR,[15,2]],[390,-10,-10,39,3,3,10,2,2,0,-1,-1,-1,0,0,0,1,-1,0,0,0,10,-2, 1,-4,-4,0,0,0,0,0,1,-1,-1], [TENSOR,[17,2]],[416,16,0,-16,2,2,16,0,0,1,-2,0,0,0,-1,1,-2,0,0,0,1,16,0,-2,0, 0,0,0,0,1,1,0,0,0], [TENSOR,[19,2]],[416,16,0,-16,2,2,-16,0,0,1,-2,0,0,0,-1,1,2,0,0,0,-1,0,0,0,0, 0,0,0,0,E(5)-E(5)^2-E(5)^3+E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4,0,0,0], [TENSOR,[21,2]],[832,-32,0,-32,4,4,0,0,0,2,4,0,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0],[468,-8,-4,-18,9,0,-10,0,2,-2,1,2,-1,0,0,2,-1,0,0,0,0,0,0,0, 2*E(8)-2*E(8)^3,-2*E(8)+2*E(8)^3,0,E(8)-E(8)^3,-E(8)+E(8)^3,0,0,0, -E(8)+E(8)^3,E(8)-E(8)^3], [TENSOR,[24,2]],[1170,10,2,36,9,0,-10,-6,-2,0,1,-4,-1,2,0,0,-1,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0],[1280,0,0,-16,-16,2,0,0,0,0,0,0,0,0,2,0,0,0, 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)^11,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[27,2]],[729,9,9,0,0,0,9,-3,1,-1,0,0,0,-1,0,-1,0,0,1,1,-1,-9,3,0,-3, -3,1,-1,-1,1,1,0,0,0], [TENSOR,[29,2]],[780,-20,12,-3,6,-3,0,4,0,0,-2,-3,0,0,0,0,0,1,0,0,0,10,2,1,-2, -2,-2,0,0,0,0,-1,1,1], [TENSOR,[31,2]],[1040,0,-16,14,-4,-4,0,0,0,0,0,2,2,0,-1,0,0,0,0,0,0,0,0,0, 4*E(8)-4*E(8)^3,-4*E(8)+4*E(8)^3,0,0,0,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3], [TENSOR,[33,2]]], [(30,31),(25,26)(28,29)(33,34),(19,20)]); ARC("L4(3).2_3","CAS",[rec(name:="psl(4,3).2", permchars:=( 3, 5)( 6, 7)( 8,10, 9)(11,21,19,17,15,13)(12,24,22,20,18,16,14) (23,29,26,32,28,34,31,27,33,30,25), permclasses:=(28,29)(33,34), text:=[ "names:= psl[4,3].2\n", " order: 2^8.3^6.5.13 = 12,130,560\n", " number of classes: 34\n", " source:private communication of atlas compound table\n", " from cambridge 1980/81;\n", " blown up using cas\n", " comments: - \n", ""])]); ARC("L4(3).2_3","projectives",["2.L4(3).2_3",[[40,0,0,13,4,4,0,4,0,0,0,-3,0,0, 1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,-E(12)^7+E(12)^11,E(12)^7-E(12)^11, -E(12)^7+E(12)^11],[416,0,0,-16,2,2,0,0,0,-4,0,0,0,0,-1,0,3*E(8)+3*E(8)^3,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[2,5]],[520,0,0,34,-20,-2,0,4,0,0,0,-6,0,0,-2,0,0,-2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0],[832,0,0,-32,4,4,0,0,0,2,0,0,0,0,-2,0,0,0,0,0, -E(40)^7+E(40)^13-E(40)^21-E(40)^23-E(40)^29+E(40)^31+E(40)^37+E(40)^39,0,0,0, 0,0,0,0,0,0,0,0,0,0], [GALOIS,[5,7]],[480,0,0,48,12,3,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,0,0,0,3,0,0,0,0, 0,0,0,0,0,0],[520,0,0,-20,16,-2,0,4,0,0,0,0,0,0,1,0,0,-2,0,0,0,0,0,0,0,0,0,0, 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],[ 1040,0,0,14,-4,-4,0,8,0,0,0,6,0,0,-1,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[ 1280,0,0,-16,-16,2,0,0,0,0,0,0,0,0,2,0,0,0,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, 0,0,0,0,0,0,0,0,0,0], [GALOIS,[10,2]],[1560,0,0,-6,12,-6,0,-4,0,0,0,-6,0,0,0,0,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0],[1080,0,0,27,0,0,0,-4,0,0,0,3,0,0,0,0,0,-1,1,1,0,0,0,0,0,0,0, 0,0,0,0,-E(12)^7+E(12)^11,-E(12)^7+E(12)^11,E(12)^7-E(12)^11]],]); ALF("L4(3).2_3","L4(3).2^2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18, 19,20,21,48,49,50,51,51,52,53,53,54,54,55,56,56],[ "fusion map is unique up to table automorphisms" ]); ALN("L4(3).2_3",["O6+(3).2_3","psl(4,3).2"]); MOT("L4(3).2^2", [ "origin: CAS library,\n", "tests: 1.o.r., pow[2,3,5,13],\n", "constructions: Aut(L4(3)), PGL(4,3) extended by transpose-inverse" ], [24261120,11520,4608,23328,3888,324,5760,384,128,80,144,288,72,32,54,80,72,48, 26,26,40,22464,64,216,36,192,80,64,24,26,26,40,40,103680,2304,384,192,1296, 432,216,144,36,32,20,48,24,18,2880,192,36,192,64,16,20,24,24], [,[1,1,1,4,5,6,2,3,2,10,5,4,5,8,15,10,11,12,20,19,16,1,3,4,6,8,7,8,18,20,19, 21,21,1,1,3,2,4,5,5,5,6,8,10,12,11,15,1,3,6,8,8,9,10,12,18],[1,2,3,1,1,1,7,8, 9,10,2,3,3,14,4,16,7,8,19,20,21,22,23,22,22,26,27,28,26,30,31,32,33,34,35,36, 37,34,34,34,35,35,43,44,36,37,38,48,49,48,51,52,53,54,49,51],,[1,2,3,4,5,6,7, 8,9,1,11,12,13,14,15,2,17,18,20,19,7,22,23,24,25,26,27,28,29,31,30,27,27,34, 35,36,37,38,39,40,41,42,43,34,45,46,47,48,49,50,51,52,53,48,55,56],,,,,,,,[1, 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,1,21,22,23,24,25,26,27,28,29,22, 22,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55, 56]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, -1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1, -1,-1,-1,-1,-1,-1,-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]],[39,-1,7,12,3,3,-1,3,-1,-1,-1,4,1,1,0,-1,-1,0,0,0,-1,13,1,4,1, 3,-1,-1,0,0,0,-1,-1,9,1,-3,1,0,-3,3,1,1,-1,-1,0,1,0,-1,3,-1,-3,1,1,-1,0,0], [TENSOR,[5,2]], [TENSOR,[5,3]], [TENSOR,[5,4]],[52,12,4,-2,7,-2,8,4,0,2,3,-2,1,0,1,2,-1,-2,0,0,-2,0,0,0,0,0,0, 0,0,0,0,0,0,20,4,-4,4,2,5,-1,1,-2,0,0,2,1,-1,0,0,0,0,0,0,0,0,0], [TENSOR,[9,2]],[90,10,10,9,9,0,10,-2,2,0,1,1,1,0,0,0,1,1,-1,-1,0,12,0,3,0,-2, 0,2,1,-1,-1,0,0,30,6,2,2,3,3,3,3,0,0,0,-1,-1,0,0,4,0,2,-2,0,0,1,-1], [TENSOR,[11,2]], [TENSOR,[11,3]], [TENSOR,[11,4]],[104,16,-8,-4,14,-4,-20,0,4,4,-2,4,-2,0,2,-4,-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],[260,20,4,17, -10,-1,0,4,0,0,2,1,-2,0,-1,0,0,1,0,0,0,26,2,-1,-1,2,0,2,-1,0,0,0,0,20,4,4,0, -7,2,2,-2,1,0,0,1,0,-1,10,2,1,2,2,0,0,-1,-1], [TENSOR,[16,2]], [TENSOR,[16,3]], [TENSOR,[16,4]],[351,-9,15,27,0,0,-9,-1,-1,1,0,3,0,-1,0,1,0,-1,0,0,1,39,-1,3, 0,-1,1,-1,-1,0,0,1,1,9,9,1,-3,9,0,0,0,0,1,-1,1,0,0,9,1,0,1,1,-1,-1,1,1], [TENSOR,[20,2]], [TENSOR,[20,3]], [TENSOR,[20,4]],[390,-10,-10,39,3,3,10,2,2,0,-1,-1,-1,0,0,0,1,-1,0,0,0,26,-2, -1,-1,4,0,0,1,0,0,0,0,30,-10,2,-2,3,3,3,-1,-1,0,0,-1,1,0,-10,2,-1,4,0,0,0,-1, 1], [TENSOR,[24,2]], [TENSOR,[24,3]], [TENSOR,[24,4]],[416,16,0,-16,2,2,16,0,0,1,-2,0,0,0,-1,1,-2,0,0,0,1,0,0,0,0,0, 4,0,0,0,0,-1,-1,64,0,0,0,-8,4,-2,0,0,0,-1,0,0,1,16,0,-2,0,0,0,1,0,0], [TENSOR,[28,2]], [TENSOR,[28,3]], [TENSOR,[28,4]],[468,28,4,-18,9,0,-8,4,0,-2,1,-2,1,0,0,-2,1,-2,0,0,2,0,0,0,0, 0,0,0,0,0,0,0,0,-60,-12,-4,-4,-6,3,3,3,0,0,0,2,-1,0,0,0,0,0,0,0,0,0,0], [TENSOR,[32,2]],[729,9,9,0,0,0,9,-3,1,-1,0,0,0,-1,0,-1,0,0,1,1,-1,-27,1,0,0,3, 1,-1,0,-1,-1,1,1,-81,-9,3,3,0,0,0,0,0,1,-1,0,0,0,-9,3,0,-3,1,-1,1,0,0], [TENSOR,[34,2]], [TENSOR,[34,3]], [TENSOR,[34,4]],[780,-20,12,-3,6,-3,0,4,0,0,-2,-3,0,0,0,0,0,1,0,0,0,26,2,-1, -1,-2,0,-2,1,0,0,0,0,60,-4,4,0,-3,-6,0,2,-1,0,0,1,0,0,10,2,1,-2,-2,0,0,-1,1], [TENSOR,[38,2]], [TENSOR,[38,3]], [TENSOR,[38,4]],[936,-16,-8,-36,18,0,-20,0,4,-4,2,4,-2,0,0,4,-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],[2080,0,-32, 28,-8,-8,0,0,0,0,0,4,4,0,-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],[832,32,0,-32,4,4,-32,0,0,2,-4,0,0,0,-2,2,4, 0,0,0,-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],[832,-32,0,-32,4,4,0,0,0,2,4,0,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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)^39,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[45,3]],[1280,0,0,-16,-16,2,0,0,0,0,0,0,0,0,2,0,0,0, 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)^11,0,32,0,-4,2,0,0,0,0,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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[47,3]], [GALOIS,[47,2]], [TENSOR,[49,3]],[130,10,-14,22,13,4,-10,2,-2,0,1,-2,1,-2,1,0,-1,2,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,-10,6,-2,-2,-10,-1,-1,3,0,2,0,-2,1,-1,0,0,0,0,0,0,0,0,0], [TENSOR,[51,2]],[520,0,-8,-20,16,-2,20,0,-4,0,0,4,-2,0,1,0,2,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,80,-16,0,0,8,2,-4,2,2,0,0,0,0,-1,0,0,0,0,0,0,0,0,0], [TENSOR,[53,2]],[1170,10,2,36,9,0,-10,-6,-2,0,1,-4,-1,2,0,0,-1,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,-90,6,6,-2,0,3,-3,3,0,-2,0,0,1,0,0,0,0,0,0,0,0,0,0], [TENSOR,[55,2]]], [(32,33),(19,20)(30,31)]); ALF("L4(3).2^2","F4(2).2",[1,3,4,6,5,6,9,14,15,18,22,24,23,32,34,36,39,44, 47,47,56,63,65,66,66,69,67,69,82,85,85,90,90,2,4,14,13,21,19,20,23,24,32, 35,44,42,55,63,65,66,69,69,73,74,75,82],[ "fusion map is unique" ]); ALN("L4(3).2^2",["O6+(3).2^2","psl(4,3).v4"]); MOT("L5(2)", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,31]" ], [9999360,21504,1536,504,180,384,128,32,15,24,12,42,42,16,12,14,14,15,15,21,21, 31,31,31,31,31,31], [,[1,1,1,4,5,2,2,3,9,4,5,12,13,7,10,12,13,18,19,20,21,22,23,24,25,26,27],[1,2, 3,1,1,6,7,8,9,2,3,13,12,14,6,17,16,9,9,13,12,27,26,23,22,25,24],,[1,2,3,4,5,6, 7,8,1,10,11,13,12,14,15,17,16,5,5,21,20,24,25,26,27,22,23],,[1,2,3,4,5,6,7,8, 9,10,11,1,1,14,15,2,2,19,18,4,4,26,27,22,23,24,25],,,,,,,,,,,,,,,,,,,,,,,,[1, 2,3,4,5,6,7,8,9,10,11,13,12,14,15,17,16,18,19,21,20,1,1,1,1,1,1]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[30,14,6,6,0,6,2,2,0, 2,0,2,2,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1],[124,28,12,1,4,4,4,0,-1,1,0,-2, -2,0,1,0,0,-1,-1,1,1,0,0,0,0,0,0],[155,27,-5,8,5,3,-5,-1,0,0,1,1,1,-1,0,-1,-1, 0,0,1,1,0,0,0,0,0,0],[217,-7,9,7,4,-7,1,1,2,-1,0,0,0,1,-1,0,0,-1,-1,0,0,0,0,0, 0,0,0],[280,56,8,7,-5,8,0,0,0,-1,-1,0,0,0,-1,0,0,0,0,0,0,1,1,1,1,1,1],[315, -21,3,0,0,3,-1,-1,0,0,0,0,0,1,0,0,0,0,0,0,0,E(31)+E(31)^2+E(31)^4+E(31)^8 +E(31)^16,E(31)^15+E(31)^23+E(31)^27+E(31)^29+E(31)^30, E(31)^5+E(31)^9+E(31)^10+E(31)^18+E(31)^20,E(31)^11+E(31)^13+E(31)^21+E(31)^22 +E(31)^26,E(31)^7+E(31)^14+E(31)^19+E(31)^25+E(31)^28, E(31)^3+E(31)^6+E(31)^12+E(31)^17+E(31)^24], [GALOIS,[7,15]], [GALOIS,[7,7]], [GALOIS,[7,3]], [GALOIS,[7,5]], [GALOIS,[7,11]],[465,-31,9,3,0,1,-3,1,0,-1,0,E(7)+E(7)^2+E(7)^4, E(7)^3+E(7)^5+E(7)^6,-1,1,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,0,0, E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,0,0,0,0,0], [GALOIS,[13,3]],[465,17,-15,3,0,1,1,1,0,-1,0,E(7)+E(7)^2+E(7)^4, E(7)^3+E(7)^5+E(7)^6,1,1,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,0, E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,0,0,0,0,0], [GALOIS,[15,3]],[496,48,16,-8,1,0,0,0,1,0,1,-1,-1,0,0,-1,-1,1,1,-1,-1,0,0,0,0, 0,0],[651,-21,-5,0,6,3,3,-1,1,0,-2,0,0,-1,0,0,0,1,1,0,0,0,0,0,0,0,0],[651,-21, -5,0,-3,3,3,-1,1,0,1,0,0,-1,0,0,0,-E(15)^7-E(15)^11-E(15)^13-E(15)^14, -E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,0,0,0,0,0,0], [GALOIS,[19,7]],[868,-28,4,7,1,-4,4,0,-2,-1,1,0,0,0,-1,0,0,1,1,0,0,0,0,0,0,0, 0],[930,50,-6,6,0,-6,-2,-2,0,2,0,-1,-1,0,0,1,1,0,0,-1,-1,0,0,0,0,0,0],[930, -14,-6,-3,0,2,-2,2,0,1,0,2*E(7)+2*E(7)^2+2*E(7)^4,2*E(7)^3+2*E(7)^5+2*E(7)^6, 0,-1,0,0,0,0,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,0,0,0,0,0,0], [GALOIS,[23,3]],[960,64,0,-6,0,0,0,0,0,-2,0,1,1,0,0,1,1,0,0,1,1,-1,-1,-1,-1, -1,-1],[1024,0,0,-8,4,0,0,0,-1,0,0,2,2,0,0,0,0,-1,-1,-1,-1,1,1,1,1,1,1],[1240, -8,8,1,-5,-8,0,0,0,1,-1,1,1,0,1,-1,-1,0,0,1,1,0,0,0,0,0,0]], [(22,27,24,23,26,25),(18,19),(12,13)(16,17)(20,21),(22,23)(24,25)(26,27), (22,26,24)(23,27,25)]); ARC("L5(2)","CAS",[rec(name:="psl(5,2)", permchars:=( 9,11,10,12)(13,15)(14,16), permclasses:=(24,26,25,27), text:=[ "names:=psl[5,2]; psl[5,2]\n", " a4[5] [lie-not.]\n", " order: 2^10.3^2.5.7.31 = 9,999,360\n", " number of classes: 27\n", " source:private communication of atlas compound table\n", " from cambridge 1980/81;\n", " blown up using cas\n", " comments: - \n", ""])]); ARC("L5(2)","isSimple",true); ARC("L5(2)","extInfo",["","2"]); ARC("L5(2)","maxes",["2^4:a8","2^4:a8","2^6:(psl(3,2)xs3)", "2^6:(psl(3,2)xs3)","31:5"]); ARC("L5(2)","tomfusion",rec(name:="L5(2)",map:=[1,2,3,4,5,16,17,18,19,23, 24,25,25,80,102,103,103,104,104,245,245,291,291,291,291,291,291],text:=[ "fusion map is unique" ])); ALF("L5(2)","L5(2).2",[1,2,3,4,5,6,7,8,9,10,11,12,12,13,14,15,15,16,16,17, 17,18,18,19,19,20,20],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); ALF("L5(2)","2^5:L5(2)",[1,3,6,9,11,13,16,20,22,25,27,29,31,34,35,37,39, 41,43,45,46,47,48,49,50,51,52],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); ALF("L5(2)","P1L62",[1,3,6,24,20,12,9,15,31,26,22,37,42,18,29,39,44,33,35, 41,46,47,52,49,51,50,48],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); ALF("L5(2)","2^10:L5(2)",[1,4,10,17,21,24,30,37,43,45,51,54,56,58,62,66, 68,70,71,72,74,76,77,78,79,80,81],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); ALN("L5(2)",["psl(5,2)","L5(2).2M1"]); MOT("L5(2).2", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,31],\n", "constructions: Aut(L5(2))" ], [19998720,43008,3072,1008,360,768,256,64,30,48,24,42,32,24,14,15,21,31,31,31, 1440,96,36,36,192,192,32,10,12,16,16,24,24], [,[1,1,1,4,5,2,2,3,9,4,5,12,7,10,12,16,17,18,19,20,1,3,4,5,6,6,6,9,11,13,13, 14,14],[1,2,3,1,1,6,7,8,9,2,3,12,13,6,15,9,12,20,18,19,21,22,21,21,26,25,27, 28,22,31,30,26,25],,[1,2,3,4,5,6,7,8,1,10,11,12,13,14,15,5,17,19,20,18,21,22, 23,24,26,25,27,21,29,31,30,33,32],,[1,2,3,4,5,6,7,8,9,10,11,1,13,14,2,16,4,20, 18,19,21,22,23,24,25,26,27,28,29,30,31,32,33],,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,4, 5,6,7,8,9,10,11,12,13,14,15,16,17,1,1,1,21,22,23,24,25,26,27,28,29,30,31,32, 33]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[30, 14,6,6,0,6,2,2,0,2,0,2,0,0,0,0,-1,-1,-1,-1,0,0,0,0,2*E(8)-2*E(8)^3, -2*E(8)+2*E(8)^3,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3], [TENSOR,[3,2]],[124,28,12,1,4,4,4,0,-1,1,0,-2,0,1,0,-1,1,0,0,0,4,0,1,-2,4,4,0, -1,0,0,0,1,1], [TENSOR,[5,2]],[155,27,-5,8,5,3,-5,-1,0,0,1,1,-1,0,-1,0,1,0,0,0,5,1,2,-1,-3, -3,1,0,1,-1,-1,0,0], [TENSOR,[7,2]],[217,-7,9,7,4,-7,1,1,2,-1,0,0,1,-1,0,-1,0,0,0,0,5,-3,-1,2,1,1, 1,0,0,-1,-1,1,1], [TENSOR,[9,2]],[280,56,8,7,-5,8,0,0,0,-1,-1,0,0,-1,0,0,0,1,1,1,10,2,1,1,2,2,2, 0,-1,0,0,-1,-1], [TENSOR,[11,2]],[630,-42,6,0,0,6,-2,-2,0,0,0,0,2,0,0,0,0,E(31)+E(31)^2+E(31)^4 +E(31)^8+E(31)^15+E(31)^16+E(31)^23+E(31)^27+E(31)^29+E(31)^30, E(31)^5+E(31)^9+E(31)^10+E(31)^11+E(31)^13+E(31)^18+E(31)^20+E(31)^21+E(31)^22 +E(31)^26,E(31)^3+E(31)^6+E(31)^7+E(31)^12+E(31)^14+E(31)^17+E(31)^19 +E(31)^24+E(31)^25+E(31)^28,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[13,3]], [GALOIS,[13,5]],[930,-62,18,6,0,2,-6,2,0,-2,0,-1,-2,2,1,0,-1,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0],[930,34,-30,6,0,2,2,2,0,-2,0,-1,2,2,-1,0,-1,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0],[496,48,16,-8,1,0,0,0,1,0,1,-1,0,0,-1,1,-1,0,0,0,4,4,-2,1,0, 0,0,-1,1,0,0,0,0], [TENSOR,[18,2]],[651,-21,-5,0,6,3,3,-1,1,0,-2,0,-1,0,0,1,0,0,0,0,9,-3,0,0,-3, -3,1,-1,0,1,1,0,0], [TENSOR,[20,2]],[1302,-42,-10,0,-6,6,6,-2,2,0,2,0,-2,0,0,-1,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0],[868,-28,4,7,1,-4,4,0,-2,-1,1,0,0,-1,0,1,0,0,0,0,10,-2,1,1,2, 2,-2,0,1,0,0,-1,-1], 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test: orth.1, min \n", ""])]); ALN("L5(2).2",["psl(5,2).2"]); MOT("L6(2)", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,31]" ], [20158709760,10321920,147456,86016,181440,60480,1080,43008,2048,1536,768,256, 90,576,576,360,288,72,24,3528,3528,1176,1176,49,64,32,63,30,48,48,24,56,56,56, 56,90,90,45,45,45,63,63,21,21,28,28,30,30,31,31,31,31,31,31,63,63,63,63,63, 63], [,[1,1,1,1,5,6,7,2,2,3,3,3,13,5,6,7,6,7,7,20,21,22,23,24,9,10,27,13,14,15,17, 20,21,22,23,36,37,38,39,40,41,42,43,44,34,35,36,37,49,50,51,52,53,54,55,56,57, 58,59,60],[1,2,3,4,1,1,1,8,9,10,11,12,13,3,2,2,3,3,4,21,20,23,22,24,25,26,5, 28,10,8,11,33,32,35,34,13,13,13,13,13,21,20,23,22,46,45,28,28,54,53,50,49,52, 51,42,41,42,41,42,41],,[1,2,3,4,5,6,7,8,9,10,11,12,1,14,15,16,17,18,19,21,20, 23,22,24,25,26,27,2,29,30,31,33,32,35,34,7,7,6,5,5,42,41,44,43,46,45,16,16,51, 52,53,54,49,50,58,57,60,59,56,55],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17, 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20,21,21,22,23,24,25,26,27,28,29,30,30,31,31,32,32,33,34,34,35,35,36,36, 37,37,38,38,39,39,40,40,41,41,42,42,43,43,44,44]); ALF("L6(2)","2^6:L6(2)",[1,3,6,9,93,39,31,11,14,18,20,23,51,110,41,33,44, 35,37,105,106,63,72,112,26,29,98,53,111,46,49,107,108,65,74,55,59,109,94, 95,96,97,70,79,68,77,57,61,81,91,85,89,87,83,99,104,100,102,101,103],[ "fusion map is unique up to table automorphisms" ]); ALN("L6(2)",["l6f2"]); MOT("L6(2).2", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,31],\n", "constructions: Aut(L6(2))" ], [40317419520,20643840,294912,172032,362880,120960,2160,86016,4096,3072,1536, 512,180,1152,1152,720,576,144,48,3528,1176,98,128,64,126,60,96,96,48,56,56,90, 90,45,63,21,28,30,31,31,31,63,63,63,2903040,46080,9216,3072,768,4320,1296,288, 216,72,192,192,128,128,60,20,288,144,96,72,24,14,32,32,18,24,24,30], [,[1,1,1,1,5,6,7,2,2,3,3,3,13,5,6,7,6,7,7,20,21,22,9,10,25,13,14,15,17,20,21, 32,33,34,35,36,31,32,39,40,41,42,43,44,1,1,3,3,3,6,5,6,7,7,8,10,10,10,13,13, 17,14,17,18,18,22,23,23,25,28,27,33],[1,2,3,4,1,1,1,8,9,10,11,12,13,3,2,2,3,3, 4,20,21,22,23,24,5,26,10,8,11,30,31,13,13,13,20,21,37,26,41,39,40,35,35,35,45, 46,47,48,49,45,45,46,45,46,55,56,57,58,59,60,47,47,48,47,49,66,68,67,51,55,56, 59],,[1,2,3,4,5,6,7,8,9,10,11,12,1,14,15,16,17,18,19,20,21,22,23,24,25,2,27, 28,29,30,31,7,6,5,35,36,37,16,40,41,39,43,44,42,45,46,47,48,49,50,51,52,53,54, 55,56,57,58,45,46,61,62,63,64,65,66,68,67,69,70,71,50],,[1,2,3,4,5,6,7,8,9,10, 11,12,13,14,15,16,17,18,19,1,1,1,23,24,25,26,27,28,29,4,2,32,33,34,5,6,8,38, 41,39,40,25,25,25,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64, 65,45,67,68,69,70,71,72],,,,,,,,,,,,,,,,,,,,,,,,[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, 1,1,1,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65, 66,67,68,69,70,71,72]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 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2026-05-26