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## #W ctoline4.tbl GAP table library Thomas Breuer ## ## This file contains the ordinary character tables related to the ## linear groups $L_3(q)$ for $q$ in [ 2, 3, 5, 7, 8 ] of the ATLAS. ## #H ctbllib history #H --------------- #H $Log: ctoline4.tbl,v $ #H Revision 4.36 2012/01/30 08:31:44 gap #H removed #H entries from the headers #H TB #H #H Revision 4.35 2012/01/26 11:14:32 gap #H added fusion "L3(2).2" -> "O8-(2).2" #H TB #H #H Revision 4.34 2011/09/28 14:32:13 gap #H removed revision entry and SET_TABLEFILENAME call #H TB #H #H Revision 4.33 2010/12/01 17:47:55 gap #H renamed "Sym(4)" to "Symm(4)"; #H note that the table constructed with `CharacterTable( "Symmetric", 4 )' #H gets the identifier `"Sym(4)"', and this table is sorted differently #H TB #H #H Revision 4.32 2010/09/15 08:08:25 gap #H adjusted the "tom:<n>" information in some fusions #H TB #H #H Revision 4.31 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 4.30 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 4.29 2009/07/29 13:59:26 gap #H added fusion L3(3) -> A13 #H TB #H #H Revision 4.28 2009/04/27 08:27:21 gap #H removed some superfluous explicit <nam>M<n> names, #H which are created automatically #H TB #H #H Revision 4.27 2009/04/22 12:39:02 gap #H added missing maxes of He.2, ON.2, HN.2, Fi24, and B #H TB #H #H Revision 4.26 2008/06/24 16:23:05 gap #H added several fusions and names #H TB #H #H Revision 4.25 2007/07/03 08:41:12 gap #H added "maxes" of 2.L3(2), L3(2) #H TB #H #H Revision 4.24 2006/06/07 07:54:27 gap #H unified ConstructMixed and ConstructMGA (for better programmatic access) #H TB #H #H Revision 4.23 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 4.22 2003/06/10 16:19:07 gap #H store in several fusions between character tables to which subgroup number #H in the table of marks of the supergroup the subgroup belongs #H (in order to make the commutative diagrams testable) #H TB #H #H Revision 4.21 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 4.20 2003/05/05 14:23:10 gap #H fixed fusion G2(3)M6 -> G2(3) (must be the fusion of G2(3)M5, mapped under #H the outer automorphism) #H TB #H #H Revision 4.19 2003/01/24 15:57:30 gap #H replaced several fusions by ones that are compatible with Brauer tables #H TB #H #H Revision 4.18 2003/01/21 16:25:31 gap #H further standardizations of `InfoText' strings, #H added and corrected `Maxes' infos, #H added some fusions #H TB #H #H Revision 4.17 2003/01/14 17:28:49 gap #H changed `InfoText' values (for a better programmatic access) #H and replaced `ConstructDirectProduct' by `ConstructPermuted' where #H there is only one factor (again better programmatic handling) #H TB #H #H Revision 4.16 2002/11/04 16:33:47 gap #H added fusions of maxes of U3(3).2, #H added fusion U3(3).2 -> Fi24' (this took me a whole afternoon ...) #H TB #H #H Revision 4.15 2002/09/23 14:47:42 gap #H removed trailing blanks #H TB #H #H Revision 4.14 2002/09/18 15:22:00 gap #H changed the `text' components of many fusions, #H in order to use them as a status information (for evaluation) #H TB #H #H Revision 4.13 2002/08/01 13:41:55 gap #H added 2-modular tables of L3(7).S3, 3.L3(7).S3, 3.U3(5).S3, U3(11).S3, #H and 3.U3(11).S3 #H TB #H #H Revision 4.12 2002/08/01 08:24:22 gap #H added tables of 3.L3(7).S3, L3(7).S3, 3.U3(5).S3, 3.U3(11).S3, U3(11).S3 #H TB #H #H Revision 4.11 2002/07/12 06:45:55 gap #H further tidying up: removed `irredinfo' stuff, rearranged constructions #H TB #H #H Revision 4.10 2002/07/08 16:06:56 gap #H changed `construction' component from function (call) to list of function #H name and arguments #H TB #H #H Revision 4.9 2001/05/04 16:47:41 gap #H first revision for ctbllib #H #H #H tbl history (GAP 4) #H ------------------- #H (Rev. 4.9 of ctbllib coincides with Rev. 4.8 of tbl in GAP 4) #H #H RCS file: /gap/CVS/GAP/4.0/tbl/ctoline4.tbl,v #H Working file: ctoline4.tbl #H head: 4.8 #H branch: #H locks: strict #H access list: #H symbolic names: #H GAP4R2: 4.7.0.6 #H GAP4R2PRE2: 4.7.0.4 #H GAP4R2PRE1: 4.7.0.2 #H GAP4R1: 4.5.0.2 #H keyword substitution: kv #H total revisions: 9; selected revisions: 9 #H description: #H ---------------------------- #H revision 4.8 #H date: 2000/12/27 15:03:14; author: gap; state: Exp; lines: +5 -2 #H added fusion L3(3).2 -> S6(3) #H #H TB #H ---------------------------- #H revision 4.7 #H date: 1999/10/21 14:15:46; author: gap; state: Exp; lines: +8 -15 #H added many `tomidentifer' and `tomfusion' values, which yields a better #H interface between `tom' and `tbl'; #H #H added maxes of McL.2, #H #H unified tables `J2.2M4', `2^(2+4):(3x3):2^2', `2^(2+4):(S3xS3)'. #H #H TB #H ---------------------------- #H revision 4.6 #H date: 1999/10/04 15:57:14; author: gap; state: Exp; lines: +10 -2 #H added and corrected several fusions from character tables #H to their tables of marks, #H unified two instances of the table of (A6xA6):2^2, #H corrected the name of the table of marks of 2F4(2). #H #H TB #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: 1998/04/03 13:26:52; author: gap; state: Exp; lines: +20 -2 #H added tables of maxes of G2(3) and fusions into G2(3) #H #H TB #H ---------------------------- #H revision 4.3 #H date: 1998/03/11 08:05:23; author: gap; state: Exp; lines: +7 -2 #H mainly new fusions to tables of marks added #H #H TB #H ---------------------------- #H revision 4.2 #H date: 1997/11/25 15:44:50; author: gap; state: Exp; lines: +9 -3 #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 15:40:24; author: fceller; state: Exp; lines: +2 -2 #H for version 4 #H ---------------------------- #H revision 1.1 #H date: 1996/10/21 15:59:35; author: sam; state: Exp; #H first proposal of the table library #H ========================================================================== ## MOT("2.L3(2)", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7]" ], [336,336,8,6,6,8,8,14,14,14,14], [,[1,1,2,4,4,3,3,8,8,10,10],[1,2,3,1,2,7,6,10,11,8,9],,,,[1,2,3,4,5,6,7,1,2,1, 2]], 0, [( 8,10)( 9,11),(6,7)], ["ConstructProj",[["L3(2)",[]],["2.L3(2)",[]]]]); ARC("2.L3(2)","maxes",["2.Symm(4)","2.Symm(4)","2x7:3"]); ALF("2.L3(2)","L3(2)",[1,1,2,3,3,4,4,5,5,6,6]); ALF("2.L3(2)","2.L3(2).2",[1,2,3,4,5,6,7,8,9,8,9],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); ALF("2.L3(2)","Isoclinic(2.L3(2).2)",[1,2,3,4,5,6,7,8,9,8,9],[ "fusion map is unique up to table aut." ]); ALF("2.L3(2)","2.A7",[1,2,3,6,7,8,9,13,14,15,16],[ "fusion map is unique up to table autom.,\n", "representative compatible with factors" ]); ALN("2.L3(2)",["2.L2(7)","2.A2(2)","2.A1(7)","2.U2(7)","2.S2(7)","2.O3(7)", "Isoclinic(2.L3(2).2)M1"]); MOT("2.L3(2).2", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7]" ], [672,672,16,12,12,16,16,14,14,12,12,12,16,16,16,16], [,[1,1,2,4,4,3,3,8,8,2,5,5,7,7,6,6],[1,2,3,1,2,7,6,8,9,10,10,10,15,16,14, 13],,,,[1,2,3,4,5,6,7,1,2,10,12,11,14,13,16,15]], 0, [(11,12),( 6, 7)(11,12)(13,16,14,15),( 6, 7)(13,16,14,15),(13,14)(15,16)], ["ConstructProj",[["L3(2).2",[]],["2.L3(2).2",[]]]]); ARC("2.L3(2).2","maxes",["2.L3(2)","7:12","2.D16","2.D12"]); ALF("2.L3(2).2","L3(2).2",[1,1,2,3,3,4,4,5,5,6,7,7,8,8,9,9]); ALN("2.L3(2).2",["2.L2(7).2"]); MOT("Isoclinic(2.L3(2).2)", [ "isoclinic group of the 2.L3(2).2 given in the ATLAS" ], 0, 0, 0, [(11,12),(13,14)(15,16),(6,7)(13,15,14,16)], ["ConstructIsoclinic",[["2.L3(2).2"]]]); ALF("Isoclinic(2.L3(2).2)","L3(2).2",[1,1,2,3,3,4,4,5,5,6,7,7,8,8,9,9]); ALN("Isoclinic(2.L3(2).2)",["Isoclinic(2.L2(7).2)"]); MOT("2F4(2)'M2", [ "2nd maximal subgroup of 2F4(2)',\n", "differs from 2F4(2)'M1 only by fusion map" ], 0, 0, 0, 0, ["ConstructPermuted",["L3(3).2"]]); ALF("2F4(2)'M2","2F4(2)'",[1,3,4,4,7,9,13,18,17,3,5,9,12,16,15],[ "fusion L3(3).2 -> 2F4(2)' mapped under 2F4(2)'.2" ]); MOT("3.L3(7)", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,19],\n", "constructions: SL(3,7)" ], [5630688,5630688,5630688,2016,2016,2016,36,48,48,48,36,36,36,2058,2058,2058, 147,147,147,147,147,147,147,147,147,48,48,48,48,48,48,42,42,42,48,48,48,48,48, 48,48,48,48,48,48,48,57,57,57,57,57,57,57,57,57,57,57,57,57,57,57,57,57,57], [,[1,3,2,1,3,2,7,4,6,5,7,7,7,14,16,15,17,19,18,20,22,21,23,25,24,8,10,9,8,10, 9,14,16,15,26,28,27,26,28,27,29,31,30,29,31,30,56,58,57,53,55,54,62,64,63,59, 61,60,50,52,51,47,49,48],[1,1,1,4,4,4,1,8,8,8,4,4,4,14,14,14,17,17,17,20,20, 20,23,23,23,29,29,29,26,26,26,32,32,32,41,41,41,44,44,44,38,38,38,35,35,35,56, 56,56,53,53,53,62,62,62,59,59,59,50,50,50,47,47,47],,,,[1,2,3,4,5,6,7,8,9,10, 11,12,13,1,2,3,1,2,3,1,2,3,1,2,3,26,27,28,29,30,31,4,5,6,35,36,37,38,39,40,41, 42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63, 64],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23, 24,25,29,30,31,26,27,28,32,33,34,41,42,43,44,45,46,38,39,40,35,36,37,1,2,3,1, 2,3,1,2,3,1,2,3,1,2,3,1,2,3]], 0, [(47,56,59,50,53,62)(48,57,60,51,54,63)(49,58,61,52,55,64),(35,38)(36,39) (37,40)(41,44)(42,45)(43,46),(26,29)(27,30)(28,31)(35,44,38,41)(36,45,39,42) (37,46,40,43),(17,23)(18,24)(19,25),(17,20)(18,21)(19,22),(20,23)(21,24) (22,25),( 2, 3)( 5, 6)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31) (33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64), (47,50)(48,51)(49,52)(53,56)(54,57)(55,58)(59,62)(60,63)(61,64),(47,59,53) (48,60,54)(49,61,55)(50,62,56)(51,63,57)(52,64,58)], ["ConstructProj",[["L3(7)",[]],,["3.L3(7)",[-1,-1,-1,-1,-1,-37,-37,-37,-37, -37,-37,-1,17,17,-31,-31,-31,-31,-1,-1,-1]]]]); ARC("3.L3(7)","maxes",["3x7^2:2.L2(7).2","3.L3(7)M2","3xL3(2).2","3.L3(7)M4", "3.L3(7)M5","3.(A4x3):2","3^(1+2)_+:Q8","3x19:3"]); ALF("3.L3(7)","L3(7)",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9, 10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17, 18,18,18,19,19,19,20,20,20,21,21,21,22,22,22]); ALF("3.L3(7)","3.L3(7).2",[1,2,2,3,4,4,5,6,7,7,8,9,9,10,11,11,12,13,13,14, 15,16,14,16,15,17,18,18,19,20,20,21,22,22,23,24,25,23,25,24,26,27,28,26, 28,27,29,30,31,29,31,30,32,33,34,32,34,33,35,36,37,35,37,36],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables and factors" ]); ALF("3.L3(7)","3.L3(7).3",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18, 19,17,18,19,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36, 37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables and factors" ]); MOT("3.L3(7).2", [ "origin: ATLAS of finite groups" ], [11261376,5630688,4032,2016,72,96,48,72,36,4116,2058,294,147,147,147,147,96, 48,96,48,84,42,48,48,48,48,48,48,57,57,57,57,57,57,57,57,57,672,672,12,16,12, 14,16,16,28,28], [,[1,2,1,2,5,3,4,5,5,10,11,12,13,14,16,15,6,7,6,7,10,11,17,18,18,19,20,20,32, 33,34,35,36,37,29,30,31,1,3,5,6,8,12,17,19,21,21],[1,1,3,3,1,6,6,3,3,10,10,12, 12,14,14,14,19,19,17,17,21,21,26,26,26,23,23,23,32,32,32,35,35,35,29,29,29,38, 39,38,41,39,43,45,44,46,47],,,,[1,2,3,4,5,6,7,8,9,1,2,1,2,1,2,2,17,18,19,20,3, 4,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,38,44,45,39, 39],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,19,20,17,18,21,22,26, 27,28,23,25,24,1,2,2,1,2,2,1,2,2,38,39,40,41,42,43,45,44,46,47]], 0, [(46,47),(29,32,35)(30,34,36,31,33,37),(24,25)(27,28),(24,25)(27,28)(46,47), (17,19)(18,20)(23,26)(24,28,25,27)(44,45),(17,19)(18,20)(23,26)(24,28,25,27) (44,45)(46,47),(15,16),(15,16)(24,25)(27,28)(30,31)(33,34)(36,37)], ["ConstructMGA","3.L3(7)","L3(7).2",[[23,24],[25,26],[27,28],[29,32],[30, 31],[33,36],[34,35],[37,40],[38,39],[41,44],[42,43],[45,46],[47,48],[49,50], [51,54],[52,53],[55,58],[56,57],[59,60],[61,62],[63,64]],()]); ALF("3.L3(7).2","L3(7).2",[1,1,2,2,3,4,4,5,5,6,6,7,7,8,8,8,9,9,10,10,11, 11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,18,19,20,21,22,23,24, 25,26]); ALF("3.L3(7).2","3.L3(7).S3",[1,2,3,4,5,6,7,8,9,10,11,12,13,12,13,13,14, 15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,90,91,92,93, 94,95,96,97,98,99],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); MOT("3.L3(7).3", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,19]" ], [16892064,16892064,16892064,6048,6048,6048,108,144,144,144,108,108,108,6174, 6174,6174,147,147,147,144,144,144,144,144,144,126,126,126,144,144,144,144,144, 144,144,144,144,144,144,144,171,171,171,171,171,171,171,171,171,171,171,171, 171,171,171,171,171,171,6048,6048,6048,6048,6048,6048,171,171,6048,6048,6048, 6048,6048,6048,108,108,108,108,108,108,144,144,144,144,144,144,126,126,126, 126,126,126,144,144,144,144,144,144,144,144,144,144,144,144,126,126,126,126, 126,126,144,144,144,144,144,144,144,144,144,144,144,144,144,144,144,144,144, 144,144,144,144,144,144,144,171,171,171,171,171,171,171,171,171,171,171,171, 171,171,171,171,171,171,171,171,171,171,171,171,171,171,171,171,171,171,171, 171,171,171,171,171], [,[1,3,2,1,3,2,7,4,6,5,7,7,7,14,16,15,17,19,18,8,10,9,8,10,9,14,16,15,20,22, 21,20,22,21,23,25,24,23,25,24,50,52,51,47,49,48,56,58,57,53,55,54,44,46,45,41, 43,42,62,63,64,59,60,61,66,65,62,63,64,59,60,61,62,63,64,59,60,61,70,71,72,67, 68,69,88,89,90,85,86,87,82,83,84,79,80,81,82,83,84,79,80,81,88,89,90,85,86,87, 94,95,96,91,92,93,94,95,96,91,92,93,100,101,102,97,98,99,100,101,102,97,98,99, 156,154,155,153,151,152,150,148,149,147,145,146,166,167,168,163,164,165,160, 161,162,157,158,159,142,143,144,139,140,141,136,137,138,133,134,135],[1,1,1,4, 4,4,1,8,8,8,4,4,4,14,14,14,17,17,17,23,23,23,20,20,20,26,26,26,35,35,35,38,38, 38,32,32,32,29,29,29,50,50,50,47,47,47,56,56,56,53,53,53,44,44,44,41,41,41,1, 1,1,1,1,1,2,3,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,14,14,14,14,14,14,23,23,23, 23,23,23,20,20,20,20,20,20,26,26,26,26,26,26,35,35,35,35,35,35,38,38,38,38,38, 38,32,32,32,32,32,32,29,29,29,29,29,29,51,51,51,52,52,52,48,48,48,49,49,49,57, 57,57,58,58,58,54,54,54,55,55,55,45,45,45,46,46,46,42,42,42,43,43,43],,,,[1,2, 3,4,5,6,7,8,9,10,11,12,13,1,2,3,1,2,3,20,21,22,23,24,25,4,5,6,29,30,31,32,33, 34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59, 60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,59, 60,61,62,63,64,91,92,93,94,95,96,97,98,99,100,101,102,67,68,69,70,71,72,109, 110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128, 129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147, 148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166, 167,168],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,23,24,25, 20,21,22,26,27,28,35,36,37,38,39,40,32,33,34,29,30,31,1,2,3,1,2,3,1,2,3,1,2,3, 1,2,3,1,2,3,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80, 81,82,83,84,85,86,87,88,89,90,97,98,99,100,101,102,91,92,93,94,95,96,103,104, 105,106,107,108,121,122,123,124,125,126,127,128,129,130,131,132,115,116,117, 118,119,120,109,110,111,112,113,114,65,65,65,66,66,66,65,65,65,66,66,66,65,65, 65,66,66,66,65,65,65,66,66,66,65,65,65,66,66,66,65,65,65,66,66,66]], 0, [( 59, 60, 61)( 62, 63, 64)( 67, 68, 69)( 70, 71, 72)( 73, 74, 75) ( 76, 77, 78)( 79, 80, 81)( 82, 83, 84)( 85, 86, 87)( 88, 89, 90)( 91, 92, 93) ( 94, 95, 96)( 97, 98, 99)(100,101,102)(103,104,105)(106,107,108)(109,110,111) (112,113,114)(115,116,117)(118,119,120)(121,122,123)(124,125,126)(127,128,129) (130,131,132),( 41, 50, 53, 44, 47, 56)( 42, 51, 54, 45, 48, 57) ( 43, 52, 55, 46, 49, 58)(133,151,158,141,147,163,134,152,159,139,145,164,135, 153,157,140,146,165)(136,154,161,144,150,166,137,155,162,142,148,167,138,156, 160,143,149,168),( 29, 32)( 30, 33)( 31, 34)( 35, 38)( 36, 39)( 37, 40) (109,115)(110,116)(111,117)(112,118)(113,119)(114,120)(121,127)(122,128) (123,129)(124,130)(125,131)(126,132),( 20, 23)( 21, 24)( 22, 25) ( 29, 35, 32, 38)( 30, 36, 33, 39)( 31, 37, 34, 40)( 91, 97)( 92, 98)( 93, 99) ( 94,100)( 95,101)( 96,102)(109,121,115,127)(110,122,116,128)(111,123,117,129) (112,124,118,130)(113,125,119,131)(114,126,120,132),( 2, 3)( 5, 6) ( 9, 10)( 12, 13)( 15, 16)( 18, 19)( 21, 22)( 24, 25)( 27, 28)( 30, 31) ( 33, 34)( 36, 37)( 39, 40)( 42, 43)( 45, 46)( 48, 49)( 51, 52)( 54, 55) ( 57, 58)( 59, 62)( 60, 63)( 61, 64)( 65, 66)( 67, 70)( 68, 71)( 69, 72) ( 73, 76)( 74, 77)( 75, 78)( 79, 82)( 80, 83)( 81, 84)( 85, 88)( 86, 89) ( 87, 90)( 91, 94)( 92, 95)( 93, 96)( 97,100)( 98,101)( 99,102)(103,106) (104,107)(105,108)(109,112)(110,113)(111,114)(115,118)(116,119)(117,120) (121,124)(122,125)(123,126)(127,130)(128,131)(129,132)(133,138,134,136,135,137 )(139,144,140,142,141,143)(145,150,146,148,147,149)(151,156,152,154,153,155) (157,162,158,160,159,161)(163,168,164,166,165,167),(133,135,134)(136,138,137) (139,141,140)(142,144,143)(145,147,146)(148,150,149)(151,153,152)(154,156,155) (157,159,158)(160,162,161)(163,165,164)(166,168,167)], ["ConstructProj",[["L3(7).3",[]],,["3.L3(7).3",[-1,-1,-1,-37,-37,-37,-37,-37, -37,-1,17,17,-31,-31,-31,-31,-1,-1,-1]]]]); ALF("3.L3(7).3","L3(7).3",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9, 9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17, 17,18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,24,25,25,25,26,26,26, 27,27,27,28,28,28,29,29,29,30,30,30,31,31,31,32,32,32,33,33,33,34,34,34, 35,35,35,36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,41,41,42,42,42, 43,43,43,44,44,44,45,45,45,46,46,46,47,47,47,48,48,48,49,49,49,50,50,50, 51,51,51,52,52,52,53,53,53,54,54,54,55,55,55,56,56,56,57,57,57,58,58,58]); ALF("3.L3(7).3","3.L3(7).S3",[1,2,2,3,4,4,5,6,7,7,8,9,9,10,11,11,12,13,13, 14,15,15,16,17,17,18,19,19,20,21,22,20,22,21,23,24,25,23,25,24,26,27,28, 26,28,27,29,30,31,29,31,30,32,33,34,32,34,33,35,36,37,35,36,37,38,38,39, 40,41,39,40,41,42,43,44,42,43,44,45,46,47,45,46,47,48,49,50,48,49,50,51, 52,53,51,52,53,54,55,56,54,55,56,57,58,59,57,58,59,60,61,62,63,64,65,63, 64,65,60,61,62,66,67,68,69,70,71,69,70,71,66,67,68,72,73,74,75,76,77,75, 76,77,72,73,74,78,79,80,81,82,83,81,82,83,78,79,80,84,85,86,87,88,89,87, 88,89,84,85,86],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); MOT("Isoclinic(3.L3(7).3,1)", [ "1st isoclinic group of the 3.L3(7).3 given in the ATLAS" ], 0, 0, 0, [(41,47,53)(42,48,54)(43,49,55)(44,50,56)(45,51,57)(46,52,58)(133,145,158,135, 147,157,134,146,159)(136,148,161,138,150,160,137,149,162)(139,151,164,141,153, 163,140,152,165)(142,154,167,144,156,166,143,155,168),(2,3)(5,6)(9,10)(12,13) (15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46) (48,49)(51,52)(54,55)(57,58)(59,62,60,63,61,64)(65,66)(67,70,68,71,69,72)(73, 76,74,77,75,78)(79,82,80,83,81,84)(85,88,86,89,87,90)(91,94,92,95,93,96)(97, 100,98,101,99,102)(103,106,104,107,105,108)(109,112,110,113,111,114)(115,118, 116,119,117,120)(121,124,122,125,123,126)(127,130,128,131,129,132)(133,136, 134,137,135,138)(139,142,140,143,141,144)(145,148,146,149,147,150)(151,154, 152,155,153,156)(157,160,158,161,159,162)(163,166,164,167,165,168),(20,23)(21, 24)(22,25)(29,35,32,38)(30,36,33,39)(31,37,34,40)(91,97)(92,98)(93,99)(94,100) (95,101)(96,102)(109,121,115,127)(110,122,116,128)(111,123,117,129)(112,124, 118,130)(113,125,119,131)(114,126,120,132),(59,60,61)(62,63,64)(67,68,69)(70, 71,72)(73,74,75)(76,77,78)(79,80,81)(82,83,84)(85,86,87)(88,89,90)(91,92,93) (94,95,96)(97,98,99)(100,101,102)(103,104,105)(106,107,108)(109,110,111)(112, 113,114)(115,116,117)(118,119,120)(121,122,123)(124,125,126)(127,128,129)(130, 131,132),(41,44)(42,45)(43,46)(47,50)(48,51)(49,52)(53,56)(54,57)(55,58)(133, 139)(134,140)(135,141)(136,142)(137,143)(138,144)(145,151)(146,152)(147,153) (148,154)(149,155)(150,156)(157,163)(158,164)(159,165)(160,166)(161,167)(162, 168)], ["ConstructIsoclinic",[["3.L3(7).3"]],rec(k:=1)]); ALF("Isoclinic(3.L3(7).3,1)","L3(7).3",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7, 7,7,8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16, 16,16,17,17,17,18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,24,25,25, 25,26,26,26,27,27,27,28,28,28,29,29,29,30,30,30,31,31,31,32,32,32,33,33, 33,34,34,34,35,35,35,36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,41, 41,42,42,42,43,43,43,44,44,44,45,45,45,46,46,46,47,47,47,48,48,48,49,49, 49,50,50,50,51,51,51,52,52,52,53,53,53,54,54,54,55,55,55,56,56,56,57,57, 57,58,58,58]); MOT("Isoclinic(3.L3(7).3,2)", [ "2nd isoclinic group of the 3.L3(7).3 given in the ATLAS" ], 0, 0, 0, [(41,47,53)(42,48,54)(43,49,55)(44,50,56)(45,51,57)(46,52,58)(133,145,158,135, 147,157,134,146,159)(136,148,161,138,150,160,137,149,162)(139,151,164,141,153, 163,140,152,165)(142,154,167,144,156,166,143,155,168),(2,3)(5,6)(9,10)(12,13) (15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46) (48,49)(51,52)(54,55)(57,58)(59,62,61,64,60,63)(65,66)(67,70,69,72,68,71)(73, 76,75,78,74,77)(79,82,81,84,80,83)(85,88,87,90,86,89)(91,94,93,96,92,95)(97, 100,99,102,98,101)(103,106,105,108,104,107)(109,112,111,114,110,113)(115,118, 117,120,116,119)(121,124,123,126,122,125)(127,130,129,132,128,131)(133,136, 135,138,134,137)(139,142,141,144,140,143)(145,148,147,150,146,149)(151,154, 153,156,152,155)(157,160,159,162,158,161)(163,166,165,168,164,167),(20,23)(21, 24)(22,25)(29,35,32,38)(30,36,33,39)(31,37,34,40)(91,97)(92,98)(93,99)(94,100) (95,101)(96,102)(109,121,115,127)(110,122,116,128)(111,123,117,129)(112,124, 118,130)(113,125,119,131)(114,126,120,132),(59,60,61)(62,63,64)(67,68,69)(70, 71,72)(73,74,75)(76,77,78)(79,80,81)(82,83,84)(85,86,87)(88,89,90)(91,92,93) (94,95,96)(97,98,99)(100,101,102)(103,104,105)(106,107,108)(109,110,111)(112, 113,114)(115,116,117)(118,119,120)(121,122,123)(124,125,126)(127,128,129)(130, 131,132),(41,44)(42,45)(43,46)(47,50)(48,51)(49,52)(53,56)(54,57)(55,58)(133, 139)(134,140)(135,141)(136,142)(137,143)(138,144)(145,151)(146,152)(147,153) (148,154)(149,155)(150,156)(157,163)(158,164)(159,165)(160,166)(161,167)(162, 168)], ["ConstructIsoclinic",[["3.L3(7).3"]],rec(k:=2)]); ALF("Isoclinic(3.L3(7).3,2)","L3(7).3",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7, 7,7,8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16, 16,16,17,17,17,18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,24,25,25, 25,26,26,26,27,27,27,28,28,28,29,29,29,30,30,30,31,31,31,32,32,32,33,33, 33,34,34,34,35,35,35,36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,41, 41,42,42,42,43,43,43,44,44,44,45,45,45,46,46,46,47,47,47,48,48,48,49,49, 49,50,50,50,51,51,51,52,52,52,53,53,53,54,54,54,55,55,55,56,56,56,57,57, 57,58,58,58]); MOT("3.L3(7).S3", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,19]" ], [33784128,16892064,12096,6048,216,288,144,216,108,12348,6174,294,147,288,144, 288,144,252,126,144,144,144,144,144,144,171,171,171,171,171,171,171,171,171, 6048,6048,6048,171,6048,6048,6048,108,108,108,144,144,144,126,126,126,144,144, 144,144,144,144,126,126,126,144,144,144,144,144,144,144,144,144,144,144,144, 171,171,171,171,171,171,171,171,171,171,171,171,171,171,171,171,171,171,672, 672,12,16,12,14,16,16,28,28], [,[1,2,1,2,5,3,4,5,5,10,11,12,13,6,7,6,7,10,11,14,15,15,16,17,17,29,30,31,32, 33,34,26,27,28,35,36,37,38,35,36,37,35,36,37,39,40,41,48,49,50,45,46,47,45,46, 47,48,49,50,51,52,53,51,52,53,54,55,56,54,55,56,80,78,79,83,81,82,84,85,86,87, 88,89,72,73,74,75,76,77,1,3,5,6,8,12,14,16,18,18],[1,1,3,3,1,6,6,3,3,10,10,12, 12,16,16,14,14,18,18,23,23,23,20,20,20,29,29,29,32,32,32,26,26,26,1,1,1,2,3,3, 3,3,3,3,6,6,6,10,10,10,16,16,16,14,14,14,18,18,18,23,23,23,23,23,23,20,20,20, 20,20,20,31,31,31,30,30,30,34,34,34,33,33,33,28,28,28,27,27,27,90,91,90,93,91, 95,97,96,98,99],,,,[1,2,3,4,5,6,7,8,9,1,2,1,2,14,15,16,17,3,4,20,21,22,23,24, 25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,35,36,37, 51,52,53,54,55,56,39,40,41,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76, 77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,90,96,97,91,91],,,,,,,,, ,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,16,17,14,15,18,19,23,24,25,20,22,21,1,2,2,1, 2,2,1,2,2,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,54,55,56,51,52,53,57 ,58,59,66,67,68,69,70,71,63,64,65,60,61,62,38,38,38,38,38,38,38,38,38,38,38,38 ,38,38,38,38,38,38,90,91,92,93,94,95,97,96,98,99]], 0, [(98,99),(35,36,37)(39,40,41)(42,43,44)(45,46,47)(48,49,50)(51,52,53)(54,55, 56)(57,58,59)(60,61,62)(63,64,65)(66,67,68)(69,70,71),(21,22)(24,25)(60,63) (61,64)(62,65)(66,69)(67,70)(68,71),(14,16)(15,17)(20,23)(21,24,22,25)(51,54) (52,55)(53,56)(60,66,63,69)(61,67,64,70)(62,68,65,71)(96,97),(72,73,74)(75,76, 77)(78,79,80)(81,82,83)(84,85,86)(87,88,89),(27,28)(30,31)(33,34)(72,75)(73, 76)(74,77)(78,81)(79,82)(80,83)(84,87)(85,88)(86,89),(26,29,32)(27,30,33)(28, 31,34)(72,78,85,74,80,84,73,79,86)(75,81,88,77,83,87,76,82,89)], ["ConstructGS3","3.L3(7).2","3.L3(7).3",[7,8,29],[[2,3],[5,6],[8,9],[11,14], [13,15],[12,16],[17,20],[19,21],[18,22],[23,26],[25,27],[24,28],[30,31],[33, 34],[36,37],[38,41],[40,42],[39,43],[44,47],[46,48],[45,49],[51,52],[54,55], [57,58],[59,62],[61,63],[60,64],[65,68],[67,69],[66,70],[76,79],[78,80],[77, 81],[73,82],[75,83],[74,84],[88,91],[90,92],[89,93],[85,94],[87,95],[86,96], [100,103],[102,104],[101,105],[97,106],[99,107],[98,108],[109,112],[111,113], [110,114],[115,118],[117,119],[116,120],[121,124],[123,125],[122,126],[130, 133],[132,134],[131,135],[127,136],[129,137],[128,138],[142,145],[144,146], [143,147],[139,148],[141,149],[140,150],[151,154],[153,155],[152,156],[157, 160],[159,161],[158,162],[163,166],[165,167],[164,168]],[[1,1],[4,3],[7,5], [29,13],[32,15],[35,17],[50,21],[53,23],[56,25]],(1,10,15,19,30,46,67,88,21, 31,48,68,90,24,34,55,73,91,25,38,54,71,87,8,14,20,32,50,66,80,99,43,58,76,94, 36,56,75,92,27,44,60,77,96,39,53,72,86,7,12,16,23,35,57,74,93,28,45,59,78,95, 37,52,70,85,5,6,9,13,18,29,47,69,89,22,33,49,64,79,97,40,61,82)(2,11,17,26,41, 63,83)(3,51,65,81,98,42,62,84,4)]); ALF("3.L3(7).S3","L3(7).S3",[1,1,2,2,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11, 11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,18,18,18,19,19,19, 20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,25,25,26,26,26,27,27,27, 28,28,28,29,29,29,30,30,30,31,31,31,32,32,32,33,33,33,34,34,34,35,36,37, 38,39,40,41,42,43,44]); MOT("L3(2)", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7]" ], [168,8,3,4,7,7], [,[1,1,3,2,5,6],[1,2,1,4,6,5],,,,[1,2,3,4,1,1]], [[1,1,1,1,1,1],[3,-1,0,1,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6], [GALOIS,[2,3]],[6,2,0,0,-1,-1],[7,-1,1,-1,0,0],[8,0,-1,0,1,1]], [(5,6)]); ARC("L3(2)","CAS",[rec(name:="psl(2,7)", permchars:=(), permclasses:=(), text:=[ "names:=psl[2,7]; psl2[7], psu2[7], psp2[7], pom3[7]\n", " a1[7] 2a1[7] c1[7] b1[7] [lie-not.]\n", " psl3[2], sl3[2], gl3[2]\n", " a2[2] [lie-not.]\n", " order: 2^3.3.7 = 168\n", " number of classes: 6\n", " source:mckay, john\n", " the non-abelian simple groups g,\n", " ord[g]<10^6 - character tables\n", " comm.algebra 7\n", " [1979],1407-1445\n", " comments: psl[2,7] is maximal subgroup of m24 \n", ""])]); ARC("L3(2)","projectives",["2.L3(2)",[[4,0,1,0,-E(7)-E(7)^2-E(7)^4, -E(7)^3-E(7)^5-E(7)^6], [GALOIS,[1,3]],[6,0,0,E(8)-E(8)^3,-1,-1], [GALOIS,[3,3]],[8,0,-1,0,1,1]],]); ARC("L3(2)","maxes",["Symm(4)","Symm(4)","7:3"]); ARC("L3(2)","isSimple",true); ARC("L3(2)","extInfo",["2","2"]); ARC("L3(2)","tomfusion",rec(name:="L2(7)",map:=[1,2,3,6,8,8],text:=[ "fusion map is unique" ])); ALF("L3(2)","L3(2).2",[1,2,3,4,5,5]); ALF("L3(2)","A7",[1,2,4,5,8,9],[ "fusion map is unique up to table automorphisms" ]); ALF("L3(2)","L3(4)",[1,2,3,4,9,10],[ "fusion map is unique up to table autom." ],"tom:87"); ALF("L3(2)","L3(8)",[1,2,3,4,11,12],[ "fusion map is unique up to table autom." ]); ALF("L3(2)","L3(11)",[1,2,3,4,12,13],[ "fusion map is unique up to table autom." ]); ALF("L3(2)","M24",[1,3,5,8,12,13],[ "any maximal L3(2) in M24 contains elements of 2B and 3B;\n", "together with that the fusion is unique up to automorphisms,\n", "the representative is equal to that on the CAS table" ]); ALF("L3(2)","O8-(2)",[1,4,7,11,19,19],[ "fusion of the maximal subgroup, determined by the fact that 2C and 3C\n", "elements are contained" ]); ALF("L3(2)","U3(3)",[1,2,4,7,9,10],[ "fusion map is unique up to table autom." ]); ALF("L3(2)","2^3:sl(3,2)",[1,3,8,6,10,11],[ "fusion map is unique up to table automorphisms" ]); ALN("L3(2)",["L2(7)","A2(2)","A1(7)","U2(7)","S2(7)","O3(7)","psl(2,7)"]); MOT("L3(2).2", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7],\n", "constructions: Aut(L3(2))" ], [336,16,6,8,7,12,6,8,8], [,[1,1,3,2,5,1,3,4,4],[1,2,1,4,5,6,6,9,8],,,,[1,2,3,4,1,6,7,8,9]], [[1,1,1,1,1,1,1,1,1],[1,1,1,1,1,-1,-1,-1,-1],[6,-2,0,2,-1,0,0,0,0],[6,2,0,0, -1,0,0,E(8)-E(8)^3,-E(8)+E(8)^3], [TENSOR,[4,2]],[7,-1,1,-1,0,1,1,-1,-1], [TENSOR,[6,2]],[8,0,-1,0,1,2,-1,0,0], [TENSOR,[8,2]]], [(8,9)]); ARC("L3(2).2","CAS",[rec(name:="pgl(2,7)", permchars:=(), permclasses:=(), text:=[ "names:= pgl[2,7]\n", " order: 336 = 2^4 . 3 . 7\n", " number of classes: 9\n", " source: private communication of atlas compound table\n", " from cambridge 1980/81\n", " comments: extension of psl[2,7] with an outer\n", " automorphism of order 2\n", " test: orth.1, min and restricted characters of j2 \n", ""])]); ARC("L3(2).2","projectives",["2.L3(2).2",[[8,0,2,0,1,0,0,0,0],[6,0,0, E(8)-E(8)^3,-1,0,0,E(16)-E(16)^7,E(16)^3-E(16)^5], [GALOIS,[2,5]],[8,0,-1,0,1,0,-E(12)^7+E(12)^11,0,0]],]); ARC("L3(2).2","maxes",["L3(2)","7:6","D16","S3x2"]); ARC("L3(2).2","tomfusion",rec(name:="L2(7).2",map:=[1,2,4,6,11,3,8,13,13], text:=[ "fusion map is unique" ])); ALF("L3(2).2","A8.2",[1,2,5,6,11,14,19,20,20],[ "fusion map is unique" ]); ALF("L3(2).2","J2",[1,2,5,6,13,3,12,14,14],[ "fusion map is unique, equal to that on the CAS table" ]); ALF("L3(2).2","U3(3).2",[1,2,4,6,8,11,13,14,14],[ "fusion map is unique" ]); ALF("L3(2).2","U3(5).2",[1,2,3,4,9,12,14,15,15],[ "fusion map is unique" ]); ALF("L3(2).2","L3(4).2_1",[1,2,3,4,8,9,11,12,12],[ "fusion map is unique up to table autom." ],"tom:141"); ALF("L3(2).2","L3(4).2_3",[1,2,3,4,8,9,10,12,12],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); ALF("L3(2).2","L3(7)",[1,2,3,4,7,2,5,11,10],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ],"tom:95"); ALF("L3(2).2","L3(8).2",[1,2,3,4,8,42,43,44,45],[ "fusion map is unique up to table autom.", ]); ALF("L3(2).2","U3(7)",[1,2,3,6,9,2,7,17,16],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); ALF("L3(2).2","O8-(2).2",[1,4,7,11,19,35,45,49,49],[ "fusion map of the maximal subgroup, determined by the fact that\n", "2C elements are contained" ]); ALF("L3(2).2","ON.2",[1,2,3,5,9,26,27,30,30],[ "fusion determined using that the group does not lie inside ON,\n", "and that the intersection with ON lies in A7,\n", "which contains 7B elements,\n", "compatible with Brauer tables" ]); ALN("L3(2).2",["L2(7).2","pgl(2,7)","L3(8).2M6","O8-(2).2M9"]); MOT("L3(3)", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,13]" ], [5616,48,54,9,8,6,8,8,13,13,13,13], [,[1,1,3,4,2,3,5,5,11,12,10,9],[1,2,1,1,5,2,7,8,9,10,11,12],,,,,,,,,,[1,2,3,4, 5,6,8,7,1,1,1,1]], [[1,1,1,1,1,1,1,1,1,1,1,1],[12,4,3,0,0,1,0,0,-1,-1,-1,-1],[13,-3,4,1,1,0,-1, -1,0,0,0,0],[16,0,-2,1,0,0,0,0,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], [GALOIS,[4,4]], [GALOIS,[4,7]], [GALOIS,[4,2]],[26,2,-1,-1,2,-1,0,0,0,0,0,0],[26,-2,-1,-1,0,1,E(8)+E(8)^3, -E(8)-E(8)^3,0,0,0,0], [GALOIS,[9,5]],[27,3,0,0,-1,0,-1,-1,1,1,1,1],[39,-1,3,0,-1,-1,1,1,0,0,0,0]], [( 9,11,10,12),(7,8),( 9,10)(11,12),( 9,12,10,11)]); ARC("L3(3)","CAS",[rec(name:="psl(3,3)", permchars:=(6,7), permclasses:=(), text:=[ "names:psl[3,3]; psl3[3]\n", "a2[3] [lie-not.]\n", "order: 2^4.3^3.13 = 5,616\n", "number of classes: 12\n", "source:mckay, john\n", "the non-abelian simple groups g,\n", "ord[g]<10^6 - character tables\n", "comm.algebra 7\n", "[1979])],1407-1445\n", "comments: there are 2 possibilities for subgroup fusion into r2c:\n", " 13a,13a fusing into 13a, 13b,13c into 13b or\n", " 13a,13a fusing into 13b, 13c,13d into 13a. \n", ""])]); ARC("L3(3)","isSimple",true); ARC("L3(3)","extInfo",["","2"]); ARC("L3(3)","maxes",["3^2.2.S4","3^2.2.S4","13:3","s4"]); ARC("L3(3)","tomfusion",rec(name:="L3(3)",map:=[1,2,3,4,6,10,12,12,19,19, 19,19],text:=[ "fusion map is unique" ])); ALF("L3(3)","L3(3).2",[1,2,3,4,5,6,7,7,8,8,9,9],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); ALF("L3(3)","L3(9)",[1,2,3,4,7,10,21,22,28,27,29,30],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); ALF("L3(3)","2F4(2)'",[1,3,4,4,7,9,12,12,18,18,17,17],[ "fusion is unique up to table automorphisms,\n", "the representative is equal to the fusion map on the CAS table" ]); ALF("L3(3)","A13",[1,3,7,8,12,21,25,25,39,39,40,40],[ "fusion map is unique up to table automorphisms" ]); ALF("L3(3)","Th",[1,2,4,4,7,11,14,14,23,23,23,23],[ "determined using that L3(3) = N(2A,3B,3B,4B,6C,8B,13A)" ]); ALF("L3(3)","3^6:L3(3)",[1,8,23,33,38,44,53,56,59,60,61,62],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); ALF("L3(3)","B",[1,5,7,7,17,29,45,45,75,75,75,75],[ "fusion map determined by the fact that the group contains no 4E elements,\n", "and that a 3^2:2S4 subgroup is contained in 3^2.3^3.3^6.(S4x2S4)" ]); ALN("L3(3)",["psl(3,3)"]); MOT("L3(3).2", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,13],\n", "constructions: Aut(L3(3))" ], [11232,96,108,18,16,12,8,13,13,48,48,6,8,12,12], [,[1,1,3,4,2,3,5,9,8,1,2,4,5,6,6],[1,2,1,1,5,2,7,8,9,10,11,10,13,11, 11],,,,,,,,,,[1,2,3,4,5,6,7,1,1,10,11,12,13,14,15]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1],[12,4, 3,0,0,1,0,-1,-1,0,0,0,0,-E(12)^7+E(12)^11,E(12)^7-E(12)^11], [TENSOR,[3,2]],[13,-3,4,1,1,0,-1,0,0,1,-3,1,-1,0,0], [TENSOR,[5,2]],[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], [GALOIS,[7,2]],[26,2,-1,-1,2,-1,0,0,0,2,-2,-1,0,1,1], [TENSOR,[9,2]],[52,-4,-2,-2,0,2,0,0,0,0,0,0,0,0,0],[27,3,0,0,-1,0,-1,1,1,3,3, 0,-1,0,0], [TENSOR,[12,2]],[39,-1,3,0,-1,-1,1,0,0,3,-1,0,1,-1,-1], [TENSOR,[14,2]]], [(14,15),(8,9)]); ARC("L3(3).2","CAS",[rec(name:="psl(3,3):2", permchars:=(), permclasses:=(), text:=[ "names:= psl[3,3].2\n", " order: 11,232 = 2^5 . 3^3 . 13\n", " number of classes: 15\n", " source: private communication of atlas compound table\n", " from cambridge 1980/81\n", " comments: extension of psl[3,3] with an outer\n", " automorphism of order 2\n", " test: orth.1, min \n", ""])]); ARC("L3(3).2","tomfusion",rec(name:="L3(3).2",map:=[1,2,4,5,9,14,24,33,33,3,6, 15,22,30,30],text:=[ "fusion map is unique" ])); ARC("L3(3).2","maxes",["L3(3)","3^(1+2):D8","group6","13:6","2xSymm(4)"]); ALF("L3(3).2","Suz",[1,2,5,6,9,16,21,32,33,3,8,17,21,31,31],[ "fusion is unique up to table automorphisms,\n", "the representative is equal to the fusion map on the CAS table" ]); ALF("L3(3).2","2F4(2)'",[1,3,4,4,7,9,12,17,18,3,5,9,13,15,16],[ "fusion is unique up to table automorphisms" ],"tom:433"); ALF("L3(3).2","G2(3)",[1,2,3,6,9,10,16,22,23,2,8,12,16,20,20],[ "fusion is unique up to table automorphisms,\n", "compatible with Brauer tables" ],"tom:428"); ALF("L3(3).2","S6(3)",[1,2,7,10,13,24,32,58,57,3,12,30,33,54,54],[ "fusion is unique up to table automorphisms,\n", "unique map that is compatible with Brauer tables" ]); ALN("L3(3).2",["psl(3,3).2","psl(3,3):2"]); MOT("G2(3)M6", [ "6th maximal subgroup of G2(3),\n", "differs from G2(3)M5 only by fusion map" ], 0, 0, 0, 0, ["ConstructPermuted",["L3(3).2"]]); ALF("G2(3)M6","G2(3)",[1,2,4,6,8,11,15,23,22,2,9,12,15,21,21],[ "fusion L3(3).2 -> G2(3) mapped under G2(3).2" ]); MOT("L3(5)", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,31]" ], [372000,480,24,480,480,16,500,25,24,24,24,20,24,24,20,20,24,24,24,24,31,31,31, 31,31,31,31,31,31,31], [,[1,1,3,2,2,2,7,8,3,4,5,7,9,9,12,12,13,14,13,14,23,24,25,26,27,28,29,30,21, 22],[1,2,1,5,4,6,7,8,2,11,10,12,5,4,16,15,11,10,11,10,30,29,22,21,24,23,26,25, 28,27],,[1,2,3,4,5,6,1,1,9,10,11,2,13,14,4,5,17,18,19,20,21,22,23,24,25,26,27, 28,29,30],,,,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,5,4,6,7,8,9,11,10,12,14,13,16,15,20, 19,18,17,1,1,1,1,1,1,1,1,1,1]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[30,6,0,6,6,2, 5,0,0,0,0,1,0,0,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[31,7,1,-5,-5,-1,6, 1,1,-1,-1,2,1,1,0,0,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],[31,-5,1,-1+6*E(4), -1-6*E(4),1,6,1,1,E(4),-E(4),0,-1,-1,-1+E(4),-1-E(4),E(4),-E(4),E(4),-E(4),0, 0,0,0,0,0,0,0,0,0], [GALOIS,[4,3]],[96,0,0,0,0,0,-4,1,0,0,0,0,0,0,0,0,0,0,0,0, E(31)+E(31)^5+E(31)^25,E(31)^6+E(31)^26+E(31)^30,E(31)^2+E(31)^10+E(31)^19, E(31)^12+E(31)^21+E(31)^29,E(31)^4+E(31)^7+E(31)^20,E(31)^11+E(31)^24+E(31)^27 ,E(31)^8+E(31)^9+E(31)^14,E(31)^17+E(31)^22+E(31)^23,E(31)^16+E(31)^18 +E(31)^28,E(31)^3+E(31)^13+E(31)^15], [GALOIS,[6,6]], [GALOIS,[6,16]], [GALOIS,[6,3]], [GALOIS,[6,8]], [GALOIS,[6,17]], [GALOIS,[6,4]], [GALOIS,[6,11]], [GALOIS,[6,2]], [GALOIS,[6,12]],[124,4,1,4,4,0,-1,-1,1,2,2,-1,1,1,-1,-1,-1,-1,-1,-1,0,0,0,0,0, 0,0,0,0,0],[124,4,1,4,4,0,-1,-1,1,-2,-2,-1,1,1,-1,-1,1,1,1,1,0,0,0,0,0,0,0,0, 0,0],[124,4,1,-4,-4,0,-1,-1,1,2*E(4),-2*E(4),-1,-1,-1,1,1,-E(4),E(4),-E(4), E(4),0,0,0,0,0,0,0,0,0,0], [GALOIS,[18,3]],[124,-4,-2,4*E(4),-4*E(4),0,-1,-1,2,0,0,1,-2*E(4),2*E(4), -E(4),E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[20,3]],[124,-4,1,-4*E(4),4*E(4),0,-1,-1,-1,0,0,1,-E(4),E(4),E(4), -E(4),E(24)-E(24)^17,-E(24)^11+E(24)^19,-E(24)+E(24)^17,E(24)^11-E(24)^19,0,0, 0,0,0,0,0,0,0,0], [GALOIS,[22,19]], [GALOIS,[22,13]], [GALOIS,[22,7]],[125,5,-1,5,5,1,0,0,-1,-1,-1,0,-1,-1,0,0,-1,-1,-1,-1,1,1,1,1, 1,1,1,1,1,1],[155,11,-1,-1,-1,-1,5,0,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,0,0,0,0,0,0, 0,0,0,0],[155,-1,-1,-5+6*E(4),-5-6*E(4),1,5,0,-1,-E(4),E(4),-1,1,1,E(4),-E(4), -E(4),E(4),-E(4),E(4),0,0,0,0,0,0,0,0,0,0], [GALOIS,[28,3]],[186,-6,0,6,6,-2,11,1,0,0,0,-1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0, 0,0,0]], [(21,30,27,26,23,22,29,28,25,24),(17,19)(18,20),( 4, 5)(10,11)(13,14)(15,16) (17,18)(19,20),( 4, 5)(10,11)(13,14)(15,16)(17,20)(18,19),(21,22)(23,24) (25,26)(27,28)(29,30),(21,29,27,25,23)(22,30,28,26,24)]); ARC("L3(5)","CAS",[rec(name:="psl(3,5)", permchars:=( 7,11,13, 9)( 8,12,14,10)(20,24,22,23)(21,25), permclasses:=(18,20,19)(22,26,24,30)(23,25,29,27), text:=[ "names:=psl[3,5]; psl3[5]\n", " a2[5] [lie-not.]\n", " order: 2^5.3.5^3.31 = 372,000\n", " number of classes: 30\n", " source:mckay, john\n", " the non-abelian simple groups g,\n", " ord[g]<10^6 - character tables\n", " comm.algebra 7\n", " [1979],1407-1445\n", " comments: - \n", ""])]); ARC("L3(5)","isSimple",true); ARC("L3(5)","extInfo",["","2"]); ARC("L3(5)","maxes",["5^2:4s5","5^2:4s5","A5.2","4^2:s3","31:3"]); ARC("L3(5)","tomfusion",rec(name:="L3(5)",map:=[1,2,3,4,4,5,7,8,9,12,12,18,21, 21,32,32,36,36,36,36,42,42,42,42,42,42,42,42,42,42],text:=[ "fusion map is unique" ])); ALF("L3(5)","L3(5).2",[1,2,3,4,4,5,6,7,8,9,9,10,11,11,12,12,13,13,14,14, 15,15,16,16,17,17,18,18,19,19],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); ALN("L3(5)",["psl(3,5)","L3(5).2M1"]); MOT("L3(5).2", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,31],\n", "constructions: Aut(L3(5))" ], [744000,960,48,480,32,1000,50,48,24,40,24,20,24,24,31,31,31,31,31,240,240,12, 8,10,12,20,20], [,[1,1,3,2,2,6,7,3,4,6,8,10,11,11,16,17,18,19,15,1,2,3,5,7,8,10,10],[1,2,1,4, 5,6,7,2,9,10,4,12,9,9,19,15,16,17,18,20,21,20,23,24,21,27,26],,[1,2,3,4,5,1,1, 8,9,2,11,4,13,14,15,16,17,18,19,20,21,22,23,20,25,21, 21],,,,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,14,13,1,1,1,1,1,20, 21,22,23,24,25,26,27]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1],[30,6,0,6,2,5,0,0,0,1,0,1,0,0,-1, -1,-1,-1,-1,0,0,0,0,0,0,E(5)-E(5)^2-E(5)^3+E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4], [TENSOR,[3,2]],[31,7,1,-5,-1,6,1,1,-1,2,1,0,-1,-1,0,0,0,0,0,1,5,1,-1,1,-1,0, 0], [TENSOR,[5,2]],[62,-10,2,-2,2,12,2,2,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0],[192,0,0,0,0,-8,2,0,0,0,0,0,0,0,E(31)+E(31)^5+E(31)^6+E(31)^25+E(31)^26 +E(31)^30,E(31)^2+E(31)^10+E(31)^12+E(31)^19+E(31)^21+E(31)^29, E(31)^4+E(31)^7+E(31)^11+E(31)^20+E(31)^24+E(31)^27,E(31)^8+E(31)^9+E(31)^14 +E(31)^17+E(31)^22+E(31)^23,E(31)^3+E(31)^13+E(31)^15+E(31)^16+E(31)^18 +E(31)^28,0,0,0,0,0,0,0,0], [GALOIS,[8,3]], [GALOIS,[8,8]], [GALOIS,[8,4]], [GALOIS,[8,2]],[124,4,1,4,0,-1,-1,1,2,-1,1,-1,-1,-1,0,0,0,0,0,4,-4,1,0,-1,-1, 1,1], [TENSOR,[13,2]],[124,4,1,4,0,-1,-1,1,-2,-1,1,-1,1,1,0,0,0,0,0,4,4,1,0,-1,1,-1, -1], [TENSOR,[15,2]],[248,8,2,-8,0,-2,-2,2,0,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0],[248,-8,-4,0,0,-2,-2,4,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[248,-8,2,0, 0,-2,-2,-2,0,2,0,0,E(24)-E(24)^11-E(24)^17+E(24)^19,-E(24)+E(24)^11+E(24)^17 -E(24)^19,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[19,7]],[125,5,-1,5,1,0,0,-1,-1,0,-1,0,-1,-1,1,1,1,1,1,5,5,-1,1,0,-1, 0,0], [TENSOR,[21,2]],[155,11,-1,-1,-1,5,0,-1,1,1,-1,-1,1,1,0,0,0,0,0,5,1,-1,-1,0,1, 1,1], [TENSOR,[23,2]],[310,-2,-2,-10,2,10,0,-2,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0],[186,-6,0,6,-2,11,1,0,0,-1,0,1,0,0,0,0,0,0,0,6,-6,0,0,1,0,-1,-1], [TENSOR,[26,2]]], [(26,27),(15,19,18,17,16),(13,14)]); ARC("L3(5).2","CAS",[rec(name:="psl(3,5).2", permchars:=(), permclasses:=(), text:=[ "names:= psl[3,5].2\n", " order: 744,000 = 2^6 . 3 . 5^3 . 31\n", " number of classes: 27\n", " source: private communication of atlas compound table\n", " from cambridge 1980/81\n", " comments: extension of psl[3,5] with an outer\n", " automorphism of order 2\n", " test: orth.1, min \n", ""])]); ALF("L3(5).2","G2(5)",[1,2,4,6,5,7,11,13,17,18,23,30,35,36,40,41,42,43,44, 2,6,14,16,21,23,30,30],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); ALN("L3(5).2",["psl(3,5).2"]); MOT("L3(7)", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,19]" ], [1876896,672,36,16,12,686,49,49,49,16,16,14,16,16,16,16,19,19,19,19,19,19], [,[1,1,3,2,3,6,7,8,9,4,4,6,10,10,11,11,20,19,22,21,18,17],[1,2,1,4,2,6,7,8,9, 11,10,12,15,16,14,13,20,19,22,21,18,17],,,,[1,2,3,4,5,1,1,1,1,10,11,2,13,14, 15,16,17,18,19,20,21,22],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,11,10,12,15,16,14,13,1, 1,1,1,1,1]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[56,8,2,0,2,7,0,0,0,0,0,1,0,0, 0,0,-1,-1,-1,-1,-1,-1],[57,-7,3,1,-1,8,1,1,1,1,1,0,-1,-1,-1,-1,0,0,0,0,0,0],[ 152,8,-1,0,-1,5,5,-2,-2,0,0,1,0,0,0,0,0,0,0,0,0,0],[152,8,-1,0,-1,5,-2,5,-2,0, 0,1,0,0,0,0,0,0,0,0,0,0],[152,8,-1,0,-1,5,-2,-2,5,0,0,1,0,0,0,0,0,0,0,0,0,0],[ 288,0,0,0,0,-6,1,1,1,0,0,0,0,0,0,0,E(19)+E(19)^7+E(19)^11,E(19)^8+E(19)^12 +E(19)^18,E(19)^5+E(19)^16+E(19)^17,E(19)^2+E(19)^3+E(19)^14, E(19)^4+E(19)^6+E(19)^9,E(19)^10+E(19)^13+E(19)^15], [GALOIS,[7,8]], [GALOIS,[7,4]], [GALOIS,[7,10]], [GALOIS,[7,5]], [GALOIS,[7,2]],[342,6,0,-2,0,-1,-1,-1,-1,2,2,-1,0,0,0,0,0,0,0,0,0,0],[342,6,0, 2,0,-1,-1,-1,-1,0,0,-1,E(8)-E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3,0,0, 0,0,0,0], [GALOIS,[14,3]],[342,-6,0,0,0,-1,-1,-1,-1,-E(8)+E(8)^3,E(8)-E(8)^3,1, E(16)+E(16)^7,-E(16)-E(16)^7,E(16)^3+E(16)^5,-E(16)^3-E(16)^5,0,0,0,0,0,0], [GALOIS,[16,9]], [GALOIS,[16,11]], [GALOIS,[16,3]],[343,7,1,-1,1,0,0,0,0,-1,-1,0,-1,-1,-1,-1,1,1,1,1,1,1],[399, -1,3,-1,-1,7,0,0,0,-1,-1,-1,1,1,1,1,0,0,0,0,0,0],[456,-8,-3,0,1,15,1,1,1,0,0, -1,0,0,0,0,0,0,0,0,0,0]], [(17,20,21,18,19,22),(13,14)(15,16),(10,11)(13,16,14,15),(7,9),(7,8),(8,9), (17,18)(19,20)(21,22),(17,21,19)(18,22,20)]); ARC("L3(7)","projectives",["3.L3(7)",[[57,9,0,1,0,8,1,1,1,1,1,2,1,1,1,1,0,0,0, 0,0,0],[57,-7,0,1,2,8,1,1,1,1,1,0,-1,-1,-1,-1,0,0,0,0,0,0],[96,0,0,0,0,-2,5, -2,-2,0,0,0,0,0,0,0,1,1,1,1,1,1],[96,0,0,0,0,-2,-2,5,-2,0,0,0,0,0,0,0,1,1,1,1, 1,1],[96,0,0,0,0,-2,-2,-2,5,0,0,0,0,0,0,0,1,1,1,1,1,1],[288,0,0,0,0,-6,1,1,1, 0,0,0,0,0,0,0,E(19)+E(19)^7+E(19)^11,E(19)^8+E(19)^12+E(19)^18, E(19)^5+E(19)^16+E(19)^17,E(19)^2+E(19)^3+E(19)^14,E(19)^4+E(19)^6+E(19)^9, E(19)^10+E(19)^13+E(19)^15], [GALOIS,[6,8]], [GALOIS,[6,4]], [GALOIS,[6,10]], [GALOIS,[6,5]], [GALOIS,[6,2]],[342,6,0,-2,0,-1,-1,-1,-1,2,2,-1,0,0,0,0,0,0,0,0,0,0],[342,6,0, 2,0,-1,-1,-1,-1,0,0,-1,E(8)-E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3,0,0, 0,0,0,0], [GALOIS,[13,3]],[342,-6,0,0,0,-1,-1,-1,-1,-E(8)+E(8)^3,E(8)-E(8)^3,1, E(16)+E(16)^7,-E(16)-E(16)^7,E(16)^3+E(16)^5,-E(16)^3-E(16)^5,0,0,0,0,0,0], [GALOIS,[15,9]], [GALOIS,[15,11]], [GALOIS,[15,3]],[399,15,0,-1,0,7,0,0,0,-1,-1,1,-1,-1,-1,-1,0,0,0,0,0,0],[399, -1,0,-1,2,7,0,0,0,-1,-1,-1,1,1,1,1,0,0,0,0,0,0],[456,-8,0,0,-2,15,1,1,1,0,0, -1,0,0,0,0,0,0,0,0,0,0]],]); ARC("L3(7)","isSimple",true); ARC("L3(7)","extInfo",["3","3.2"]); ARC("L3(7)","maxes",["7^2:2.L2(7).2","L3(7)M2","L3(2).2","L3(7)M4","L3(7)M5", "(A4x3):2","3^2:Q8","19:3"]); ARC("L3(7)","tomfusion",rec(name:="L3(7)",map:=[1,2,3,5,6,8,11,9,10,13,13, 27,29,29,29,29,32,32,32,32,32,32],text:=[ "unique fusion map compatible with AtlasRep" ],perm:=(3,4))); ALF("L3(7)","L3(7).2",[1,2,3,4,5,6,7,8,8,9,10,11,12,12,13,13,14,14,15,15, 16,16],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); ALF("L3(7)","L3(7).3",[1,2,3,4,5,6,7,7,7,8,9,10,11,12,13,14,15,16,17,18, 19,20],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); ALN("L3(7)",["L3(7).2M1"]); MOT("L3(7).2", [ "origin: ATLAS of finite groups,\n", "2nd power map determined only up to matrix automorphism (9,10)" ], [3753792,1344,72,32,24,1372,98,49,32,32,28,16,16,19,19,19,672,672,12,16,12,14, 16,16,28,28], [,[1,1,3,2,3,6,7,8,4,4,6,9,10,15,16,14,1,2,3,4,5,7,9,10,11,11],[1,2,1,4,2,6,7, 8,10,9,11,13,12,15,16,14,17,18,17,20,18,22,24,23,25,26],,,,[1,2,3,4,5,1,1,1,9, 10,2,12,13,14,15,16,17,18,19,20,21,17,23,24,18,18],,,,,,,,,,,,[1,2,3,4,5,6,7, 8,10,9,11,13,12,1,1,1,17,18,19,20,21,22,24,23,25,26]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[56,8,2,0,2,7,0,0,0,0,1,0,0,-1,-1,-1, 0,0,0,0,0,0,0,0,E(28)^3-E(28)^11-E(28)^15+E(28)^19-E(28)^23+E(28)^27, -E(28)^3+E(28)^11+E(28)^15-E(28)^19+E(28)^23-E(28)^27], [TENSOR,[3,2]],[57,-7,3,1,-1,8,1,1,1,1,0,-1,-1,0,0,0,1,-7,1,1,-1,1,-1,-1,0,0], [TENSOR,[5,2]],[152,8,-1,0,-1,5,5,-2,0,0,1,0,0,0,0,0,8,8,-1,0,-1,1,0,0,1,1], [TENSOR,[7,2]],[304,16,-2,0,-2,10,-4,3,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[ 576,0,0,0,0,-12,2,2,0,0,0,0,0,E(19)+E(19)^7+E(19)^8+E(19)^11+E(19)^12+E(19)^18 ,E(19)^2+E(19)^3+E(19)^5+E(19)^14+E(19)^16+E(19)^17,E(19)^4+E(19)^6+E(19)^9 +E(19)^10+E(19)^13+E(19)^15,0,0,0,0,0,0,0,0,0,0], [GALOIS,[10,4]], [GALOIS,[10,2]],[342,6,0,-2,0,-1,-1,-1,2,2,-1,0,0,0,0,0,6,6,0,2,0,-1,0,0,-1, -1], [TENSOR,[13,2]],[342,6,0,2,0,-1,-1,-1,0,0,-1,E(8)-E(8)^3,-E(8)+E(8)^3,0,0,0,6, -6,0,0,0,-1,-E(8)+E(8)^3,E(8)-E(8)^3,1,1], [TENSOR,[15,2]], [GALOIS,[15,3]], [TENSOR,[17,2]],[684,-12,0,0,0,-2,-2,-2,-2*E(8)+2*E(8)^3,2*E(8)-2*E(8)^3,2,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[19,3]],[343,7,1,-1,1,0,0,0,-1,-1,0,-1,-1,1,1,1,7,7,1,-1,1,0,-1,-1,0, 0], [TENSOR,[21,2]],[399,-1,3,-1,-1,7,0,0,-1,-1,-1,1,1,0,0,0,7,-1,1,-1,-1,0,1,1, -1,-1], [TENSOR,[23,2]],[456,-8,-3,0,1,15,1,1,0,0,-1,0,0,0,0,0,8,-8,-1,0,1,1,0,0,-1, -1], [TENSOR,[25,2]]], [(25,26),(14,15,16),(14,16,15),( 9,10)(12,13)(23,24)]); ALF("L3(7).2","L3(7).S3",[1,2,3,4,5,6,7,7,8,9,10,11,12,13,14,15,35,36,37, 38,39,40,41,42,43,44],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); ALF("L3(7).2","ON",[1,2,3,5,7,8,8,9,10,10,15,18,19,22,23,24,2,4,7,10,14, 15,19,18,27,28],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); MOT("L3(7).3", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,19],\n", "constructions: PGL(3,7)" ], [5630688,2016,108,48,36,2058,49,48,48,42,48,48,48,48,57,57,57,57,57,57,2016, 2016,171,171,2016,2016,36,36,48,48,42,42,48,48,48,48,42,42,48,48,48,48,48,48, 48,48,57,57,57,57,57,57,57,57,57,57,57,57], [,[1,1,3,2,3,6,7,4,4,6,8,8,9,9,18,17,20,19,16,15,22,21,24,23,22,21,22,21,26, 25,32,31,30,29,30,29,32,31,34,33,34,33,36,35,36,35,54,53,52,51,58,57,56,55,50, 49,48,47],[1,2,1,4,2,6,7,9,8,10,13,14,12,11,18,17,20,19,16,15,1,1,1,1,2,2,2,2, 4,4,6,6,9,9,8,8,10,10,13,13,14,14,12,12,11,11,18,18,17,17,20,20,19,19,16,16, 15,15],,,,[1,2,3,4,5,1,1,8,9,2,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25, 26,27,28,29,30,21,22,33,34,35,36,25,26,39,40,41,42,43,44,45,46,47,48,49,50,51, 52,53,54,55,56,57,58],,,,,,,,,,,,[1,2,3,4,5,6,7,9,8,10,13,14,12,11,1,1,1,1,1, 1,21,22,23,24,25,26,27,28,29,30,31,32,35,36,33,34,37,38,43,44,45,46,41,42,39, 40,23,24,23,24,23,24,23,24,23,24,23,24]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2, E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3), E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3), E(3)^2], [TENSOR,[2,2]],[56,8,2,0,2,7,0,0,0,1,0,0,0,0,-1,-1,-1,-1,-1,-1,8,8,-1,-1,8,8, 2,2,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1], [TENSOR,[4,2]], [TENSOR,[4,3]],[57,-7,3,1,-1,8,1,1,1,0,-1,-1,-1,-1,0,0,0,0,0,0,9,9,0,0,-7,-7, -1,-1,1,1,2,2,1,1,1,1,0,0,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[7,2]], [TENSOR,[7,3]],[456,24,-3,0,-3,15,1,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[288,0,0,0,0,-6, 1,0,0,0,0,0,0,0,E(19)+E(19)^7+E(19)^11,E(19)^8+E(19)^12+E(19)^18, E(19)^5+E(19)^16+E(19)^17,E(19)^2+E(19)^3+E(19)^14,E(19)^4+E(19)^6+E(19)^9, E(19)^10+E(19)^13+E(19)^15,0,0,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,E(19)+E(19)^7+E(19)^11,E(19)+E(19)^7+E(19)^11,E(19)^8+E(19)^12+E(19)^18, E(19)^8+E(19)^12+E(19)^18,E(19)^5+E(19)^16+E(19)^17,E(19)^5+E(19)^16+E(19)^17, E(19)^2+E(19)^3+E(19)^14,E(19)^2+E(19)^3+E(19)^14,E(19)^4+E(19)^6+E(19)^9, E(19)^4+E(19)^6+E(19)^9,E(19)^10+E(19)^13+E(19)^15,E(19)^10+E(19)^13+E(19)^15 ], [TENSOR,[11,2]], [TENSOR,[11,3]], [GALOIS,[11,8]], [TENSOR,[14,2]], [TENSOR,[14,3]], [GALOIS,[11,4]], [TENSOR,[17,2]], [TENSOR,[17,3]], [GALOIS,[11,10]], [TENSOR,[20,2]], [TENSOR,[20,3]], [GALOIS,[11,5]], [TENSOR,[23,2]], [TENSOR,[23,3]], [GALOIS,[11,2]], [TENSOR,[26,2]], [TENSOR,[26,3]],[342,6,0,-2,0,-1,-1,2,2,-1,0,0,0,0,0,0,0,0,0,0,6,6,0,0,6,6,0, 0,-2,-2,-1,-1,2,2,2,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[29,2]], [TENSOR,[29,3]],[342,6,0,2,0,-1,-1,0,0,-1,E(8)-E(8)^3,E(8)-E(8)^3, -E(8)+E(8)^3,-E(8)+E(8)^3,0,0,0,0,0,0,6,6,0,0,6,6,0,0,2,2,-1,-1,0,0,0,0,-1,-1, E(8)-E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3, -E(8)+E(8)^3,-E(8)+E(8)^3,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[32,2]], [TENSOR,[32,3]], [GALOIS,[32,3]], [TENSOR,[35,2]], [TENSOR,[35,3]],[342,-6,0,0,0,-1,-1,-E(8)+E(8)^3,E(8)-E(8)^3,1,E(16)+E(16)^7, -E(16)-E(16)^7,E(16)^3+E(16)^5,-E(16)^3-E(16)^5,0,0,0,0,0,0,6,6,0,0,-6,-6,0,0, 0,0,-1,-1,-E(8)+E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,1,1,E(16)+E(16)^7, E(16)+E(16)^7,-E(16)-E(16)^7,-E(16)-E(16)^7,E(16)^3+E(16)^5,E(16)^3+E(16)^5, -E(16)^3-E(16)^5,-E(16)^3-E(16)^5,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[38,2]], [TENSOR,[38,3]], [GALOIS,[38,9]], [TENSOR,[41,2]], [TENSOR,[41,3]], [GALOIS,[38,11]], [TENSOR,[44,2]], [TENSOR,[44,3]], [GALOIS,[38,3]], [TENSOR,[47,2]], [TENSOR,[47,3]],[343,7,1,-1,1,0,0,-1,-1,0,-1,-1,-1,-1,1,1,1,1,1,1,7,7,1,1,7,7, 1,1,-1,-1,0,0,-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], [TENSOR,[50,2]], [TENSOR,[50,3]],[399,-1,3,-1,-1,7,0,-1,-1,-1,1,1,1,1,0,0,0,0,0,0,15,15,0,0,-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], [TENSOR,[53,2]], [TENSOR,[53,3]],[456,-8,-3,0,1,15,1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,16,16, -2,-2,0,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[56,2]], [TENSOR,[56,3]]], [(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42) (43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58),(15,18,19,16,17,20) (47,53,55,49,51,57)(48,54,56,50,52,58),(11,12)(13,14)(39,41)(40,42)(43,45) (44,46),( 8, 9)(11,14,12,13)(33,35)(34,36)(39,45,41,43)(40,46,42,44),(15,16) (17,18)(19,20)(47,49)(48,50)(51,53)(52,54)(55,57)(56,58),(15,19,17)(16,20,18) (47,55,51)(48,56,52)(49,57,53)(50,58,54)]); ARC("L3(7).3","projectives",["3.L3(7).3",[[57,9,0,1,0,8,1,1,1,2,1,1,1,1,0,0,0, 0,0,0,-E(3)+7*E(3)^2,7*E(3)-E(3)^2,0,0,-E(3)+7*E(3)^2,7*E(3)-E(3)^2, -E(3)+E(3)^2,E(3)-E(3)^2,1,1,-E(3),-E(3)^2,1,1,1,1,-E(3),-E(3)^2,1,1,1,1,1,1, 1,1,0,0,0,0,0,0,0,0,0,0,0,0],[57,-7,0,1,2,8,1,1,1,0,-1,-1,-1,-1,0,0,0,0,0,0, -E(3)+7*E(3)^2,7*E(3)-E(3)^2,0,0,-E(3)-9*E(3)^2,-9*E(3)-E(3)^2,-1,-1,1,1, -E(3),-E(3)^2,1,1,1,1,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,-1,-1,-1,-1,-1,-1,-1,-1,0, 0,0,0,0,0,0,0,0,0,0,0],[288,0,0,0,0,-6,1,0,0,0,0,0,0,0,3,3,3,3,3,3,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[288,0,0,0, 0,-6,1,0,0,0,0,0,0,0,E(19)+E(19)^7+E(19)^11,E(19)^8+E(19)^12+E(19)^18, E(19)^5+E(19)^16+E(19)^17,E(19)^2+E(19)^3+E(19)^14,E(19)^4+E(19)^6+E(19)^9, E(19)^10+E(19)^13+E(19)^15,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,E(171)^4+E(171)^25-E(171)^85-E(171)^142,E(171)^23-E(171)^47+E(171)^101 -E(171)^104,-E(171)^67+E(171)^70-E(171)^124+E(171)^148,-E(171)^29-E(171)^86 +E(171)^146+E(171)^167,E(171)^7+E(171)^49-E(171)^58-E(171)^115, -E(171)^20+E(171)^68-E(171)^77+E(171)^83,E(171)^88-E(171)^94+E(171)^103 -E(171)^151,-E(171)^56-E(171)^113+E(171)^122+E(171)^164,-E(171)^16-E(171)^130 +E(171)^157+E(171)^169,E(171)^5+E(171)^74-E(171)^92-E(171)^149, -E(171)^22-E(171)^79+E(171)^97+E(171)^166,E(171)^2+E(171)^14-E(171)^41 -E(171)^155], [GALOIS,[4,37]], [GALOIS,[4,61]], [GALOIS,[4,34]], [GALOIS,[4,43]], [GALOIS,[4,22]],[342,6,0,-2,0,-1,-1,2,2,-1,0,0,0,0,0,0,0,0,0,0,6,6,0,0,6,6,0, 0,-2,-2,-1,-1,2,2,2,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[342,6,0, 2,0,-1,-1,0,0,-1,E(8)-E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3,0,0,0,0,0, 0,6,6,0,0,6,6,0,0,2,2,-1,-1,0,0,0,0,-1,-1,E(8)-E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3, E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3,0,0,0,0,0,0,0, 0,0,0,0,0], [GALOIS,[11,3]],[342,-6,0,0,0,-1,-1,-E(8)+E(8)^3,E(8)-E(8)^3,1,E(16)+E(16)^7, -E(16)-E(16)^7,E(16)^3+E(16)^5,-E(16)^3-E(16)^5,0,0,0,0,0,0,6,6,0,0,-6,-6,0,0, 0,0,-1,-1,-E(8)+E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,1,1,E(16)+E(16)^7, E(16)+E(16)^7,-E(16)-E(16)^7,-E(16)-E(16)^7,E(16)^3+E(16)^5,E(16)^3+E(16)^5, -E(16)^3-E(16)^5,-E(16)^3-E(16)^5,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[13,9]], [GALOIS,[13,11]], [GALOIS,[13,3]],[399,15,0,-1,0,7,0,-1,-1,1,-1,-1,-1,-1,0,0,0,0,0,0, -7*E(3)+E(3)^2,E(3)-7*E(3)^2,0,0,-7*E(3)+E(3)^2,E(3)-7*E(3)^2,-E(3)+E(3)^2, E(3)-E(3)^2,-1,-1,E(3)^2,E(3),-1,-1,-1,-1,E(3)^2,E(3),-1,-1,-1,-1,-1,-1,-1,-1, 0,0,0,0,0,0,0,0,0,0,0,0],[399,-1,0,-1,2,7,0,-1,-1,-1,1,1,1,1,0,0,0,0,0,0, -7*E(3)+E(3)^2,E(3)-7*E(3)^2,0,0,-7*E(3)-15*E(3)^2,-15*E(3)-7*E(3)^2,-1,-1,-1, -1,E(3)^2,E(3),-1,-1,-1,-1,-E(3)^2,-E(3),1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0, 0,0],[456,-8,0,0,-2,15,1,0,0,-1,0,0,0,0,0,0,0,0,0,0,-8*E(3)+8*E(3)^2, 8*E(3)-8*E(3)^2,0,0,-8,-8,-2*E(3)^2,-2*E(3),0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,0, 0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],]); ALF("L3(7).3","L3(7).S3",[1,2,3,4,5,6,7,8,9,10,11,11,12,12,13,13,14,14,15, 15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,26,26,25,27, 28,28,27,29,30,30,29,31,32,32,31,33,34,34,33],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); MOT("L3(7).S3", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,19],\n", "constructions: Aut(L3(7))" ], [11261376,4032,216,96,72,4116,98,96,96,84,48,48,57,57,57,2016,171,2016,36,48, 42,48,48,42,48,48,48,48,57,57,57,57,57,57,672,672,12,16,12,14,16,16,28,28], [,[1,1,3,2,3,6,7,4,4,6,8,9,14,15,13,16,17,16,16,18,21,20,20,21,22,22,23,23,31, 32,33,34,29,30,1,2,3,4,5,7,8,9,10,10],[1,2,1,4,2,6,7,9,8,10,12,11,14,15,13,1,1 ,2,2,4,6,9,8,10,12,12,11,11,14,14,15,15,13,13,35,36,35,38,36,40,42,41,43,44],, ,,[1,2,3,4,5,1,1,8,9,2,11,12,13,14,15,16,17,18,19,20,16,22,23,18,25,26,27,28, 29,30,31,32,33,34,35,36,37,38,39,35,41,42,36,36],,,,,,,,,,,,[1,2,3,4,5,6,7,9,8 ,10,12,11,1,1,1,16,17,18,19,20,21,23,22,24,27,28,26,25,17,17,17,17,17,17,35,36 ,37,38,39,40,42,41,43,44]], 0, [(43,44),(25,26)(27,28),(8,9)(11,12)(22,23)(25,27,26,28)(41,42),(29,30)(31,32) (33,34),(13,14,15)(29,31,33)(30,32,34)], ["ConstructGS3","L3(7).2","L3(7).3",[7,8],[[2,3],[5,6],[8,9],[11,14],[13,15], [12,16],[17,20],[19,21],[18,22],[23,26],[25,27],[24,28],[30,31],[33,34],[36, 37],[38,41],[40,42],[39,43],[44,47],[46,48],[45,49],[51,52],[54,55],[57,58]], [[1,1],[4,3],[7,5],[29,13],[32,15],[35,17],[50,21],[53,23],[56,25]],(1,10,17, 29,4,6,12,18,30,5,9,15,23,34,22,35,24,38,28,2,11,16,26,44,43,42,40,37,27)(7, 14,19,32,8,13,20,31)(21,33)(25,41,39,36)]); ALN("L3(7).S3",["L3(7).3.2"]); MOT("L3(8)", [ "origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,73]" ], [16482816,3584,63,64,3528,3528,3528,3528,3528,3528,49,49,49,49,49,63,63,63,56, 56,56,56,56,56,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63, 63,63,63,73,73,73,73,73,73,73,73,73,73,73,73,73,73,73,73,73,73,73,73,73,73,73, 73], [,[1,1,3,2,7,8,9,10,5,6,11,12,14,15,13,17,18,16,7,8,9,10,5,6,27,28,29,30,25, 26,33,34,35,36,31,32,39,40,41,42,37,38,45,46,47,48,43,44,51,52,53,54,49,50,57, 58,59,60,55,56,63,64,65,66,61,62,69,70,71,72,67,68],[1,2,1,4,10,9,6,5,8,7,12, 11,15,13,14,3,3,3,24,23,20,19,22,21,10,9,6,5,8,7,30,29,26,25,28,27,26,25,28, 27,30,29,28,27,30,29,26,25,62,61,64,63,66,65,68,67,70,69,72,71,49,50,51,52,53, 54,55,56,57,58,59,60],,,,[1,2,3,4,1,1,1,1,1,1,1,1,1,1,1,17,18,16,2,2,2,2,2,2, 3,3,3,3,3,3,17,17,18,18,16,16,16,16,17,17,18,18,18,18,16,16,17,17,55,56,57,58, 59,60,61,62,63,64,65,66,67,68,69,70,71,72,50,49,52,51,54, 53],,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,4, 10,9,6,5,8,7,12,11,15,13,14,16,17,18,24,23,20,19,22,21,30,29,26,25,28,27,40, 39,42,41,38,37,46,45,48,47,44,43,34,33,36,35,32,31,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[72,8,0, 0,9,9,9,9,9,9,2,2,2,2,2,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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],[73,9,1,1,E(7)+9*E(7)^3,9*E(7)^4+E(7)^6,E(7)^2+9*E(7)^6,9*E(7)+E(7)^5, E(7)^4+9*E(7)^5,9*E(7)^2+E(7)^3,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6, -E(7)^2-E(7)^3-E(7)^4-E(7)^5,-E(7)-E(7)^3-E(7)^4-E(7)^6,-E(7)-E(7)^2-E(7)^5 -E(7)^6,1,1,1,E(7)+E(7)^3,E(7)^4+E(7)^6,E(7)^2+E(7)^6,E(7)+E(7)^5, E(7)^4+E(7)^5,E(7)^2+E(7)^3,E(7),E(7)^6,E(7)^2,E(7)^5,E(7)^4,E(7)^3,E(7), E(7)^6,E(7)^2,E(7)^5,E(7)^4,E(7)^3,E(7)^2,E(7)^5,E(7)^4,E(7)^3,E(7),E(7)^6, E(7)^4,E(7)^3,E(7),E(7)^6,E(7)^2,E(7)^5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0], [GALOIS,[3,6]], [GALOIS,[3,4]], [GALOIS,[3,3]], [GALOIS,[3,2]], [GALOIS,[3,5]],[441,-7,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(73)+E(73)^8+E(73)^64,E(73)^9+E(73)^65 +E(73)^72,E(73)^2+E(73)^16+E(73)^55,E(73)^18+E(73)^57+E(73)^71, E(73)^4+E(73)^32+E(73)^37,E(73)^36+E(73)^41+E(73)^69,E(73)^7+E(73)^10+E(73)^56 ,E(73)^17+E(73)^63+E(73)^66,E(73)^14+E(73)^20+E(73)^39,E(73)^34+E(73)^53 +E(73)^59,E(73)^5+E(73)^28+E(73)^40,E(73)^33+E(73)^45+E(73)^68, E(73)^27+E(73)^49+E(73)^70,E(73)^3+E(73)^24+E(73)^46,E(73)^25+E(73)^54 +E(73)^67,E(73)^6+E(73)^19+E(73)^48,E(73)^35+E(73)^50+E(73)^61, E(73)^12+E(73)^23+E(73)^38,E(73)^43+E(73)^51+E(73)^52,E(73)^21+E(73)^22 +E(73)^30,E(73)^13+E(73)^29+E(73)^31,E(73)^42+E(73)^44+E(73)^60, E(73)^26+E(73)^58+E(73)^62,E(73)^11+E(73)^15+E(73)^47], [GALOIS,[9,9]], [GALOIS,[9,4]], [GALOIS,[9,36]], [GALOIS,[9,2]], [GALOIS,[9,18]], [GALOIS,[9,21]], [GALOIS,[9,43]], [GALOIS,[9,11]], [GALOIS,[9,26]], [GALOIS,[9,42]], [GALOIS,[9,13]], [GALOIS,[9,3]], [GALOIS,[9,27]], [GALOIS,[9,12]], [GALOIS,[9,35]], [GALOIS,[9,6]], [GALOIS,[9,25]], [GALOIS,[9,17]], [GALOIS,[9,7]], [GALOIS,[9,33]], [GALOIS,[9,5]], [GALOIS,[9,34]], [GALOIS,[9,14]],[511,-1,-2,-1,7,7,7,7,7,7,0,0,0,0,0,1,1,1,-1,-1,-1,-1,-1,-1, -2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0],[511,-1,1,-1,7,7,7,7,7,7,0,0,0,0,0, E(9)^2+E(9)^4+E(9)^5+E(9)^7,-E(9)^2-E(9)^7,-E(9)^4-E(9)^5,-1,-1,-1,-1,-1,-1,1, 1,1,1,1,1,E(9)^2+E(9)^4+E(9)^5+E(9)^7,E(9)^2+E(9)^4+E(9)^5+E(9)^7, -E(9)^2-E(9)^7,-E(9)^2-E(9)^7,-E(9)^4-E(9)^5,-E(9)^4-E(9)^5,-E(9)^4-E(9)^5, -E(9)^4-E(9)^5,E(9)^2+E(9)^4+E(9)^5+E(9)^7,E(9)^2+E(9)^4+E(9)^5+E(9)^7, -E(9)^2-E(9)^7,-E(9)^2-E(9)^7,-E(9)^2-E(9)^7,-E(9)^2-E(9)^7,-E(9)^4-E(9)^5, -E(9)^4-E(9)^5,E(9)^2+E(9)^4+E(9)^5+E(9)^7,E(9)^2+E(9)^4+E(9)^5+E(9)^7,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[34,4]], [GALOIS,[34,2]],[511,-1,-2,-1,7*E(7),7*E(7)^6,7*E(7)^2,7*E(7)^5,7*E(7)^4, 7*E(7)^3,0,0,0,0,0,1,1,1,-E(7),-E(7)^6,-E(7)^2,-E(7)^5,-E(7)^4,-E(7)^3, -2*E(7),-2*E(7)^6,-2*E(7)^2,-2*E(7)^5,-2*E(7)^4,-2*E(7)^3,E(7),E(7)^6,E(7)^2, E(7)^5,E(7)^4,E(7)^3,E(7)^2,E(7)^5,E(7)^4,E(7)^3,E(7),E(7)^6,E(7)^4,E(7)^3, E(7),E(7)^6,E(7)^2,E(7)^5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[37,6]], [GALOIS,[37,4]], [GALOIS,[37,3]], [GALOIS,[37,2]], [GALOIS,[37,5]],[511,-1,1,-1,7*E(7),7*E(7)^6,7*E(7)^2,7*E(7)^5,7*E(7)^4, 7*E(7)^3,0,0,0,0,0,E(9)^2+E(9)^4+E(9)^5+E(9)^7,-E(9)^2-E(9)^7,-E(9)^4-E(9)^5, -E(7),-E(7)^6,-E(7)^2,-E(7)^5,-E(7)^4,-E(7)^3,E(7),E(7)^6,E(7)^2,E(7)^5, E(7)^4,E(7)^3,E(63)^23+E(63)^37+E(63)^44+E(63)^58,E(63)^5+E(63)^19+E(63)^26 --> -------------------- --> maximum size reached --> -------------------- [ Dauer der Verarbeitung: 0.16 Sekunden (vorverarbeitet) ] |
2026-03-28