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Spracherkennung für: .tbl vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen] #############################################################################
## #W ctoline6.tbl GAP table library Thomas Breuer ## ## This file contains the ordinary character tables of ## $L_4(4)$, $L_4(4).2_1$, $L_4(4).2_2$, $L_4(4).2_3$, $L_4(4).2^2$, ## $L_7(2)$, $L_7(2).2$, $L_5(3)$, $L_5(3).2$. ## #H ctbllib history #H --------------- #H $Log: ctoline6.tbl,v $ #H Revision 4.10 2012/01/30 08:31:44 gap #H removed #H entries from the headers #H TB #H #H Revision 4.9 2012/01/26 11:13:43 gap #H added maxes entry for L7(2) #H TB #H #H Revision 4.8 2011/09/28 14:32:13 gap #H removed revision entry and SET_TABLEFILENAME call #H TB #H #H Revision 4.7 2010/05/05 13:20:02 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 4.6 2008/06/24 16:23:05 gap #H added several fusions and names #H TB #H #H Revision 4.5 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 4.4 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 4.3 2001/05/04 16:47:49 gap #H first revision for ctbllib #H #H #H tbl history (GAP 4) #H ------------------- #H (Rev. 4.3 of ctbllib coincides with Rev. 4.2 of tbl in GAP 4) #H #H RCS file: /gap/CVS/GAP/4.0/tbl/ctoline6.tbl,v #H Working file: ctoline6.tbl #H head: 4.2 #H branch: #H locks: strict #H access list: #H symbolic names: #H GAP4R2: 4.2.0.8 #H GAP4R2PRE2: 4.2.0.6 #H GAP4R2PRE1: 4.2.0.4 #H GAP4R1: 4.2.0.2 #H keyword substitution: kv #H total revisions: 3; selected revisions: 3 #H description: #H ---------------------------- #H revision 4.2 #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 4.1 #H date: 1997/07/17 15:40:49; author: fceller; state: Exp; lines: +2 -2 #H for version 4 #H ---------------------------- #H revision 1.1 #H date: 1996/10/21 15:59:41; author: sam; state: Exp; #H first proposal of the table library #H ========================================================================== ## MOT("L4(4)", [ "origin: constructed by T. Breuer using the perm. repr. on 85 points\n", "and the table of the subgroup 3.L3(4).3" ], [987033600,184320,15360,181440,181440,10800,540,768,64,20400,20400,900,900,75, 720,720,576,576,48,36,63,63,63,63,80,80,60,60,48,48,900,900,900,900,75,75,75, 75,45,45,45,45,45,45,85,85,85,85,63,63,63,63,60,60,60,60,63,63,63,63,63,63,63, 63,63,63,63,63,85,85,85,85,85,85,85,85,85,85,85,85,85,85,85,85], [,[1,1,1,5,4,6,7,2,3,11,10,13,12,14,6,6,5,4,6,7,21,22,24,23,11,10,12,13,17,18, 32,31,34,33,35,36,38,37,40,39,44,43,42,41,46,45,48,47,51,52,49,50,33,32,31,34, 63,62,66,65,67,58,57,68,60,59,61,64,79,82,76,78,81,83,80,71,84,72,69,75,73,70, 74,77],[1,2,3,1,1,1,1,8,9,11,10,13,12,14,2,2,2,2,3,2,22,21,4,5,26,25,28,27,8, 8,12,13,12,13,14,14,11,10,12,13,13,12,13,12,48,47,45,46,21,22,21,22,27,28,27, 28,52,51,51,50,51,49,50,52,52,49,49,50,77,83,70,79,78,75,81,82,71,69,84,73,72, 74,80,76],,[1,2,3,5,4,6,7,8,9,1,1,1,1,1,16,15,18,17,19,20,22,21,24,23,3,3,2,2, 30,29,6,6,6,6,6,6,6,6,7,7,5,5,4,4,48,47,45,46,52,51,50,49,15,15,16,16,66,63, 68,58,60,57,59,67,62,64,65,61,47,46,48,45,48,48,46,47,45,46,48,45,47,45,47, 46],,[1,2,3,4,5,6,7,8,9,11,10,13,12,14,15,16,17,18,19,20,1,1,23,24,26,25,28, 27,29,30,34,33,32,31,36,35,38,37,40,39,42,41,44,43,47,48,46,45,5,5,4,4,54,53, 56,55,23,23,23,24,23,24,24,23,23,24,24,24,70,73,80,76,77,72,79,75,83,71,82,69, 84,81,78,74],,,,,,,,,,[1,2,3,5,4,6,7,8,9,11,10,13,12,14,16,15,18,17,19,20,22, 21,24,23,26,25,28,27,30,29,32,31,34,33,35,36,38,37,40,39,44,43,42,41,1,1,1,1, 52,51,50,49,56,55,54,53,66,63,68,58,60,57,59,67,62,64,65,61,11,10,11,11,11,10, 11,10,10,10,10,10,10,11,11,11]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1],[84,20,4,21,21,9,6,4,0,-1,-1,4,4,-1,5,5,5,5,1,2,0,0,0,0,-1,-1, 0,0,1,1,4,4,4,4,-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, 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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],[3825,-15,-15,45,45,0,0, 1,1,0,0,0,0,0,0,0,-3,-3,0,0,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,3,3,0,0,0, 0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,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)^6,0,0,0,0, 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)^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)+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)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[ 3825,-15,-15,45,45,0,0,1,1,0,0,0,0,0,0,0,-3,-3,0,0,E(7)^3+E(7)^5+E(7)^6, E(7)+E(7)^2+E(7)^4,3*E(3)^2,3*E(3),0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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)^6,0,0,0,0,E(21)^5+E(21)^17+E(21)^20, E(21)^2+E(21)^8+E(21)^11,E(21)^2+E(21)^8+E(21)^11,E(21)^10+E(21)^13+E(21)^19, E(21)^2+E(21)^8+E(21)^11,E(21)+E(21)^4+E(21)^16,E(21)^10+E(21)^13+E(21)^19, E(21)^5+E(21)^17+E(21)^20,E(21)^5+E(21)^17+E(21)^20,E(21)+E(21)^4+E(21)^16, E(21)+E(21)^4+E(21)^16,E(21)^10+E(21)^13+E(21)^19,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [GALOIS,[13,2]], [GALOIS,[12,3]], [GALOIS,[13,10]], [GALOIS,[13,5]],[3825,-15,-15,45*E(3)^2,45*E(3),0,0,1,1,0,0,0,0,0,0,0, -3*E(3)^2,-3*E(3),0,0,3,3,0,0,0,0,0,0,E(3),E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,3*E(3),3*E(3),3*E(3)^2,3*E(3)^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],[3825,-15,-15,45*E(3)^2,45*E(3),0,0,1,1,0,0,0,0,0, 0,0,-3*E(3)^2,-3*E(3),0,0,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,0,0,0,0,0,0, E(3),E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(21)^10+E(21)^13+E(21)^19, E(21)+E(21)^4+E(21)^16,E(21)^5+E(21)^17+E(21)^20,E(21)^2+E(21)^8+E(21)^11,0,0, 0,0,-E(63)^8+E(63)^23-E(63)^50+E(63)^53,-E(63)^5-E(63)^26+E(63)^59+E(63)^62, -E(63)^17+E(63)^26+E(63)^41-E(63)^59,-E(63)^4+E(63)^22+E(63)^37-E(63)^46, E(63)^5+E(63)^17-E(63)^41-E(63)^62,-E(63)^19+E(63)^31-E(63)^40+E(63)^55, 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,-1,-4*E(3)^2,-4*E(3),-E(3)^2,-E(3),0,-1,0,0,0,0,E(5)^2+E(5)^3,E(5)+E(5)^4,1, 1,-E(3),-E(3)^2,3*E(15)^2-4*E(15)^7+3*E(15)^8+3*E(15)^11-4*E(15)^13+3*E(15)^14 ,3*E(15)+3*E(15)^4+3*E(15)^7-4*E(15)^11+3*E(15)^13-4*E(15)^14, 3*E(15)-4*E(15)^2+3*E(15)^4+3*E(15)^7-4*E(15)^8+3*E(15)^13,-4*E(15)+3*E(15)^2 -4*E(15)^4+3*E(15)^8+3*E(15)^11+3*E(15)^14,E(15)+E(15)^2+E(15)^4+E(15)^8, E(15)^7+E(15)^11+E(15)^13+E(15)^14,-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(5)-E(5)^4, -E(5)^2-E(5)^3,-E(15)-E(15)^4,-E(15)^7-E(15)^13,-E(15)^11-E(15)^14, -E(15)^2-E(15)^8,0,0,0,0,0,0,0,0,E(3),E(3),E(3)^2,E(3)^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], [GALOIS,[58,11]], [GALOIS,[56,11]], [GALOIS,[58,2]], [GALOIS,[54,2]], [GALOIS,[74,11]], [GALOIS,[56,2]], [GALOIS,[74,7]], [GALOIS,[53,7]], [GALOIS,[69,2]], [GALOIS,[74,2]]], [(57,64,65)(58,59,61)(60,63,68)(62,66,67),(21,22)(49,50)(51,52) (57,58,65,61,64,59)(60,67,68,66,63,62),( 4, 5)(15,16)(17,18)(23,24)(29,30) (31,33)(32,34)(35,36)(41,43)(42,44)(49,51)(50,52)(53,55)(54,56) (57,60,64,63,65,68)(58,67,59,62,61,66),(69,83)(70,78)(71,73)(72,82)(74,79) (75,84)(76,81)(77,80),(45,46)(47,48)(69,71,83,73)(70,80,78,77)(72,84,82,75) (74,81,79,76),(45,47,46,48)(69,75,71,72,83,84,73,82)(70,79,80,76,78,74,77,81), (10,11)(12,13)(25,26)(27,28)(31,34)(32,33)(35,36)(37,38)(39,40)(41,42)(43,44) (53,54)(55,56)(69,76,83,81)(70,75,78,84)(71,74,73,79)(72,77,82,80)]); ARC("L4(4)","isSimple",true); ARC("L4(4)","extInfo",["2","2^2"]); ALF("L4(4)","L4(4).2_1",[1,2,3,4,4,5,6,7,8,9,9,10,10,11,12,12,13,13,14,15, 16,17,18,18,19,19,20,20,21,21,22,22,23,23,24,25,26,26,29,29,27,28,28,27, 30,30,31,31,33,32,33,32,34,35,35,34,36,38,41,40,37,38,36,39,40,41,37,39, 45,43,47,49,46,48,44,47,42,49,45,44,46,43,48,42],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); ALF("L4(4)","L4(4).2_2",[1,3,7,4,4,8,14,12,35,5,6,10,11,32,18,18,23,23,38, 50,51,51,52,52,31,30,36,37,64,64,16,15,16,15,49,49,34,33,40,39,65,66,65, 66,26,29,28,27,53,54,54,53,61,62,61,62,55,60,58,58,56,57,56,57,59,59,55, 60,45,47,46,41,46,48,42,43,44,47,48,44,43,41,45,42],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); ALF("L4(4)","L4(4).2_3",[1,2,3,4,5,6,7,8,9,10,10,11,11,12,13,14,16,15,17, 18,19,19,21,20,22,22,23,23,24,25,26,27,27,26,28,28,29,29,30,30,32,32,31, 31,33,33,34,34,36,36,35,35,37,37,38,38,39,40,41,44,39,42,43,40,41,44,43, 42,46,45,48,45,50,46,49,50,49,51,52,47,48,51,52,47],[ "fusion map is unique up to table autom.,\n", "compatible with Brauer tables" ]); ALN("L4(4)",["O6+(4)"]); MOT("L4(4).2_1", [ "origin: constructed by T. Breuer using the perm. repr. on 85 points\n", "and the table of the subgroup L4(4),\n", "constructions: PSigmaL(4,4)" ], [1974067200,368640,30720,181440,21600,1080,1536,128,20400,900,150,720,576,96, 72,126,126,63,80,60,48,900,900,150,150,75,45,45,45,85,85,63,63,60,60,63,63,63, 63,63,63,85,85,85,85,85,85,85,85,40320,384,192,360,36,32,16,30,24,12,14,14,30, 30], [,[1,1,1,4,5,6,2,3,9,10,11,5,4,5,6,16,17,18,9,10,13,22,23,24,25,26,27,28,29, 30,31,32,33,23,22,36,37,38,39,40,41,42,43,44,45,46,47,48,49,1,2,3,5,6,7,8,11, 14,15,17,16,24,25],[1,2,3,1,1,1,7,8,9,10,11,2,2,3,2,17,16,4,19,20,7,10,10,11, 11,9,10,10,10,31,30,17,16,20,20,32,33,33,32,32,33,47,48,46,42,49,43,44,45,50, 51,52,50,50,55,56,57,52,51,61,60,57,57],,[1,2,3,4,5,6,7,8,1,1,1,12,13,14,15, 17,16,18,3,2,21,5,5,5,5,5,4,4,6,31,30,33,32,12,12,41,40,36,37,38,39,30,30,30, 31,31,31,31,30,50,51,52,53,54,55,56,50,58,59,61,60,53,53],,[1,2,3,4,5,6,7,8,9, 10,11,12,13,14,15,1,1,18,19,20,21,23,22,25,24,26,28,27,29,31,30,4,4,35,34,18, 18,18,18,18,18,48,46,45,43,42,44,49,47,50,51,52,53,54,55,56,57,58,59,50,50,63, 62],,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,16,18,19,20,21,22,23,24, 25,26,27,28,29,1,1,33,32,34,35,41,40,36,37,38,39,9,9,9,9,9,9,9,9,50,51,52,53, 54,55,56,57,58,59,61,60,62,63]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1, -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[84,20,4,21,9,6,4,0,-1,4,-1,5,5,1,2,0,0, 0,-1,0,1,4,4,-1,-1,-1,1,1,1,-1,-1,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1, 14,6,2,-1,2,2,0,-1,-1,0,0,0,-1,-1], [TENSOR,[3,2]],[170,42,10,-19,-10,8,10,2,0,10,0,-6,-3,-2,0,2,2,-1,0,2,1,-5,-5, 0,0,0,1,1,-2,0,0,2,2,-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],[378,-6,26,0,18,0,-6,2,33,3,-2,-6,0,2,0,0,0,0,1,-1,0,3,3,-2,-2,3, 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Breuer using the perm. repr. on 170 points\n", "and the table of the subgroup L4(4),\n", "constructions: PSL(4,4) extended by transpose-inverse" ], [1974067200,1958400,368640,181440,40800,40800,30720,21600,7680,1800,1800,1536, 1280,1080,900,900,768,720,600,600,600,600,576,360,360,170,170,170,170,160,160, 150,150,150,128,120,120,96,90,90,85,85,85,85,85,85,85,85,75,72,63,63,63,63,63, 63,63,63,63,63,60,60,50,48,45,45,40,40,40,40,34,34,34,34,32,30,30,30,30,24, 24], [,[1,1,1,4,6,5,1,8,1,11,10,3,7,14,16,15,7,8,6,5,10,11,4,14,8,29,28,27,26,5,6, 32,34,33,7,10,11,8,40,39,47,44,46,42,48,43,41,45,49,14,51,52,54,53,56,55,60, 59,58,57,16,15,32,23,66,65,11,10,30,31,27,26,28,29,12,39,40,34,33,14,38],[1,2, 3,1,6,5,7,1,9,11,10,12,13,1,11,10,17,3,20,19,22,21,3,2,2,27,29,26,28,31,30,32, 5,6,35,37,36,7,11,10,48,43,41,46,44,47,45,42,32,3,51,4,51,51,53,54,53,54,53, 54,36,37,63,12,11,10,68,67,70,69,74,71,72,73,75,22,21,19,20,9,17],,[1,2,3,4,1, 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ALF("L4(4).2_2","L4(4).2^2",[1,49,2,4,9,9,3,5,50,10,10,7,51,6,21,21,52,12, 53,53,54,54,13,55,56,26,27,27,26,18,18,11,23,23,8,19,19,14,25,25,34,33,36, 33,35,36,34,35,22,15,16,17,28,28,30,30,31,32,32,31,29,29,57,20,24,24,58, 58,59,59,60,61,60,61,62,63,63,64,64,65,66],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); ALN("L4(4).2_2",["O6+(4).2_2"]); MOT("L4(4).2_3", [ "origin: constructed by T. Breuer using the perm. repr. on 170 points\n", "and the table of the subgroup L4(4),\n", "L4(4).2_3 is the simple group L4(4) extended by the product of,\n", "the Frobenius automorphism and ``transpose inverse''" ], [1974067200,368640,30720,362880,362880,21600,1080,1536,128,20400,900,150,1440, 1440,1152,1152,96,72,63,126,126,80,60,96,96,900,900,75,75,45,45,45,85,85,63, 63,60,60,63,63,63,63,63,63,85,85,85,85,85,85,85,85,51840,1152,192,1296,1296, 216,108,96,16,10,144,144,72,72,36,24,18,18,24,24], [,[1,1,1,5,4,6,7,2,3,10,11,12,6,6,4,5,6,7,19,21,20,10,11,16,15,27,26,28,29,30, 32,31,33,34,36,35,27,26,43,42,44,40,39,41,51,52,49,50,47,48,45,46,1,2,3,5,4,6, 7,8,9,12,16,15,13,14,18,17,20,21,25,24],[1,2,3,1,1,1,1,8,9,10,11,12,2,2,2,2,3, 2,19,5,4,22,23,8,8,11,11,12,10,11,11,11,34,33,19,19,23,23,35,35,35,36,36,36, 52,49,50,45,48,51,46,47,53,54,55,53,53,53,53,60,61,62,54,54,54,54,54,55,56,57, 60,60],,[1,2,3,5,4,6,7,8,9,1,1,1,14,13,16,15,17,18,19,21,20,3,2,25,24,6,6,6,6, 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(46,48,52,50),(33,34)(45,46,47,48,51,52,49,50)]); ALF("L4(4).2_3","L4(4).2^2",[1,2,3,4,4,5,6,7,8,9,10,11,12,12,13,13,14,15, 16,17,17,18,19,20,20,21,21,22,23,25,24,24,26,27,28,28,29,29,30,31,32,31, 30,32,34,35,33,36,33,36,34,35,67,68,69,70,70,71,72,73,74,75,76,76,77,77, 78,79,80,80,81,81],[ "fusion map is unique up to table autom.,\n", "unique map that is compatible with Brauer tables" ]); ALN("L4(4).2_3",["O6+(4).2_3"]); MOT("L4(4).2^2", [ "constructed using `PossibleCharacterTablesOfTypeGV4',\n", "constructions: Aut(L4(4)), PSigmaL(4,4) extended by transpose-inverse" ], [3948134400,737280,61440,362880,43200,2160,3072,256,40800,1800,300,1440,1152, 192,144,126,126,160,120,96,900,150,150,45,90,170,170,63,60,63,63,63,85,85,85, 85,80640,768,384,720,72,64,32,60,48,24,14,30,3916800,15360,2560,1536,600,600, 720,720,100,40,40,34,34,64,30,30,48,48,103680,2304,384,1296,432,216,192,32,20, 144,72,72,48,18,24], [,[1,1,1,4,5,6,2,3,9,10,11,5,4,5,6,16,17,9,10,13,21,22,23,24,25,26,27,28,21,30 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[(30,31,32),(33,34)(35,36),(26,27)(33,35,34,36)(60,61)]); ALN("L4(4).2^2",["O6+(4).2^2"]); MOT("L7(2)", [ "origin: CAS library,\n", "tests: 1.o.r., pow[2,3,5,7,31]" ], [163849992929280,20478689280,66060288,5505024,20643840,196608,98304,86016, 24576,4096,2048,1536,512,128,64,30240,1440,720,2016,96,48,29998080,64512,4608, 1152,384,96,48,2520,120,60,2520,120,60,2520,120,60,141120,1344,672,112,56,126, 42,141120,1344,672,112,56,126,42,186,62,186,62,186,62,186,62,186,62,186,62, 181440,45,45,63,63,63,63,63,63,63,63,63,3528,3528,56,56,45,576,48,49,1260, 1260,93,93,93,93,93,93,105,105,105,105,105,105,84,84,127,127,127,127,127,127, 127,127,127,127,127,127,127,127,127,127,127,127], [,[1,1,1,1,2,2,2,3,3,3,4,6,6,9,11,16,16,17,16,16,17,22,22,22,23,23,24,26,29, 29,30,32,32,33,35,35,36,38,38,38,39,40,43,43,45,45,45,46,47,50,50,52,52,54,54, 56,56,58,58,60,60,62,62,64,65,66,67,68,69,70,71,72,73,74,75,76,77,76,77,80,64, 81,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,84,85,100,101,102,103,104,105, 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[(100,101,104,111,106,112,115,103,109,116,113,117,108,110,105,102,107,114), (70,71,72)(73,74,75),(52,54,56,62,58,60)(53,55,57,63,59,61)(86,87,88,91,89,90 ),(38,45)(39,46)(40,47)(41,48)(42,49)(43,50)(44,51)(67,68)(70,73,72,75,71,74) (76,77)(78,79)(84,85)(92,93)(94,96)(95,97)(98,99),(32,35)(33,36)(34,37)(65,66) (94,95)(96,97),(32,35)(33,36)(34,37)(65,66)(70,71,72)(73,74,75)(94,95) (96,97)]); ARC("L7(2)","isSimple",true); ARC("L7(2)","extInfo",["","2"]); ARC("L7(2)","maxes",["2^6:L6(2)","2^10:(L5(2)xS3)","2^12:(L4(2)xL3(2))", "127:7"]); ALN("L7(2)",["L7F2","L7(2).2M1"]); ALF("L7(2)","L7(2).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20, 21,22,23,24,25,26,27,28,29,30,31,32,33,34,32,33,34,35,36,37,38,39,40,41, 35,36,37,38,39,40,41,42,43,44,45,46,47,44,45,46,47,42,43,48,49,49,50,50, 51,52,53,54,53,54,52,55,55,56,56,57,58,59,60,61,61,62,63,64,63,64,62,65, 65,66,67,67,66,68,68,69,70,71,72,73,74,75,72,76,77,75,76,74,70,77,71,69, 73],[ "fusion map is unique up to table automorphisms" ]); ALF("L7(2)","P1L82",[1,3,6,9,12,15,19,22,25,28,32,35,38,41,44,46,48,51,53, 55,58,60,62,65,68,71,74,77,79,81,84,86,88,91,93,95,98,100,102,105,107,110, 112,114,116,118,121,123,126,128,130,132,134,136,138,140,142,144,146,148, 150,152,154,156,158,160,162,164,166,168,170,172,174,176,178,180,182,184, 186,188,190,192,194,196,197,198,199,200,201,202,203,204,205,206,207,208, 209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226, 227,228,229],[ "fusion map is unique up to table automorphisms" ]); MOT("L7(2).2", [ "origin/source : M.R. Darafsheh,\n", "table of the automorphism group of GL_7(2),\n", "tests: 1.o.r., pow[2,3,5,7,31,127], sym[2,3,5,7],\n", "constructions: Aut(L7(2))" ], [327699985858560,40957378560,132120576,11010048,41287680,393216,196608,172032, 49152,8192,4096,3072,1024,256,128,60480,2880,1440,4032,192,96,59996160,129024, 9216,2304,768,192,96,5040,240,120,2520,120,60,141120,1344,672,112,56,126,42, 186,62,186,62,186,62,362880,45,63,126,63,63,63,3528,56,90,1152,96,98,1260,93, 93,93,105,105,105,84,127,127,127,127,127,127,127,127,127,2903040,9216,3072, 92160,92160,768,256,1536,1536,384,384,128,128,32,32,4320,216,1296,144,72,288, 24,96,576,576,144,144,48,48,48,48,60,40,40,14,18,30], [,[1,1,1,1,2,2,2,3,3,3,4,6,6,9,11,16,16,17,16,16,17,22,22,22,23,23,24,26,29, 29,30,32,32,33,35,35,35,36,37,40,40,42,42,44,44,46,46,48,49,50,51,52,53,54,55, 55,57,48,58,60,61,62,63,64,65,66,67,61,69,70,71,72,73,74,75,76,77,1,3,5,5,5,9, 9,7,7,12,12,12,12,15,15,22,16,48,58,19,24,59,25,25,25,18,18,21,21,28,28,29,31, 31,60,51,57],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,5,3,4,7,1,2,3,5,6,8,12, 29,30,31,29,30,31,35,36,37,38,39,35,36,44,45,46,47,42,43,1,29,55,48,50,50,50, 55,56,29,3,9,60,35,44,46,42,65,65,65,37,70,73,72,77,76,71,74,75,69,78,79,80, 82,81,83,84,86,85,88,87,90,89,92,91,78,78,78,79,79,79,83,80,81,82,82,81,85,86, 87,88,109,111,110,112,95,109],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18, 19,20,21,22,23,24,25,26,27,28,1,2,5,16,17,18,35,36,37,38,39,40,41,46,47,42,43, 44,45,48,48,50,51,53,54,52,55,56,22,58,59,60,61,64,62,63,35,61,61,68,71,72,76, 75,77,73,70,69,74,78,79,80,82,81,83,84,86,85,88,87,90,89,92,91,93,94,95,96,97, 98,99,100,102,101,104,103,106,105,108,107,78,81,82,112,113,93],,[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, 34,1,2,3,5,8,22,23,44,45,46,47,42,43,48,49,48,51,51,51,51,1,4,57,58,59,1,16, 63,64,62,29,32,32,19,72,77,75,74,69,76,73,70,71,78,79,80,81,82,83,84,85,86,87, 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Darafsheh,\M. Rajabi Tarkhorani,\n", "The Character table of The group $SL_{5}(3)$} ,to appear;\n", "tests: 1.o.r., pow[2,3,5,11,13]." ], [237783237120,24261120,269568,5760,384,44928,5760,5760,64,64,64,44928,44928, 384,384,80,80,24564384,314928,34992,4374,486,81,23328,324,2592,432,33696,324, 54,3888,72,48,432,72,54,72,72,432,432,72,72,48,48,80,80,80,80,80,80,80,80,80, 80,80,80,80,80,80,80,121,121,121,121,121,121,121,121,121,121,121,121,121,121, 121,121,121,121,121,121,121,121,121,121,624,624,624,624,624,624,624,624,52,52, 52,52,78,78,78,78,104,104,104,104,78,78,78,78,104,104,104,104,104,104,104, 104], [,[1,1,1,2,3,3,4,4,5,5,4,6,6,6,6,7,8,18,19,20,21,22,23,18,20,18,20,18,19,21, 19,31,26,26,27,22,32,32,34,34,35,35,34,34,45,45,46,46,48,48,47,47,49,50,51,52, 51,50,49,52,62,61,65,69,78,81,82,70,73,77,84,83,74,68,64,80,79,76,71,75,72,66, 63,67,87,88,86,85,87,88,86,85,87,85,88,86,99,100,98,97,91,92,90,89,99,100,98, 97,103,101,104,102,103,101,104,102],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16, 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0,1,1,-1,-1,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, -E(40)^13-E(40)^31-E(40)^37-E(40)^39,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)^7+E(40)^21+E(40)^23+E(40)^29, -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)^13-E(40)^31-E(40)^37-E(40)^39,E(40)^7+E(40)^21+E(40)^23+E(40)^29,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[111,13]], [GALOIS,[111,11]], [GALOIS,[111,7]],[50336,416,0,16,0,0,-16,-16,0,0,0,0,0,0,0,0,0,-208,-46,8,8, -1,-1,-16,2,0,0,0,0,0,2,-2,0,0,0,-1,2,2,0,0,0,0,0,0,1,1,1,1,-1,-1,-1,-1, -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, 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)^17,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[115,11]]], [( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 95)( 94, 96)( 97, 98)( 99,100) (101,102)(103,104)(105,106)(107,108)(109,111)(110,112)(113,115)(114,116), ( 85, 87, 86, 88)( 89, 91, 90, 92)( 93, 96, 95, 94)( 97, 99, 98,100) (101,103,102,104)(105,107,106,108)(109,112,111,110)(113,116,115,114),(53,59) (54,58)(55,57)(56,60),(47,48)(49,51)(50,52)(53,55,59,57)(54,60,58,56), ( 7, 8)( 9, 10)( 12, 13)( 14, 15)( 16, 17)( 37, 38)( 39, 40)( 41, 42) ( 43, 44)( 49, 50)( 51, 52)( 53, 54, 59, 58)( 55, 60, 57, 56)(109,113) (110,114)(111,115)(112,116),(63,64,77,66,78,73,71,72,80,68,67)(65,69,79,81,76, 74,84,83,75,70,82),(61,62)(63,65,78,76,80,75,64,69,73,74,68,70,77,79,71,84, 67,82,66,81,72,83)]); ARC("L5(3)","isSimple",true); ARC("L5(3)","extInfo",["","2"]); ALF("L5(3)","L5(3).2",[1,2,3,4,5,6,7,7,8,8,9,10,10,11,11,12,12,13,14,15, 16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,32,33,33,34,34,35,35, 36,37,38,38,39,40,40,39,41,42,43,44,42,43,44,41,45,45,46,47,48,49,50,51, 49,46,52,53,54,53,50,52,48,55,55,56,54,47,51,56,57,57,58,58,59,59,60,60, 61,62,61,62,63,63,64,64,65,65,66,66,67,67,68,68,69,70,71,72,71,72,69,70],[ "fusion is unique up to table automorphisms" ]); ALN("L5(3)",["SL(5,3)"]); MOT("L5(3).2", [ "origin/source : M.R. Darafsheh,\n", "table of the automorphism group of SL_5(3),\n", "tests: 1.o.r., pow[2,3,5,11,13],\n", "constructions: Aut(L5(3))" ], [475566474240,48522240,539136,11520,768,89856,5760,64,128,44928,384,80, 49128768,629856,69984,8748,972,162,46656,648,5184,864,67392,648,108,7776,144, 96,864,144,108,72,432,72,48,160,160,80,80,80,80,80,80,80,121,121,121,121,121, 121,121,121,121,121,121,121,624,624,624,624,52,52,78,78,104,104,78,78,104,104, 104,104,103680,103680,1152,192,192,192,16,1296,432,216,18,2592,2592,144,288, 288,36,36,432,216,24,48,48,24,36,36,20,20], [,[1,1,1,2,3,3,4,5,4,6,6,7,13,14,15,16,17,18,13,15,13,15,13,14,16,14,26,21,21, 22,17,27,29,30,29,36,36,37,38,38,39,40,40,39,45,48,49,55,54,47,46,56,51,53,52, 50,58,57,58,57,58,57,64,63,60,59,64,63,66,65,66,65,1,2,3,4,5,6,9,14,15,15,18, 19,19,22,23,23,25,25,26,26,27,28,28,30,31,31,36,37],[1,2,3,4,5,6,7,8,9,10,11, 12,1,1,1,1,13,14,2,2,3,3,3,3,3,2,4,5,6,6,19,7,10,10,11,36,37,38,39,40,41,42, 43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,57,58,65,66,59,60, 69,70,71,72,73,74,75,76,77,78,79,73,73,73,80,74,74,75,75,75,75,75,74,74,76,77, 77,78,85,84,99,100],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21, 22,23,24,25,26,27,28,29,30,31,32,33,34,35,1,2,4,7,7,12,12,12,12,45,54,52,53, 56,55,49,46,47,50,51,48,58,57,60,59,62,61,64,63,66,65,68,67,70,71,72,69,73,74, 75,76,77,78,79,80,81,82,83,85,84,86,88,87,90,89,91,92,93,95,94,96,98,97,73, 74],,[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, 28,29,30,31,32,33,34,35,36,37,38,40,39,43,41,44,42,45,49,55,54,52,48,47,51,50, 56,53,46,58,57,60,59,62,61,64,63,66,65,68,67,72,69,70,71,73,74,75,76,77,78,79, 80,81,82,83,85,84,86,88,87,90,89,91,92,93,95,94,96,98,97,99,100],,,,[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, 32,33,34,35,36,37,38,40,39,42,44,41,43,1,45,45,45,45,45,45,45,45,45,45,45,58, 57,60,59,62,61,64,63,66,65,68,67,70,71,72,69,73,74,75,76,77,78,79,80,81,82,83, 84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100],,[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, 37,38,39,40,44,43,42,41,45,55,54,52,53,49,48,50,46,51,56,47,1,1,3,3,2,2,13,13, 6,6,23,23,10,10,10,10,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90, 91,92,93,94,95,96,97,98,99,100]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[120,40,16,0,4,12,0,0,0,12,4,0,39, 12,12,3,3,0,13,4,7,4,13,4,1,4,0,1,3,0,1,0,3,0,1,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1, 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(46,47,48,49,55,54,52,53,56,51,50)]); ALN("L5(3).2",["SL(5,3).2"]); LIBTABLE.LOADSTATUS.ctoline6:="userloaded"; ############################################################################# ## #E [Dauer der Verarbeitung: 0.29 Sekunden, vorverarbeitet 2026-04-25] |
2026-05-26