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Spracherkennung für: .tbl vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen] #############################################################################
## #W ctounit5.tbl GAP table library Thomas Breuer ## ## This file contains the ordinary character tables related to the unitary ## groups $U_4(4)$, $U_4(5)$, and $U_5(4)$. ## #H ctbllib history #H --------------- #H $Log: ctounit5.tbl,v $ #H Revision 4.11 2012/03/21 16:16:51 gap #H added fusion U5(3) -> O10-(3) #H TB #H #H Revision 4.10 2012/01/30 08:32:05 gap #H removed #H entries from the headers #H TB #H #H Revision 4.9 2011/09/28 14:22:13 gap #H - removed revision entry and SET_TABLEFILENAME call, #H - added tables of U4(5).2_i, U4(5).2^2 #H TB #H #H Revision 4.8 2009/08/14 08:40:26 gap #H added table of U5(3) #H TB #H #H Revision 4.7 2008/06/24 16:23:06 gap #H added several fusions and names #H TB #H #H Revision 4.6 2007/07/03 08:37:56 gap #H added table of U4(5).2^2 #H TB #H #H Revision 4.5 2005/04/20 15:36:06 gap #H added tables of U5(4) and U5(4).2 #H TB #H #H Revision 4.4 2005/01/26 15:14:32 gap #H added the table of U4(4).4 #H TB #H #H Revision 4.3 2003/07/24 07:10:25 gap #H added table of U4(5) (computed for answering a question of Jan Saxl) #H TB #H #H Revision 4.2 2001/05/04 16:50:50 gap #H first revision for ctbllib #H #H #H tbl history (GAP 4) #H ------------------- #H (Rev. 4.2 of ctbllib coincides with Rev. 4.1 of tbl in GAP 4) #H #H RCS file: /gap/CVS/GAP/4.0/tbl/ctounit5.tbl,v #H Working file: ctounit5.tbl #H head: 4.1 #H branch: #H locks: strict #H access list: #H symbolic names: #H keyword substitution: kv #H total revisions: 1; selected revisions: 1 #H description: #H ---------------------------- #H revision 4.1 #H date: 2001/02/06 14:49:18; author: gap; state: Exp; #H added tables of S6(4) and U4(4) #H #H TB #H ========================================================================== ## MOT("U4(4)", [ "origin: computed using Dixon's algorithm and character theoretic methods,\n", "Thomas Breuer, Sep. 04th, 1999" ], [1018368000,307200,15360,12240,900,1280,64,312000,312000,312000,312000,18000, 18000,1500,1500,1500,1500,1500,1500,125,60,48,1600,1600,1600,1600,1200,1200, 1200,1200,100,100,100,100,100,100,80,80,65,65,65,65,900,900,900,900,75,75,75, 75,75,75,75,75,75,75,45,45,51,51,51,51,80,80,80,80,60,60,60,60,51,51,51,51,51, 51,51,51,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65], [,[1,1,1,4,5,2,3,9,11,8,10,13,12,15,17,14,16,19,18,20,5,4,11,9,10,8,12,13,13, 12,14,16,15,17,18,19,13,12,40,41,42,39,44,45,46,43,48,49,50,47,52,53,54,51,56, 55,58,57,60,59,62,61,23,24,25,26,43,44,46,45,72,73,76,75,77,71,78,74,80,82,83, 85,88,86,79,89,91,93,94,92,90,87,81,84],[1,2,3,1,1,6,7,10,8,11,9,13,12,16,14, 17,15,19,18,20,2,3,24,26,23,25,28,30,27,29,32,34,31,33,36,35,38,37,39,40,41,42 ,13,12,13,12,14,15,17,16,11,10,8,9,19,18,12,13,61,62,60,59,64,66,63,65,28,27, 30,29,61,62,61,60,59,62,60,59,81,83,86,88,89,87,93,91,85,94,90,80,79,82,84,92] ,,[1,2,3,4,5,6,7,1,1,1,1,1,1,1,1,1,1,1,1,1,21,22,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3 ,3,40,41,42,39,5,5,5,5,5,5,5,5,5,5,5,5,5,5,4,4,61,62,60,59,6,6,6,6,21,21,21,21 ,74,75,77,72,73,78,76,71,39,40,39,41,40,42,42,39,42,41,40,40,39,41,42,41],,,,, ,,,[1,2,3,4,5,6,7,10,8,11,9,13,12,16,14,17,15,19,18,20,21,22,24,26,23,25,28,30 ,27,29,32,34,31,33,36,35,38,37,1,1,1,1,46,43,44,45,50,47,48,49,54,51,52,53,56, 55,58,57,59,60,61,62,64,66,63,65,69,67,70,68,73,76,71,77,78,72,74,75,8,9,10,11 ,8,9,10,11,8,9,10,11,9,10,11,8],,,,[1,2,3,4,5,6,7,9,11,8,10,13,12,15,17,14,16, 19,18,20,21,22,25,23,26,24,29,27,30,28,33,31,34,32,36,35,38,37,41,42,39,40,44, 45,46,43,48,49,50,47,52,53,54,51,56,55,58,57,1,1,1,1,65,63,66,64,68,70,67,69,4 ,4,4,4,4,4,4,4,88,93,94,81,84,90,83,92,80,86,87,85,82,79,89,91]], [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[51,-13,3,0,3,3,-1,-13*E(5)-E(5)^2, -13*E(5)^2-E(5)^4,-E(5)-13*E(5)^3,-E(5)^3-13*E(5)^4,3*E(5)+3*E(5)^4, 3*E(5)^2+3*E(5)^3,4*E(5)^2+E(5)^3+E(5)^4,E(5)+E(5)^3+4*E(5)^4, 4*E(5)+E(5)^2+E(5)^4,E(5)+E(5)^2+4*E(5)^3,-4*E(5)-3*E(5)^2-3*E(5)^3-4*E(5)^4, -3*E(5)-4*E(5)^2-4*E(5)^3-3*E(5)^4,1,-1,0,3*E(5)^2-E(5)^4,3*E(5)-E(5)^2, -E(5)^3+3*E(5)^4,-E(5)+3*E(5)^3,3*E(5)^2-E(5)^3,3*E(5)-E(5)^4,-E(5)+3*E(5)^4, -E(5)^2+3*E(5)^3,E(5)^2+E(5)^4,E(5)+E(5)^2,E(5)^3+E(5)^4,E(5)+E(5)^3, E(5)+E(5)^4,E(5)^2+E(5)^3,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,-1,-1,-1,3*E(5), 3*E(5)^2,3*E(5)^4,3*E(5)^3,E(5)+E(5)^3+E(5)^4,E(5)+E(5)^2+E(5)^3, E(5)+E(5)^2+E(5)^4,E(5)^2+E(5)^3+E(5)^4,-E(5)-E(5)^3,-E(5)-E(5)^2, -E(5)^2-E(5)^4,-E(5)^3-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,0,0, -E(5)-E(5)^2,-E(5)-E(5)^3,-E(5)^2-E(5)^4,-E(5)^3-E(5)^4,-E(5)^3,-E(5),-E(5)^4, -E(5)^2,0,0,0,0,0,0,0,0,-E(5)^4,-E(5)^3,-E(5)^2,-E(5),-E(5)^4,-E(5)^3,-E(5)^2, -E(5),-E(5)^4,-E(5)^3,-E(5)^2,-E(5),-E(5)^3,-E(5)^2,-E(5),-E(5)^4], [GALOIS,[2,4]], [GALOIS,[2,3]], [GALOIS,[2,2]],[52,-12,4,1,4,4,0,-13,-13,-13,-13,7,7,2,2,2,2,2,2,-3,0,1,3,3,3 ,3,3,3,3,3,-2,-2,-2,-2,-2,-2,-1,-1,0,0,0,0,4,4,4,4,-1,-1,-1,-1,-1,-1,-1,-1,-1, -1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,0,0],[221,29,13,17,2,-3,1,13*E(5)^2+13*E(5)^3,13*E(5)+13*E(5)^4, 13*E(5)+13*E(5)^4,13*E(5)^2+13*E(5)^3,-9*E(5)-8*E(5)^2-8*E(5)^3-9*E(5)^4, -8*E(5)-9*E(5)^2-9*E(5)^3-8*E(5)^4,E(5)-3*E(5)^2-3*E(5)^3+E(5)^4, -3*E(5)+E(5)^2+E(5)^3-3*E(5)^4,-3*E(5)+E(5)^2+E(5)^3-3*E(5)^4, E(5)-3*E(5)^2-3*E(5)^3+E(5)^4,-5*E(5)-2*E(5)^2-2*E(5)^3-5*E(5)^4, -2*E(5)-5*E(5)^2-5*E(5)^3-2*E(5)^4,1,2,1,-3*E(5)-3*E(5)^4,-3*E(5)^2-3*E(5)^3, -3*E(5)^2-3*E(5)^3,-3*E(5)-3*E(5)^4,4*E(5)+3*E(5)^2+3*E(5)^3+4*E(5)^4, 3*E(5)+4*E(5)^2+4*E(5)^3+3*E(5)^4,3*E(5)+4*E(5)^2+4*E(5)^3+3*E(5)^4, 4*E(5)+3*E(5)^2+3*E(5)^3+4*E(5)^4,-1,-1,-1,-1,-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4, -E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0, E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4, E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3, 2,2,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,0,0,E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)+E(5)^4, E(5)^2+E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)^2+E(5)^3,E(5)+E(5)^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,[7,2]],[272,16,16,17,5,0,0,12,12,12,12,17,17,-3,-3,-3,-3,-3,-3,2,1,1, -4,-4,-4,-4,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,5,5,5,5,0,0,0,0,0,0,0,0,0,0,2, 2,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, -1,-1,-1,-1],[325,5,21,16,-5,5,1,0,0,0,0,25,25,0,0,0,0,0,0,0,-1,0,0,0,0,0,5,5, 5,5,0,0,0,0,0,0,1,1,0,0,0,0,-5,-5,-5,-5,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,2,0,0,0, 0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[612,36 ,-12,0,0,4,0,39*E(5)^2-12*E(5)^4,-12*E(5)^3+39*E(5)^4,39*E(5)-12*E(5)^2, -12*E(5)+39*E(5)^3,-9*E(5)^2-9*E(5)^3,-9*E(5)-9*E(5)^4, -3*E(5)-3*E(5)^3+3*E(5)^4,-3*E(5)-3*E(5)^2+3*E(5)^3,3*E(5)^2-3*E(5)^3-3*E(5)^4 ,3*E(5)-3*E(5)^2-3*E(5)^4,-6*E(5)-3*E(5)^2-3*E(5)^3-6*E(5)^4, -3*E(5)-6*E(5)^2-6*E(5)^3-3*E(5)^4,2,0,0,4*E(5)^3+7*E(5)^4,7*E(5)^2+4*E(5)^4, 4*E(5)+7*E(5)^3,7*E(5)+4*E(5)^2,3*E(5)+3*E(5)^4,3*E(5)^2+3*E(5)^3, 3*E(5)^2+3*E(5)^3,3*E(5)+3*E(5)^4,-E(5)^2+E(5)^3+E(5)^4,-E(5)+E(5)^2+E(5)^4, E(5)+E(5)^3-E(5)^4,E(5)+E(5)^2-E(5)^3,E(5)+2*E(5)^2+2*E(5)^3+E(5)^4, 2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,-E(5)^2-E(5)^3,-E(5)-E(5)^4,1,1,1,1,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(5)^2,-E(5),-E(5)^4,-E(5)^3,0,0,0,0,0,0,0,0,0,0, 0,0,E(5)^3,E(5),E(5)^4,E(5)^2,E(5)^3,E(5),E(5)^4,E(5)^2,E(5)^3,E(5),E(5)^4, E(5)^2,E(5),E(5)^4,E(5)^2,E(5)^3], [GALOIS,[11,4]], [GALOIS,[11,3]], [GALOIS,[11,2]],[663,23,-9,0,3,7,-1,13*E(5)+13*E(5)^2+52*E(5)^3, 52*E(5)+13*E(5)^2+13*E(5)^4,13*E(5)+13*E(5)^3+52*E(5)^4, 52*E(5)^2+13*E(5)^3+13*E(5)^4,-9*E(5)+3*E(5)^2+3*E(5)^3-9*E(5)^4, 3*E(5)-9*E(5)^2-9*E(5)^3+3*E(5)^4,-E(5)-E(5)^2-3*E(5)^3+3*E(5)^4, -3*E(5)-E(5)^2+3*E(5)^3-E(5)^4,-E(5)+3*E(5)^2-E(5)^3-3*E(5)^4, 3*E(5)-3*E(5)^2-E(5)^3-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-2,-1,0, 4*E(5)-3*E(5)^2-3*E(5)^4,-3*E(5)-3*E(5)^2+4*E(5)^3,4*E(5)^2-3*E(5)^3-3*E(5)^4, -3*E(5)-3*E(5)^3+4*E(5)^4,3*E(5)+3*E(5)^2+3*E(5)^3-E(5)^4, 3*E(5)-E(5)^2+3*E(5)^3+3*E(5)^4,3*E(5)+3*E(5)^2-E(5)^3+3*E(5)^4, -E(5)+3*E(5)^2+3*E(5)^3+3*E(5)^4,-E(5)-E(5)^2-E(5)^3+E(5)^4, -E(5)+E(5)^2-E(5)^3-E(5)^4,-E(5)-E(5)^2+E(5)^3-E(5)^4, E(5)-E(5)^2-E(5)^3-E(5)^4,-E(5)^2-E(5)^3,-E(5)-E(5)^4,1,1,0,0,0,0,3*E(5)^3, 3*E(5),3*E(5)^2,3*E(5)^4,-E(5)^2-E(5)^4,-E(5)^3-E(5)^4,-E(5)-E(5)^3, -E(5)-E(5)^2,E(5)+E(5)^3+E(5)^4,E(5)+E(5)^2+E(5)^3,E(5)+E(5)^2+E(5)^4, E(5)^2+E(5)^3+E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,0,0,E(5)+E(5)^2, E(5)+E(5)^3,E(5)^2+E(5)^4,E(5)^3+E(5)^4,-E(5)^4,-E(5)^3,-E(5)^2,-E(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,[15,4]], [GALOIS,[15,3]], [GALOIS,[15,2]],[663,23,-9,0,3,7,-1,-39*E(5)-52*E(5)^2-52*E(5)^3-39*E(5)^4, -52*E(5)-39*E(5)^2-39*E(5)^3-52*E(5)^4,-52*E(5)-39*E(5)^2-39*E(5)^3-52*E(5)^4, -39*E(5)-52*E(5)^2-52*E(5)^3-39*E(5)^4,-15*E(5)-6*E(5)^2-6*E(5)^3-15*E(5)^4, 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-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^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,[93,2]]], [(59,61,60,62)(71,74,72,75,73,77,76,78), (59,60)(61,62)(71,72,73,76)(74,75,77,78),(71,73)(72,76)(74,77)(75,78), ( 8, 9,11,10)(12,13)(14,15,17,16)(18,19)(23,25,26,24)(27,29,30,28) (31,33,34,32)(35,36)(37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50) (51,52,53,54)(55,56)(57,58)(63,65,66,64)(67,68,70,69)(79,80,82,85) (81,83,88,93)(84,86,89,94)(87,91,90,92), ( 8,10,11, 9)(12,13)(14,16,17,15)(18,19)(23,24,26,25)(27,28,30,29) (31,32,34,33)(35,36)(37,38)(43,46,45,44)(47,50,49,48)(51,54,53,52)(55,56) (57,58)(63,64,66,65)(67,69,70,68)(79,81,86,91)(80,83,89,90)(82,88,94,92) (84,87,85,93)]); ARC("U4(4)","isSimple",true); ARC("U4(4)","extInfo",["","4"]); ALF("U4(4)","U4(4).4",[1,2,3,4,5,6,7,8,8,8,8,9,9,11,11,11,11,10,10,12,13, 14,15,15,15,15,16,16,16,16,19,19,19,19,17,17,18,18,20,20,20,20,21,21,21, 21,25,25,25,25,24,24,24,24,22,22,23,23,26,26,27,27,28,28,28,28,29,29,29, 29,31,31,31,30,30,31,30,30,32,32,33,32,33,34,32,34,35,33,34,35,35,35,33, 34],[ "fusion map is unique up to table automorphisms" ]); ALF("U4(4)","U5(4)",[1,2,3,5,4,6,8,9,10,10,9,12,11,12,11,11,12,9,10,13,14, 15,22,21,21,22,23,26,25,24,23,26,25,24,22,21,28,27,30,32,31,33,37,34,36, 35,35,37,34,36,39,38,39,38,38,39,41,40,42,43,44,45,47,46,46,47,55,52,53, 54,74,73,75,71,68,72,70,69,83,80,76,82,78,81,81,83,79,77,80,78,76,77,79, 82],[ "fusion map is unique up to table automorphisms" ]); MOT("U4(4).4", [ "origin: computed using Dixon's algorithm and character theoretic methods,\n", "Thomas Breuer, Sep. 29th, 2004,\n", "constructions: Aut(U4(4))" ], [4073472000,1228800,61440,48960,3600,5120,256,312000,36000,3000,1500,500,240, 192,1600,1200,200,160,100,65,900,150,90,75,75,102,102,80,60,51,51,65,65,65,65, 3916800,15360,2560,1536,720,720,48,64,600,600,100,40,48,40,30,30,34,34,2880, 192,192,64,72,72,24,16,20,24,2880,192,192,64,72,72,24,16,20,24], 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E(17)^3+E(17)^5+E(17)^6+E(17)^7+E(17)^10+E(17)^11+E(17)^12+E(17)^14,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[56,2]], [GALOIS,[56,3]], [TENSOR,[58,2]],[10608,-400,48,0,12,-16,0,-117,-42,8,8,8,-4,0,-5,10,0,-2,0,0, -3,2,0,-3,2,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[11050,170,74,34,-20,10,2,0,-25,0,0,0,-4,2,0, -5,0,-1,0,0,5,0,-1,0,0,0,0,0,1,0,0,0,0,0,0,510,30,6,-10,0,-6,0,-2,0,5,0,0,2,1, 0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [TENSOR,[61,2]],[13056,-256,0,0,12,0,0,116,-24,-4,-9,-4,-4,0,4,4,4,0,-1,4,-3, 2,0,2,-3,0,0,0,1,0,0,-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 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[13260,-308,12,0,-12,12,-4,130,-30,10,-15,0,4, 0,2,2,2,2,-3,0,3,-2,0,-2,3,0,0,2,-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],[13260,-308,12,0,-12,12,-4,-195 ,-30,10,10,0,4,0,-3,2,2,2,2,0,3,-2,0,3,-2,0,0,-3,-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],[15300,-60,-60, 0,0,4,4,-300,0,0,0,0,0,0,20,0,0,0,0,-1,0,0,0,0,0,0,0,4,0,0,0,-1,-1,-1,-1,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[15300 ,-60,-60,0,0,4,4,75,0,0,0,0,0,0,-5,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0, E(65)^11+E(65)^19+E(65)^21+E(65)^22+E(65)^23+E(65)^27+E(65)^38+E(65)^42 +E(65)^43+E(65)^44+E(65)^46+E(65)^54, E(65)+E(65)^2+E(65)^4+E(65)^8+E(65)^16+E(65)^32+E(65)^33+E(65)^49+E(65)^57 +E(65)^61+E(65)^63+E(65)^64, E(65)^3+E(65)^6+E(65)^12+E(65)^17+E(65)^24+E(65)^31+E(65)^34+E(65)^41+E(65)^48 +E(65)^53+E(65)^59+E(65)^62, E(65)^7+E(65)^9+E(65)^14+E(65)^18+E(65)^28+E(65)^29+E(65)^36+E(65)^37+E(65)^47 +E(65)^51+E(65)^56+E(65)^58 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[67,11]], [GALOIS,[67,7]], [GALOIS,[67,3]],[17680,16,80,-68,4,16,0,65,-40,-20,5,0,4,-4,1,-4,-4,0,1,0,-1, 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342,321],[ "fusion map is unique up to table automorphisms" ]); MOT("U4(5)", [ "origin: computed using Dixon's algorithm and character theoretic methods,\n", "Thomas Breuer, Jul. 09th, 2003" ], [14742000000,86400,62400,1134000,1134000,43200,2160,31200,1440,96,1125000, 75000,75000,1875,125,125,43200,2160,2160,2160,216,108,96,63,63,72,63,63,1800, 300,300,200,200,1440,1440,72,72,72,48,48,52,52,52,2250,2250,1800,1800,150,150, 90,75,75,100,100,60,63,63,63,63,72,72,72,72,72,72,72,72,52,52,52,1800,1800,150 ,150,90,90,90,52,52,52,52,52,52,60,60,63,63,63,63,63,63,63,63,63,63,63,63], [,[1,1,1,5,4,6,7,3,2,3,11,12,13,14,15,16,6,7,5,4,6,7,6,24,25,9,28,27,11,12,13, 12,13,17,17,18,20,19,23,23,42,43,41,45,44,47,46,48,49,50,52,51,32,33,29,57,56, 59,58,36,36,34,35,37,38,37,38,42,43,41,46,47,48,49,50,45,44,68,69,70,68,69,70, 71,72,87,88,90,91,92,95,96,94,89,97,86,93],[1,2,3,1,1,1,1,8,9,10,11,12,13,14, 15,16,2,2,2,2,2,2,3,25,24,26,4,5,29,30,31,32,33,9,9,9,9,9,10,8,42,43,41,11,11, 11,11,12,13,11,14,14,53,54,55,24,24,25,25,26,26,26,26,26,26,26,26,69,70,68,29, 29,30,31,29,29,29,79,80,81,82,83,78,55,55,56,57,56,58,57,59,56,58,59,58,57,59] ,,[1,2,3,5,4,6,7,8,9,10,1,1,1,1,1,1,17,18,20,19,21,22,23,25,24,26,28,27,2,2,2, 3,3,35,34,36,38,37,39,40,41,42,43,4,5,6,6,6,6,7,5,4,8,8,9,58,59,56,57,60,61,63 ,62,65,64,67,66,68,69,70,17,17,17,17,18,19,20,81,82,83,78,79,80,34,35,89,91,95 ,86,97,87,93,92,96,88,94,90],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19 ,20,21,22,23,1,1,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,43,41,42,44,45, 46,47,48,49,50,51,52,53,54,55,4,5,5,4,61,60,62,63,66,67,64,65,70,68,69,71,72, 73,74,75,76,77,80,81,82,83,78,79,84,85,27,28,27,28,28,27,27,28,27,28,28,27],,, ,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,25,24,26,27,28 ,29,30,31,32,33,34,35,36,37,38,39,40,1,1,1,44,45,46,47,48,49,50,51,52,53,54,55 ,59,58,57,56,61,60,62,63,66,67,64,65,3,3,3,71,72,73,74,75,76,77,8,8,8,8,8,8,84 ,85,91,95,97,87,93,88,94,96,86,90,89,92]], 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E(21)+E(21)^4+E(21)^16,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)^2+E(21)^8+E(21)^11,E(21)^5+E(21)^17+E(21)^20, E(21)+E(21)^4+E(21)^16], [GALOIS,[75,2]], [GALOIS,[75,5]], [GALOIS,[75,10]],[15625,25,25,-125,-125,25,-5,25,5,1,0,0,0,0,0,0,25,-5,-5,-5, 1,1,1,1,1,-1,1,1,0,0,0,0,0,5,5,-1,-1,-1,1,1,-1,-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,-1,-1,-1,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,0,0,1, 1,1,1,1,1,1,1,1,1,1,1],[16380,60,-52,-126,-126,60,-6,0,-4,0,5,30,30,5,0,0,60, -6,-6,-6,0,0,-4,0,0,0,0,0,5,0,0,-2,-2,-4,-4,2,2,2,0,0,0,0,0,-1,-1,5,5,0,0,-1, -1,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,5,0,0,-1,-1,-1,0,0,0,0,0,0,1,1,0,0 ,0,0,0,0,0,0,0,0,0,0],[16380,60,-52,-126*E(3),-126*E(3)^2,-30,-6,0,-4,0,5,30, 30,5,0,0,-30,-6,-6*E(3),-6*E(3)^2,0,0,2,0,0,0,0,0,5,0,0,-2,-2,6*E(3)-10*E(3)^2 ,-10*E(3)+6*E(3)^2,2,2*E(3),2*E(3)^2,0,0,0,0,0,-E(3)^2,-E(3),5*E(3)^2,5*E(3),0 ,0,-1,-E(3),-E(3)^2,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5*E(3),5*E(3)^2,0,0,-1 ,-E(3)^2,-E(3),0,0,0,0,0,0,E(3)^2,E(3),0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[81,2]],[18144,0,-48,0,0,0,0,0,0,0,144,-6,-6,-6,-1,-1,0,0,0,0,0,0,0,0 ,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,0,-E(13)^4-E(13)^6-E(13)^7-E(13)^9, -E(13)-E(13)^5-E(13)^8-E(13)^12,-E(13)^2-E(13)^3-E(13)^10-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,E(13)^4+E(13)^6+E(13)^7+E(13)^9, E(13)+E(13)^5+E(13)^8+E(13)^12,E(13)^2+E(13)^3+E(13)^10+E(13)^11,0,0,0,0,0,0,0 ,E(52)-E(52)^5-E(52)^21+E(52)^25,-E(52)^29+E(52)^37+E(52)^41-E(52)^49, E(52)^9+E(52)^17-E(52)^33-E(52)^45,-E(52)+E(52)^5+E(52)^21-E(52)^25, E(52)^29-E(52)^37-E(52)^41+E(52)^49,-E(52)^9-E(52)^17+E(52)^33+E(52)^45,0,0,0, 0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[83,33]], [GALOIS,[83,11]], [GALOIS,[83,5]], [GALOIS,[83,7]], [GALOIS,[83,3]],[18144,0,48,0,0,0,0,48,0,0,144,-6,-6,-6,-1,-1,0,0,0,0,0,0,0,0 ,0,0,0,0,0,0,0,-2,-2,0,0,0,0,0,0,0,-E(13)^4-E(13)^6-E(13)^7-E(13)^9, -E(13)-E(13)^5-E(13)^8-E(13)^12,-E(13)^2-E(13)^3-E(13)^10-E(13)^11,0,0,0,0,0,0 ,0,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(13)^4-E(13)^6-E(13)^7-E(13)^9, -E(13)-E(13)^5-E(13)^8-E(13)^12,-E(13)^2-E(13)^3-E(13)^10-E(13)^11,0,0,0,0,0,0 ,0,-E(13)^2-E(13)^3-E(13)^10-E(13)^11,-E(13)^4-E(13)^6-E(13)^7-E(13)^9, -E(13)-E(13)^5-E(13)^8-E(13)^12,-E(13)^2-E(13)^3-E(13)^10-E(13)^11, -E(13)^4-E(13)^6-E(13)^7-E(13)^9,-E(13)-E(13)^5-E(13)^8-E(13)^12,0,0,0,0,0,0,0 ,0,0,0,0,0,0,0], [GALOIS,[89,4]], [GALOIS,[89,2]],[18144,0,48,0,0,0,0,-48,0,0,144,-6,-6,-6,-1,-1,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,-2,-2,0,0,0,0,0,0,0,-E(13)^2-E(13)^3-E(13)^10-E(13)^11, -E(13)^4-E(13)^6-E(13)^7-E(13)^9,-E(13)-E(13)^5-E(13)^8-E(13)^12,0,0,0,0,0,0,0 ,0,0,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(13)^2-E(13)^3-E(13)^10-E(13)^11, -E(13)^4-E(13)^6-E(13)^7-E(13)^9,-E(13)-E(13)^5-E(13)^8-E(13)^12,0,0,0,0,0,0,0 ,E(13)+E(13)^5+E(13)^8+E(13)^12,E(13)^2+E(13)^3+E(13)^10+E(13)^11, E(13)^4+E(13)^6+E(13)^7+E(13)^9,E(13)+E(13)^5+E(13)^8+E(13)^12, E(13)^2+E(13)^3+E(13)^10+E(13)^11,E(13)^4+E(13)^6+E(13)^7+E(13)^9,0,0,0,0,0,0, 0,0,0,0,0,0,0,0], [GALOIS,[92,4]], [GALOIS,[92,2]],[18900,-36,-24,0,0,36,0,-26,0,2,150,25,25,0,0,0,-36,0,0,0,0,0 ,0,0,0,0,0,0,-6,-1,-1,1,1,0,0,0,0,0,2,-2,-2,-2,-2,0,0,6,6,1,1,0,0,0,-1,-1,0,0, 0,0,0,0,0,0,0,0,0,0,0,2,2,2,-6,-6,-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],[19656,-72,0,0,0,-36,0,-52,0,4,156,56,56,6,1,1,36,0,0,0,0,0,0,0,0,0,0 ,0,-12,-2,-2,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,-6,-6,-1,-1,0,0,0,-2,-2,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,6,6,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[ 19656,-72,0,0,0,-36,0,52,0,-4,156,56,56,6,1,1,36,0,0,0,0,0,0,0,0,0,0,0,-12,-2, -2,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,-6,-6,-1,-1,0,0,0,2,2,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,6,6,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]], [(60,61)(64,66)(65,67),(78,81)(79,82)(80,83), (12,13)(15,16)(30,31)(32,33)(48,49)(53,54)(73,74), (41,42,43)(68,69,70)(78,79,80,81,82,83), (86,88,92)(87,90,96)(89,95,93)(91,97,94), (24,25)(56,59)(57,58)(86,91,88,97,92,94)(87,95,90,93,96,89), ( 4, 5)(19,20)(27,28)(34,35)(37,38)(44,45)(46,47)(51,52)(56,57)(58,59)(62,63) (64,65)(66,67)(71,72)(76,77)(84,85)(86,87,88,90,92,96)(89,91,95,97,93,94) ]); ARC("U4(5)","isSimple",true); ARC("U4(5)","extInfo",["2","2^2"]); ALF("U4(5)","U4(5).2_1",[1,2,3,4,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18, 18,19,20,21,22,22,23,24,24,25,26,27,28,29,30,30,31,32,32,33,34,35,36,37, 38,38,39,39,40,41,42,43,43,44,45,46,47,48,47,48,49,50,51,51,52,52,53,53, 54,55,56,57,57,58,59,60,61,61,62,63,64,62,63,64,65,65,66,67,68,66,69,67, 70,70,71,68,71,69],[ "fusion map is unique up to table automorphisms" ]); ALF("U4(5)","U4(5).2_2",[1,2,3,4,5,6,7,8,9,10,11,12,12,13,14,14,15,16,17, 18,19,20,21,22,23,24,25,26,27,28,28,29,29,30,31,32,33,34,35,36,37,38,39, 40,41,42,43,44,44,45,46,47,48,48,49,50,51,52,53,54,55,56,57,58,59,60,61, 62,63,64,65,66,67,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84, 85,86,87,88,89,90],[ "fusion map is unique up to table automorphisms" ]); ALF("U4(5)","U4(5).2_3",[1,2,3,4,4,5,6,7,8,9,10,11,11,12,13,13,14,15,16, 16,17,18,19,20,20,21,22,22,23,24,24,25,25,26,26,27,28,28,29,30,31,32,33, 34,34,35,35,36,36,37,38,38,39,39,40,41,42,41,42,43,44,45,45,46,46,47,47, 48,49,50,51,51,52,52,53,54,54,55,56,57,55,56,57,58,58,59,60,61,59,62,60, 63,63,64,61,64,62],[ "fusion map is unique up to table automorphisms" ]); ALF("U4(5)","U4(5).2^2",[1,2,3,4,4,5,6,7,8,9,10,11,11,12,13,13,14,15,16, 16,17,18,19,20,20,21,22,22,23,24,24,25,25,26,26,27,28,28,29,30,31,32,33, 34,34,35,35,36,36,37,38,38,39,39,40,41,42,41,42,43,44,45,45,46,46,47,47, 48,49,50,51,51,52,52,53,54,54,55,56,57,55,56,57,58,58,59,60,61,59,62,60, 63,63,64,61,64,62],[ "fusion map is unique up to table automorphisms" ]); MOT("U4(5).2_1", [ "origin: computed using Dixon's algorithm and character theoretic methods,\n", "Thomas Breuer, August 2005,\n", "constructions: PSigmaU(4,5), PSU(4,5) extended by transpose-inverse" ], 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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],[29952,0,0,-288,0,0,0 ,0,0,-48,-48,-48,2,2,2,0,0,0,0,0,0,-1,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0, 0,2,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, E(21)^2+E(21)^8+E(21)^10+E(21)^11+E(21)^13+E(21)^19, E(21)+E(21)^4+E(21)^5+E(21)^16+E(21)^17+E(21)^20, E(21)^2+E(21)^8+E(21)^10+E(21)^11+E(21)^13+E(21)^19, E(21)+E(21)^4+E(21)^5+E(21)^16+E(21)^17+E(21)^20, E(21)^2+E(21)^8+E(21)^10+E(21)^11+E(21)^13+E(21)^19, E(21)+E(21)^4+E(21)^5+E(21)^16+E(21)^17+E(21)^20,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[105,2]],[29952,0,0,144,0,0,0,0,0,-48,-48,-48,2,2,2,0,0,0,0,0,0,-1,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,0,0,0,0,-1,0,0,0, E(21)^2+E(21)^8+E(21)^10+E(21)^11+E(21)^13+E(21)^19, E(21)+E(21)^4+E(21)^5+E(21)^16+E(21)^17+E(21)^20,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,0,0,-E(63)^8-E(63)^13+E(63)^19+E(63)^31+E(63)^32+E(63)^44-E(63)^50-E(63)^55, E(63)-E(63)^4+E(63)^5-E(63)^17-E(63)^46+E(63)^58-E(63)^59+E(63)^62, E(63)^10+E(63)^13-E(63)^19-E(63)^23-E(63)^40-E(63)^44+E(63)^50+E(63)^53, -E(63)+E(63)^4-E(63)^22+E(63)^26+E(63)^37-E(63)^41+E(63)^59-E(63)^62, E(63)^8-E(63)^10+E(63)^23-E(63)^31-E(63)^32+E(63)^40-E(63)^53+E(63)^55, -E(63)^5+E(63)^17+E(63)^22-E(63)^26-E(63)^37+E(63)^41+E(63)^46-E(63)^58,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0], [GALOIS,[107,4]], [GALOIS,[107,16]], [GALOIS,[107,8]], [GALOIS,[107,19]], [GALOIS,[107,2]],[32760,120,-104,126,-60,-12,0,-8,0,10,60,60,10,0,0,-60,-12,6 ,0,0,4,0,0,0,10,0,0,-4,-4,4,4,-2,0,0,0,0,0,1,-5,0,0,-2,1,0,0,2,0,0,0,0,0,0,0,0 ,0,0,-5,0,0,-2,1,0,0,0,-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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[36288,0,-96,0,0,0,0,0,0, 288,-12,-12,-12,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,4,4,0,0,0,0,0, -2*E(13)-2*E(13)^5-2*E(13)^8-2*E(13)^12, -2*E(13)^2-2*E(13)^3-2*E(13)^10-2*E(13)^11, -2*E(13)^4-2*E(13)^6-2*E(13)^7-2*E(13)^9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 2*E(13)+2*E(13)^5+2*E(13)^8+2*E(13)^12, 2*E(13)^2+2*E(13)^3+2*E(13)^10+2*E(13)^11, 2*E(13)^4+2*E(13)^6+2*E(13)^7+2*E(13)^9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [GALOIS,[114,4]], [GALOIS,[114,2]]], [( 49, 50)( 52, 53)(103,104), ( 35, 36, 37)( 54, 55, 56)( 62, 63, 64)(105,106,107)(108,109,110), ( 11, 12)( 14, 15)( 26, 27)( 28, 29)( 40, 41)( 44, 45)( 58, 59)( 72, 73) ( 75, 77)( 78, 81)( 79, 82)( 80, 83)( 86, 87)( 88, 89)( 90, 91)( 92, 93) ( 95, 96)( 97, 99)(100,102)(103,104)(105,108)(106,109)(107,110)(111,114) (112,115)(113,116) ,( 66, 68, 70)( 67, 69, 71),( 47, 48)( 66, 67, 68, 69, 70, 71)]); ALF("U4(5).2_1","U4(5).2^2",[1,2,3,4,5,6,7,8,9,10,11,11,12,13,13,14,15,16, 17,18,19,20,21,22,23,24,24,25,25,26,27,28,29,30,31,32,33,34,35,36,36,37, 38,39,39,40,41,42,43,44,45,46,47,48,49,50,51,52,52,53,54,55,56,57,58,59, 60,61,62,63,64,65,65,66,67,68,67,69,70,71,69,70,71,72,73,74,74,75,75,76, 76,77,77,78,79,79,80,81,80,82,83,82,84,84,85,86,87,85,86,87,88,89,90,88, 89,90]); MOT("U4(5).2_2", [ "origin: computed using Dixon's algorithm and character theoretic methods,\n", "Thomas Breuer, August 2005,\n", "constructions: PGU(4,5)" ], [29484000000,172800,124800,2268000,2268000,86400,4320,62400,2880,192,2250000, 75000,3750,125,86400,4320,4320,4320,432,216,192,126,126,144,126,126,3600,300, 200,2880,2880,144,144,144,96,96,104,104,104,4500,4500,3600,3600,150,180,150, 150,100,120,126,126,126,126,144,144,144,144,144,144,144,144,104,104,104,3600, 3600,150,180,180,180,104,104,104,104,104,104,120,120,126,126,126,126,126,126, 126,126,126,126,126,126,2268000,288,2268000,2268000,4320,4320,4320,4320,4320, 4320,216,2880,2880,208,208,96,4500,150,288,288,144,144,144,126,126,126,126, 2880,2880,2880,2880,144,144,144,144,144,144,96,96,4500,4500,180,180,180,180, 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104,105,106,107,108,92,92,92,92,92,115,114,93,94,102,103,103,102,102,103,103, 102,103,102,106,106,107,107,107,107,107,107,107,107,108,108,140,141,114,114, 115,115,147,149,152,151,154,150,153,155,146,157,148,156,140,141,141,140,142, 143,145,144,145,142,144,145,143,142,143,144],,[1,2,3,5,4,6,7,8,9,10,1,1,1,1,15 ,16,18,17,19,20,21,23,22,24,26,25,2,2,3,31,30,32,34,33,35,36,37,38,39,4,5,6,6, 6,7,5,4,8,9,52,53,50,51,54,55,57,56,59,58,61,60,62,63,64,15,15,15,16,17,18,74, 75,76,71,72,73,30,31,82,84,88,79,90,80,86,85,89,81,87,83,91,92,94,93,96,95,98, 97,100,99,101,103,102,105,104,106,91,91,110,109,111,113,112,115,114,117,116, 120,121,118,119,124,125,122,123,127,126,129,128,94,93,97,98,99,100,95,96,93,94 ,103,102,144,145,142,143,152,153,154,155,156,157,146,147,148,149,150,151,120, 121,118,119,168,169,170,171,172,173,162,163,164,165,166,167],,[1,2,3,4,5,6,7,8 ,9,10,11,12,13,14,15,16,17,18,19,20,21,1,1,24,25,26,27,28,29,30,31,32,33,34,35 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( 22, 23)( 50, 53)( 51, 52)( 79, 84, 81, 90, 85, 87)( 80, 88, 83, 86, 89, 82) (114,115)(142,145)(143,144)(162,164,167,169,171,166)(163,165,172,168,170,173) , ( 4, 5)( 17, 18)( 25, 26)( 30, 31)( 33, 34)( 40, 41)( 42, 43)( 46, 47) ( 50, 51)( 52, 53)( 54, 55)( 56, 57)( 58, 61)( 59, 60)( 65, 66)( 69, 70) ( 77, 78)( 79, 83)( 80, 85)( 81, 89)( 82, 90)( 84, 86)( 87, 88)( 93, 94) ( 95, 96)( 97, 98)( 99,100)(109,110)(112,113)(116,117)(118,121)(119,120) (122,125)(123,124)(128,129)(130,131)(132,133)(134,135)(136,137)(138,139) (142,143)(144,145)(158,161)(159,160)(162,163)(164,165)(166,173)(167,172) (168,169)(170,171) ]); ALF("U4(5).2_2","U4(5).2^2",[1,2,3,4,4,5,6,7,8,9,10,11,12,13,14,15,16,16, 17,18,19,20,20,21,22,22,23,24,25,26,26,27,28,28,29,30,31,32,33,34,34,35, 35,36,37,38,38,39,40,41,42,41,42,43,44,45,45,46,46,47,47,48,49,50,51,51, 52,53,54,54,55,56,57,55,56,57,58,58,59,60,61,59,62,60,63,63,64,61,64,62, 91,92,93,93,94,94,95,95,96,96,97,98,98,99,99,100,101,102,103,103,104,105, 105,106,106,107,107,108,109,108,109,110,111,110,111,112,112,113,113,114, 114,115,115,116,116,117,117,118,118,119,119,120,121,120,121,122,123,124, 125,126,127,122,123,124,125,126,127,128,129,128,129,130,131,132,133,134, 135,130,131,132,133,134,135]); MOT("U4(5).2_3", [ "origin: computed using Dixon's algorithm and character theoretic methods,\n", "Thomas Breuer, August 2005" ], [29484000000,172800,124800,1134000,86400,4320,62400,2880,192,2250000,75000, 3750,125,86400,4320,2160,432,216,192,63,144,63,3600,300,200,1440,144,72,96,96, 104,104,104,2250,1800,150,180,75,100,120,63,63,144,144,72,72,72,104,104,104, 1800,150,180,90,52,52,52,60,63,63,63,63,63,63,31200,1440,48,960,960,48,48,32, 50,1440,1440,72,72,72,60,48,48,48,48,48,48,52,52,52,52,52,52,40,40,60,60], [,[1,1,1,4,5,6,3,2,3,10,11,12,13,5,6,4,5,6,5,20,8,22,10,11,11,14,15,16,19,19, 32,33,31,34,35,36,37,38,25,23,42,41,27,27,26,28,28,32,33,31,35,36,37,34,48,49, 50,51,60,61,62,63,64,59,1,2,6,8,8,9,9,8,12,15,15,15,17,17,23,29,29,29,29,27,27 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2*E(13)^4+2*E(13)^6+2*E(13)^7+2*E(13)^9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[93,4]], [GALOIS,[93,2]]], [(59,61,63)(60,62,64),(41,42)(59,60,61,62,63,64), (43,44)(46,47)(74,75)(77,78)(80,81)(82,83)(94,95), (68,69)(70,71)(74,75)(77,78)(80,82)(81,83)(84,85)(92,93)(94,95), (86,89)(87,90)(88,91),(31,32,33)(48,49,50)(55,56,57)(86,87,91)(88,89,90)]); ALF("U4(5).2_3","U4(5).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, 43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,136,137, 138,139,139,140,140,141,142,143,143,144,145,145,146,147,148,147,148,149, 149,150,151,152,150,151,152,153,153,154,154]); MOT("U4(5).2^2", [ "origin: computed using Dixon's algorithm and character theoretic methods,\n", "Thomas Breuer, July 2007;\n", "later constructed using `PossibleCharacterTablesOfTypeGV4',\n", "constructions: Aut(U4(5)), PGU(4,5) extended by 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37,38,39,40,40,41,41,42,42,43,43,44,44,45,45,46,46,47,47,48,48,49,49,50, 50,51,51,52,52,53,53,54,54,55,55,56,56,57,57],[ "fusion map is unique up to table automorphisms" ]); ARC("U5(4)","isSimple",true); ARC("U5(4)","extInfo",["5","5:4"]); MOT("U5(4).2", [ "origin: computed using character theoretic methods,\n", "Thomas Breuer, Apr. 10th, 2005" ], [106887905280000,2044723200,7864320,374400,24480,491520,32768,2048,624000, 624000,36000,36000,1250,1920,96,512,256,256,3200,3200,1200,1200,160,160,96,780 ,780,900,900,150,150,90,90,102,102,102,102,160,160,52,52,60,60,39,39,41,41,41, 41,51,51,51,51,65,65,65,65,1958400,7680,360,360,15360,15360,512,600,600,600, 600,50,24,64,64,40,40,48,48,30,30,30,30,34,34,34,34,80,80,80,80], [,[1,1,1,4,5,2,2,3,10,9,12,11,13,4,5,7,7,7,10,9,12,11,12,11,14,27,26,29,28,31, 30,33,32,35,34,37,36,19,20,26,27,28,29,45,44,47,46,49,48,51,50,53,52,55,54,57, 56,1,3,4,5,6,6,6,9,10,12,11,13,15,16,16,24,23,25,25,32,33,30,31,34,35,37,36,39 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30*E(5)+40*E(5)^2+40*E(5)^3+30*E(5)^4,0,-6,-2,0,0,0,2*E(5)+2*E(5)^4, 2*E(5)^2+2*E(5)^3,4*E(5)-2*E(5)^2-2*E(5)^3+4*E(5)^4, -2*E(5)+4*E(5)^2+4*E(5)^3-2*E(5)^4,-2*E(5)^2-2*E(5)^3,-2*E(5)-2*E(5)^4,2,0,0, E(5)-3*E(5)^2-3*E(5)^3+E(5)^4,-3*E(5)+E(5)^2+E(5)^3-3*E(5)^4,-2*E(5)-2*E(5)^4, -2*E(5)^2-2*E(5)^3,-2*E(5)^2-2*E(5)^3,-2*E(5)-2*E(5)^4,0,0,0,0, 2*E(5)^2+2*E(5)^3,2*E(5)+2*E(5)^4,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[57,2]],[999375,975,-305,0,30,15,15,-1,0,0,0,0,0,0,-2,-1,-1,-1,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,-E(17)^6-E(17)^7-E(17)^10-E(17)^11, -E(17)^3-E(17)^5-E(17)^12-E(17)^14,-E(17)-E(17)^4-E(17)^13-E(17)^16, -E(17)^2-E(17)^8-E(17)^9-E(17)^15,0,0,0,0,0,0,0,0,0,0,0,0, -E(17)^2-E(17)^8-E(17)^9-E(17)^15,-E(17)-E(17)^4-E(17)^13-E(17)^16, -E(17)^3-E(17)^5-E(17)^12-E(17)^14,-E(17)^6-E(17)^7-E(17)^10-E(17)^11,0,0,0,0, 225,-15,0,0,-15,-15,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0, E(17)^3+E(17)^5+E(17)^12+E(17)^14,E(17)^6+E(17)^7+E(17)^10+E(17)^11, E(17)+E(17)^4+E(17)^13+E(17)^16,E(17)^2+E(17)^8+E(17)^9+E(17)^15,0,0,0,0], [TENSOR,[59,2]], [GALOIS,[59,2]], [TENSOR,[61,2]], [GALOIS,[59,6]], [TENSOR,[63,2]], [GALOIS,[59,3]], [TENSOR,[65,2]],[1998750,1950,-610,0,-30,30,30,-2,0,0,0,0,0,0,2,-2,-2,-2,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(17)-2*E(17)^4-2*E(17)^13-2*E(17)^16, -2*E(17)^2-2*E(17)^8-2*E(17)^9-2*E(17)^15, -2*E(17)^3-2*E(17)^5-2*E(17)^12-2*E(17)^14, -2*E(17)^6-2*E(17)^7-2*E(17)^10-2*E(17)^11,0,0,0,0,0,0,0,0,0,0,0,0, E(17)^6+E(17)^7+E(17)^10+E(17)^11,E(17)^3+E(17)^5+E(17)^12+E(17)^14, E(17)^2+E(17)^8+E(17)^9+E(17)^15,E(17)+E(17)^4+E(17)^13+E(17)^16,0,0,0,0,0,0,0 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[67,2]], [GALOIS,[67,6]], [GALOIS,[67,3]],[2091000,-520,120,150,0,-8,-40,-8,-150,-150,0,0,0,-10,0,0,0,0 ,10,10,0,0,0,0,-2,-4*E(13)-4*E(13)^3-4*E(13)^4-4*E(13)^9-4*E(13)^10-4*E(13)^12 ,-4*E(13)^2-4*E(13)^5-4*E(13)^6-4*E(13)^7-4*E(13)^8-4*E(13)^11,0,0,0,0,0,0,0,0 ,0,0,2,2,0,0,0,0,-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)^12,0,0,0,0,0,0,0,0, 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)+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 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[71,2]],[1048576,0,0,64,16,0,0,0,-64,-64,16,16,1,0,0,0,0,0,0,0,0,0,0, 0,0,-4,-4,4,4,-1,-1,1,1,-1,-1,-1,-1,0,0,0,0,0,0,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1, 1,1,256,0,4,4,0,0,0,-4,-4,-4,-4,1,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,1,1,0,0,0,0], [TENSOR,[73,2]],[1066000,1040,16,-65,1,80,16,0,0,0,25,25,0,-1,1,0,0,0,0,0,5,5 ,1,1,-1,0,0,-5,-5,0,0,1,1,-2,-2,-2,-2,0,0,0,0,-1,-1,0,0,0,0,0,0,1,1,1,1,0,0,0, 0,340,4,-5,1,20,20,4,0,0,-5,-5,0,1,0,0,-1,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0], [TENSOR,[75,2]],[1115200,64,320,1,-17,64,0,0,-65,-65,40,40,0,1,-1,0,0,0,-1,-1 ,4,4,0,0,1,-5,-5,1,1,1,1,-2,-2,0,0,0,0,-1,-1,-1,-1,1,1,1,1,0,0,0,0,0,0,0,0,0,0 ,0,0,340,20,1,-5,4,4,4,-5,-5,0,0,0,-1,0,0,0,0,1,1,0,0,1,1,0,0,0,0,-1,-1,-1,-1] , [TENSOR,[77,2]],[1132625,1105,337,-130,17,145,17,1,0,0,25*E(5)+25*E(5)^4, 25*E(5)^2+25*E(5)^3,0,-2,1,1,1,1,0,0,5*E(5)+5*E(5)^4,5*E(5)^2+5*E(5)^3, E(5)+E(5)^4,E(5)^2+E(5)^3,-2,0,0,-5*E(5)-5*E(5)^4,-5*E(5)^2-5*E(5)^3,0,0, E(5)^2+E(5)^3,E(5)+E(5)^4,0,0,0,0,0,0,0,0,-E(5)^2-E(5)^3,-E(5)-E(5)^4,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,255,-17,0,-3,15,15,-1,0,0,-5*E(5)-5*E(5)^4, -5*E(5)^2-5*E(5)^3,0,1,-1,-1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,E(5)+E(5)^4, E(5)^2+E(5)^3,0,0,0,0,0,0,0,0,0,0], [TENSOR,[79,2]], [GALOIS,[79,2]], [TENSOR,[81,2]],[2486250,-9750,-150,0,0,-150,10,10,0,0,0,0,0,0,0,2,2,2,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, E(41)^6+E(41)^14+E(41)^15+E(41)^17+E(41)^19+E(41)^22+E(41)^24+E(41)^26 +E(41)^27+E(41)^35 , E(41)^3+E(41)^7+E(41)^11+E(41)^12+E(41)^13+E(41)^28+E(41)^29+E(41)^30+E(41)^34 +E(41)^38 , E(41)+E(41)^4+E(41)^10+E(41)^16+E(41)^18+E(41)^23+E(41)^25+E(41)^31+E(41)^37 +E(41)^40 , E(41)^2+E(41)^5+E(41)^8+E(41)^9+E(41)^20+E(41)^21+E(41)^32+E(41)^33+E(41)^36 +E(41)^39 ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ], [GALOIS,[83,2]], [GALOIS,[83,3]], [GALOIS,[83,6]],[2613750,-10250,630,-150,0,-10,-42,-10,0,0,0,0,0,10,0,-2,-2, -2,0,0,0,0,0,0,2,-5*E(13)-5*E(13)^3-5*E(13)^4-5*E(13)^9-5*E(13)^10-5*E(13)^12, -5*E(13)^2-5*E(13)^5-5*E(13)^6-5*E(13)^7-5*E(13)^8-5*E(13)^11,0,0,0,0,0,0,0,0, 0,0,0,0,-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)^12,0,0, 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)^12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [GALOIS,[87,2]]], [(62,63)(71,72)(75,76)(85,87)(86,88),(46,47)(48,49),(46,48,47,49), (26,27)(40,41)(44,45)(54,56)(55,57),(17,18), ( 9,10)(11,12)(19,20)(21,22)(23,24)(28,29)(30,31)(32,33)(38,39)(42,43)(54,57) (55,56)(65,66)(67,68)(73,74)(77,78)(79,80)(85,86)(87,88) ,(34,35)(36,37)(50,51)(52,53)(81,82)(83,84), (34,37,35,36)(50,52,51,53)(81,83,82,84)]); MOT("U5(3)", [ "origin: computed using character theoretic methods,\n", "Thomas Breuer, May 3rd, 2009" ], [258190571520,52254720,580608,52907904,629856,69984,8748,52254720,52254720, 580608,580608,96768,96768,96768,9216,9216,9216,1536,80,93312,72576,10368,7776, 1296,1296,864,108,672,672,48384,48384,5760,5760,768,768,768,768,768,768,128, 128,64,972,81,80,93312,93312,72576,72576,10368,10368,7776,7776,1728,1728,1728, 1296,1296,1296,1296,1152,1152,1152,1152,1152,1152,864,864,192,144,144,144,144, 144,144,108,108,672,672,112,112,80,80,108,80,80,84,84,864,864,96,96,96,96,96, 96,72,72,72,72,672,672,672,672,112,112,112,112,112,112,112,112,112,112,108,108 ,80,80,80,80,84,84,56,56,56,56,61,61,61,61,61,61,61,61,61,61,61,61,80,80,80,80 ,80,80,80,80,84,84,84,84], [,[1,1,1,4,5,6,7,2,2,3,3,3,2,2,2,3,3,3,19,4,4,4,5,6,5,6,7,28,29,11,10,8,9,16, 17,11,10,17,16,17,16,15,43,44,19,20,20,21,21,22,22,23,23,22,20,20,24,24,25,25, 22,22,20,20,21,21,26,26,22,26,23,24,24,25,25,27,27,28,29,28,29,32,33,43,45,45, 87,88,50,51,61,62,51,50,62,61,68,67,53,52,78,79,79,78,81,80,80,81,80,81,81,80, 78,79,84,84,85,86,86,85,87,88,101,102,103,104,128,129,130,131,132,133,134,135, 136,137,138,127,117,118,119,119,117,120,118,120,121,122,121,122],[1,2,3,1,1,1, 1,9,8,11,10,12,14,13,15,17,16,18,19,2,3,3,2,2,3,3,3,29,28,31,30,33,32,35,34,37 ,36,39,38,41,40,42,4,5,45,8,9,10,11,11,10,9,8,12,14,13,9,8,10,11,16,17,15,15, 17,16,11,10,18,12,15,14,13,17,16,10,11,79,78,81,80,83,82,20,86,85,28,29,30,31, 34,35,37,36,38,39,31,30,32,33,102,101,104,103,106,105,108,107,110,109,112,111, 114,113,46,47,118,117,120,119,78,79,124,123,126,125,133,134,135,136,137,138, 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-4*E(7)^3-4*E(7)^5-4*E(7)^6,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-1,0,0,0,-32*E(4), 32*E(4),-16*E(4),16*E(4),0,0,0,0,0,0,0,4*E(4),-4*E(4),0,0,0,0,0,0,-4*E(4), 4*E(4),0,0,0,0,0,0,0,E(4),-E(4),4*E(7)+4*E(7)^2+4*E(7)^4, 4*E(7)^3+4*E(7)^5+4*E(7)^6,0,0,0,0,0,0,0,-E(7)^3-E(7)^5-E(7)^6, -E(7)-E(7)^2-E(7)^4,0,0,0,0,0,0,0,0,0,0,0,0,4*E(28)^11+4*E(28)^15+4*E(28)^23, -4*E(28)^3-4*E(28)^19-4*E(28)^27,4*E(28)^3+4*E(28)^19+4*E(28)^27, -4*E(28)^11-4*E(28)^15-4*E(28)^23,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,-E(28)^3-E(28)^19-E(28)^27,-E(28)^11-E(28)^15-E(28)^23, E(28)^3+E(28)^19+E(28)^27,E(28)^11+E(28)^15+E(28)^23], [GALOIS,[147,5]], [GALOIS,[147,3]], [GALOIS,[147,11]]], [(139,143)(140,145)(141,142)(144,146), (117,120)(118,119)(139,144,143,146)(140,141,145,142), ( 28, 29)( 78, 79)( 80, 81)( 87, 88)(101,103)(102,104)(105,107) (106,108)(109,111)(110,112)(113,114)(121,122)(123,125)(124,126) (147,148)(149,150) , ( 8, 9)( 10, 11)( 13, 14)( 16, 17)( 30, 31)( 32, 33)( 34, 35) ( 36, 37)( 38, 39)( 40, 41)( 46, 47)( 48, 49)( 50, 51)( 52, 53) ( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68) ( 72, 73)( 74, 75)( 76, 77)( 82, 83)( 85, 86)( 89, 90)( 91, 92) ( 93, 94)( 95, 96)( 97, 98)( 99,100)(101,104)(102,103)(105,108) (106,107)(109,112)(110,111)(115,116)(117,118)(119,120)(123,126) (124,125)(139,140)(141,144)(142,146)(143,145)(147,149)(148,150) ,(127,128,129,130,131,132,133,134,135,136,137,138)]); ALF("U5(3)","O10-(3)",[1,2,3,4,7,10,12,16,16,15,15,15,16,16,16,19,19,19, 22,23,24,30,29,36,35,40,47,50,50,51,51,52,52,54,54,51,51,54,54,55,55,52, 62,69,79,83,83,81,81,82,82,95,95,82,83,83,101,101,86,86,97,97,83,83,92,92, 96,96,97,96,95,101,101,105,105,104,104,113,113,114,114,120,120,125,144, 144,145,146,149,149,150,151,149,149,150,151,157,157,156,156,160,161,161, 160,162,162,163,163,162,162,163,163,161,160,179,179,184,184,185,185,193, 192,200,201,201,200,205,206,207,208,209,210,211,212,213,214,215,216,222, 224,223,221,224,221,222,223,225,226,225,226],[ "fusion map is unique up to table automorphisms" ]); ARC("U5(3)","isSimple",true); ARC("U5(3)","extInfo",["","2"]); LIBTABLE.LOADSTATUS.ctounit5:="userloaded"; ############################################################################# ## #E [Dauer der Verarbeitung: 0.42 Sekunden, vorverarbeitet 2026-05-04] |
2026-05-26