#############################################################################
##
#A  prim13.grp                 GAP group library             Heiko Theissen
#A                                                          John Dixon
#A                                                          Brian Mortimer
#A                                                          Charles Sims
##
#A  @(#)$Id: prim13.grp,v 1.1 2000/01/12 15:45:49 ahulpke Exp $
##
#Y  Copyright (C) 1999, School of Math.&Comp. Sci. University of St Andrews
##
##  This file contains part of the primitive groups library
##
Revision.prim13_grp:=
"@(#)$Id: prim13.grp,v 1.1 2000/01/12 15:45:49 ahulpke Exp $";

PRIMGRP[514]:=
[[1,Factorial(514)/2,1,"2",[[513,1]],512,"A_n",["A",514,1],514],
[2,Factorial(514),0,"2",[[513,1]],514,"S_n",["A",514,1],514]];
PRIMGRP[515]:=
[[1,Factorial(515)/2,1,"2",[[514,1]],513,"A_n",["A",515,1],515],
[2,Factorial(515),0,"2",[[514,1]],515,"S_n",["A",515,1],515]];
PRIMGRP[516]:=
[[1,Factorial(516)/2,1,"2",[[515,1]],514,"A_n",["A",516,1],516],
[2,Factorial(516),0,"2",[[515,1]],516,"S_n",["A",516,1],516]];
PRIMGRP[517]:=
[[1,Factorial(517)/2,1,"2",[[516,1]],515,"A_n",["A",517,1],517],
[2,Factorial(517),0,"2",[[516,1]],517,"S_n",["A",517,1],517]];
PRIMGRP[518]:=
[[1,Factorial(518)/2,1,"2",[[517,1]],516,"A_n",["A",518,1],518],
[2,Factorial(518),0,"2",[[517,1]],518,"S_n",["A",518,1],518]];
PRIMGRP[519]:=
[[1,Factorial(519)/2,1,"2",[[518,1]],517,"A_n",["A",519,1],519],
[2,Factorial(519),0,"2",[[518,1]],519,"S_n",["A",519,1],519]];
PRIMGRP[520]:=
[[1,262080,1,"2",[[56,3],[63,1],[72,4]],1,"L2,64#520.1",
["L",[2,64],1],
[(2,73,22)(3,74,21)(4,75,20)(5,76,19)(6,77,18)(7,78,25)
(8,79,24)(9,80,23)(10,81,149)(11,82,155)(12,83,154)
(13,84,136)(14,85,153)(15,86,152)(16,87,151)(17,88,150)
(26,89,191)(27,90,192)(28,91,193)(29,92,194)(30,93,195)
(31,94,196)(32,95,197)(33,96,198)(34,97,199)(35,98,200)
(36,99,201)(37,100,202)(38,101,203)(39,102,204)(40,103,205)
(41,104,206)(42,105,207)(43,106,208)(44,107,209)(45,108,210)
(46,109,211)(47,110,212)(48,111,213)(49,112,214)(50,113,215)
(51,114,216)(52,115,217)(53,116,218)(54,117,219)(55,118,220)
(56,119,221)(57,120,222)(58,121,223)(59,122,224)(60,123,225)
(61,124,226)(62,125,227)(63,126,228)(64,127,229)(65,128,230)
(66,129,231)(67,130,232)(68,131,233)(69,132,234)(70,133,235)
(71,134,236)(72,135,237)(137,280,257)(138,254,426)(139,281,437)
(140,183,308)(141,282,165)(142,283,430)(143,284,317)(144,285,357)
(145,147,287)(146,286,458)(148,288,409)(156,190,267)(157,289,168)
(158,290,457)(159,291,446)(160,278,412)(161,292,379)(162,293,459)
(163,294,270)(164,295,463)(166,296,456)(167,297,447)(169,298,176)
(170,299,461)(171,300,248)(172,179,304)(173,301,329)(174,302,460)
(175,177,303)(178,240,367)(180,305,462)(181,306,444)(182,307,383)
(184,309,374)(185,310,464)(186,311,397)(187,251,424)(188,312,239)
(189,313,334)(241,399,487)(242,393,368)(243,404,497)(244,385,438)
(245,390,381)(246,373,498)(247,258,342)(249,372,277)(250,413,391)
(252,422,370)(253,325,410)(255,419,338)(256,360,470)(259,415,469)
(260,420,264)(261,336,493)(262,350,451)(263,423,432)(265,418,269)
(266,356,328)(268,347,484)(271,417,272)(273,425,483)(274,414,377)
(275,421,361)(276,344,496)(279,416,478)(314,327,479)(316,321,492)
(318,434,503)(319,474,362)(320,354,508)(322,491,517)(323,488,466)
(324,382,408)(326,348,363)(330,400,392)(331,353,511)(332,449,465)
(333,485,467)(335,396,450)(337,352,507)(339,375,429)(340,494,395)
(341,407,505)(343,495,433)(345,436,482)(346,510,428)(349,351,452)
(355,369,398)(359,473,384)(364,509,477)(365,441,504)(366,490,502)
(371,489,468)(376,516,471)(378,402,427)(380,515,472)(386,448,445)
(387,476,389)(388,435,475)(394,411,518)(401,481,439)(403,499,454)
(405,513,455)(406,440,514)(431,480,486)(443,519,453)(500,506,501),
(1,22,21,20,19,18,25,24,23)(2,48,62,61,51,50,40,31,3,55,
64,11,10,7,16,56,39,49,12,52,32,38,60,27,5,53,13,33,71,
65,69,17,68,26,4,34,66,70,43,42,37,41,15,63,67,44,72,58,
57,47,46,36,14,45,59,29,9,8,28,6,54,35,30)
(73,194,154,232,218,191,151,193,149,155,237,231,210,200,221,233,225,234,
230,235,209,214,78,201,206,216,207,208,236,220,195,153,77,215,202,226,
227,217,224,199,196,152,211,75,222,223,229,198,79,204,219,192,150,203,
197,213,80,136,228,205,76,212,74)(81,339,106,325,377,367,466,84,277,
159,358,129,242,496,349,498,167,133,291,266,147,398,471,107,442,297,186,
93,407,296,352,476,128,473,120,301,156,363,444,322,516,169,511,175,451,
288,483,456,279,340,240,420,313,458,455,272,386,393,392,270,518,418,465)
(82,504,506,366,440,448,183,311,300,181,327,500,260,316,83,310,450,357,
306,486,323,341,342,163,424,461,248,122,482,273,364,422,294,464,372,408,
176,255,268,477,474,121,519,468,91,254,333,348,271,492,145,102,111,94,
351,345,353,394,432,292,110,137,157)(85,140,326,368,415,162,457,243,381,
187,302,425,276,239,280,90,401,501,251,453,384,391,99,449,143,275,390,
114,88,434,360,164,329,89,404,429,168,144,509,472,113,489,158,369,264,
305,285,318,250,188,508,282,376,411,324,116,373,395,304,134,343,416,356)
(86,95,298,290,241,478,262,439,438,182,178,452,259,406,256,396,337,321,
307,118,379,87,346,400,135,491,427,109,138,96,142,436,274,170,421,419,
165,287,166,283,388,380,286,494,493,312,445,125,119,263,355,320,520,336,
433,426,161,172,399,315,459,344,467)(92,397,160,354,293,499,249)
(97,378,238,269,463,502,278,246,103,139,385,362,409,495,375,371,245,131,
124,514,338,101,104,503,257,359,179,189,441,435,184,117,328,403,347,284,
267,512,428,112,141,490,350,505,383,405,431,485,148,295,331,115,417,317,
334,423,258,303,430,488,146,484,469)(98,253,447,130,507,460,365,332,402,
171,410,374,177,470,100,475,127,244,123,361,513,281,387,185,510,173,319,
180,414,108,446,389,126,480,299,314,308,413,132,437,515,174,252,454,487,
443,330,190,265,517,289,261,412,479,462,481,309,105,497,382,370,335,247)]
],[2,524160,0,"2",[[56,3],[63,1],[72,4]],1,"L2,64#520.2",
["L",[2,64],1],
[(1,290,240,17,291,124,157,230,304)(2,503,421,417,178,458,182,68,335)
(3,127,377,517,396,184,152,241,36)(4,501,83,317,386,323,185,404,242)
(5,143,331,236,30,208,130,450,518)(6,447,195,164,453,243,55,470,75)
(7,238,72,392,103,395,170,486,171)(8,436,139,511,239,43,176,90,429)
(9,21,348,114,202,364,148,166,494)(10,196,11,284,280,233,147,300,177)
(12,289,313,303,305,169,141,311,16)(13,190,285,294,15,278,179,118,123)
(14,125,219,301,295,306,183,267,288)(18,356,204,363,188,376,175,45,472)
(19,91,158,261,381,59,129,266,467)(20,174,430,95,64,500,173,379,211)
(22,369,38,461,463,465,149,352,138)(23,229,320,161,512,394,50,425,474)
(24,54,452,479,316,220,142,189,413)(25,274,418,466,79,360,180,134,468)
(26,225,349,34,255,428,136,82,382)(27,151,361,424,44,485,145,218,325)
(28,77,355,433,140,265,146,52,84)(29,198,226,269,122,160,110,514,51)
(31,222,358,209,359,446,144,388,493)(32,339,155,314,454,69,167,235,362)
(33,455,46,276,268,315,131,74,154)(35,423,337,108,496,247,153,192,109)
(37,502,419,492,390,150,186,210,70)(39,371,504,410,475,237,168,445,227)
(40,478,393,165,489,484,49,318,397)(41,482,508,92,263,172,181,105,66)
(42,58,438,253,507,510,128,156,464)(47,456,187,483,439,48,137,398,505)
(53,457,262,258,412,99,94,490,341)(56,378,67,408,477,85,159,480,117)
(57,340,256,132,333,115,62,499,422)(60,387,384,71,406,487,162,420,330)
(61,119,326,65,98,460,163,246,201)(73,351,451,279,462,374,100,400,213)
(76,345,116,389,200,370,259,488,245)(78,257,343,399,107,427,215,354,324)
(80,338,207,365,448,344,264,375,471)(81,513,402,260,332,497,133,506,342)
(86,223,368,449,102,194,275,444,495)(87,403,459,469,199,244,193,346,93)
(88,96,416,520,426,519,252,272,431)(89,299,307,231,251,309,234,126,296)
(97,273,516,432,104,385,250,411,409)(101,206,334,443,277,509,271,111,228)
(112,297,308,254,283,286,113,298,302)(120,434,473,203,350,270,248,224,135)
(121,515,321,476,197,353,249,217,347)(191,367,415,481,440,442,328,327,391)
(212,232,281,310,287,312,293,282,292)(214,216,357,405,322,373,441,407,414)
(221,366,383,372,401,319,435,491,329),
(1,360,398)(2,343,440,181,86,346)(3,146,104,159,71,312)
(4,76,43,144,221,128)(5,470,227,142,421,209)(6,268,284,182,425,239)
(7,462,345,187,310,435)(8,17,476,167,171,416)(9,375,170,163,260,29)
(10,374,366,139,120,411)(11,38,121,166,156,367)(12,196,330,178,202,395)
(13,319,231,184,385,197)(14,277,434,185,299,245)(15,492,57,143,238,177)
(16,110,412,164,28,371)(18,148,414,152,69,275)(19,465,328,151,115,509)
(20,124,193,150,265,228)(21,394,302,149,417,102)(22,220,363,155,208,484)
(23,376,457,154,393,295)(24,59,64,136,169,137)(25,500,117,153,390,40)
(26,373,432)(27,203,74,172,232,195)(30,377,405,190,413,81)
(31,147,419,180,58,514)(32,276,494,176,325,253)(33,145)(34,442,318,175,
347,477)(35,45,267,168,130,418)(36,293,489,165,350,127)(37,518,483,140,
356,384)(39,337,324,94,404,308)(41,493,279,131,258,491)(42,475,92,132,
423,335)(44,108,506,129,288,498)(46,296,402,141,426,338)(47,314,83,174,
422,445)(48,441,200,160,399,212)(49,98,467)(50,344,60)
(51,223,396,157,80,278)(52,459,244,173,249,321)(53,427,380,183,342,481)
(54,349,158,188,118,68)(55,271,100)(56,87,126,179,415,519)(61,235,446)
(62,307,297)(63,424,229)(65,135,482,138,372,512)(66,370,280,161,336,499)
(67,205,256,189,215,352)(70,502,454,162,420,461)(72,453,317,186,289,109)
(73,428,93,224,480,437)(75,122,507,218,456,369)(77,201,436,211,233,510)
(78,486,329,216,487,451)(79,315,252,222,243,327)(82,226,320,452,210,458)
(84,241,463,269,479,119)(85,354,198,382,133,230)(88,368,504,443,471,388)
(89,516,520,469,389,391)(90,444,101)(91,326,207,305,511,214)(95,431,478)
(96,217,306)(97,340,505)(99,283,194)(103,450,409,290,397,281)
(105,298,359,313,448,501)(106,400,254,292,250,107)(111,332,513,403,286,112)
(113,488,264,495,273,407)(114,309,387,464,334,355)(116,272,134,248,353,262)
(123,408)(125,381,466,386,503,341)(191,364,508,206,339,311)(192,460,351,219,
300,287)(199,263,410,234,485,242)(204,433,490,225,304,358)(213,323,473)
(236,247,255)(240,449,246,379,257,348)(251,266,270)(259,496,261,282,274,474)
(285,447,362)(291,429,401)(294,515,406)(301,438,455,468,333,303)
(316,392,472,378,439,517)(322,497)(331,383,365)(357,361,430)]],
[3,786240,0,"2",[[63,1],[72,1],[168,1],[216,1]],1,
"L2,64#520.3",["L",[2,64],1],
[(1,252,292,505,449,376,298,46,96,198,327,213,417,430,395)(2,236,210,442,
17,450,448,12,125,250,342,393,81,152,187)(3,263,334,385,469,398,131,
20,88,243,317,453,354,10,407)(4,245,128,176,323,464,422,45,76,55,
322,503,455,490,307)(5,267,340,39,520,425,380,8,130,273,197,117,246,
314,36)(6,259,328,280,355,192,237,31,92,269,320,282,231,489,359)
(7,41,71,116,260,141,481,62,105,133,9,272,337,486,225)
(11,60,149,366,439,362,121,268,126,79,274,318,517,33,420)
(13,426,511,445,49,14,487,397,78,223,332,410,114,119,234)
(15,216,498,173,483,204,70,219,108,193,316,281,392,300,83)
(16,518,360,462,509,167,478,348,115,215,344,159,164,189,472)
(18,406,73,261,120,57,295,186,112,52,330,47,370,90,264)
(19,352,165,34,405,123,251,319,111,279,333,91,67,331,221)
(21,200,421,356,209,180,169,303,109,182,293,375,381,361,502)
(22,389,56,508,27,214,286,99,85,270,97,254,134,266,53)
(23,38,431,233,383,438,313,207,80,113,253,161,206,285,311)
(24,162,371,132,240,336,196,411,110,258,37,384,190,235,516)
(25,288,440,492,174,401,89,238,103,275,153,388,432,63,357)
(26,416,171,484,145,146,224,394,84,276,343,423,299,499,137)
(28,306,228,184,437,466,382,409,124,248,194,495,436,379,451)
(29,181,480,69,66,519,144,400,107,242,339,87,106,265,329)
(30,369,471,500,412,364,367,129,100,170,325,365,514,166,64)
(32,301,310,515,297,178,358,391,75,256,220,226,443,218,284)
(35,143,283,473,413,501,59,172,86,262,335,150,459,404,95)
(40,138,479,296,201,287,427,408,93,247,289,497,195,156,199)
(42,387,493,72,373,217,127,185,77,249,341,118,148,68,183)
(43,463,353,222,504,434,202,351,102,157,324,510,304,458,374)
(44,345,396,82,244)(48,461,158,386,232,474,435,136,122,257,294,452,476,
230,347)(50,482,512,154,58,441,467,188,135,278,175,402,98,241,321)
(51,414,475,346,160,460,457,211,101,271,315,446,140,290,513)
(54,488,403,104,255,338,139,399,74,239,61,465,444,494,305)
(65,208,456,308,163,415,491,177,94,277,326,468,203,470,428)
(142,227,496,349,507,205,506,291,363,447,350,302,390,168,477)
(147,368,419,454,229)(151,429,433,424,309,312,179,485,191,378,372,377,418,
155,212),(1,453,350,61,54,38,203,458,357)(2,98,510,336,88,204,
285,323,142)(3,492,506,321,298,240,469,243,356)(4,518,214,210,379,158,
164,43,275)(5,220,119,103,140,320,53,124,355)(6,64,312,272,215,430,
455,184,353)(7,147,49,293,437,452,426,208,192)(8,268,341,339,397,114,
396,395,126)(9,475,479,317,446,418,106,364,70)(10,493,157,440,461,193,
499,488,154)(11,17,500,435,84,447,448,294,244)(12,319,407,219,225,300,
185,129,359)(13,373,75,246,456,161,104,477,354)(14,223,388,372,176,415,
495,385,347)(15,135,44,442,289,449,460,443,91)(16,145,444,433,457,109,
30,25,314)(18,514,428,190,85,454,102,340,301)(19,376,327,94,463,206,
265,497,130)(20,45,87,188,409,270,351,46,370)(21,110,478,182,329,310,
508,231,352)(22,235,181,150,156,93,178,252,216)(23,267,209,166,308,174,
51,427,369)(24,470,250,162,227,445,283,163,345)(26,144,505,414,228,450,
200,152,241)(27,108,92,229,68,343,139,422,304)(28,337,417,256,81,122,
386,97,325)(29,360,65,121,239,309,334,34,349)(31,371,408,402,367,36,
307,286,362)(32,143,194,361,67,148,306,78,82)(33,59,146,101,47,424,
324,519,226)(35,462,451,251,66,205,56,276,168)(37,277,262,365,69,296,
107,496,257)(39,50,271,501,287,383,259,199,290)(40,375,416,224,464,249,
171,466,366)(41,196,413,471,165,284,297,509,368)(42,465,221,118,412,180,
332,378,358)(48,502,112,305,282,120,291,438,274)(52,441,151,387,191,189,
513,183,232)(55,377,279,484,248,116,202,494,338)(57,344,346,72,459,382,
468,86,269)(58,374,281)(60,76,230,490,175,138,198,511,363)
(62,394,391,133,303,405,197,404,348)(63,476,128,507,83,295,201,331,73)
(71,136,398,411,172,207,105,211,186)(74,512,132,170,491,326,473,487,236)
(77,489,384,153,480,313,117,390,431)(79,420,234,141,504,173,436,485,96)
(80,333,401,187,254,393,399,99,406)(89,439,472,292,503,419,432,278,516)
(90,517,169,335,111,421,392,330,212)(95,280,260,315,434,127,381,247,273)
(100,159,423,342,242,474,389,233,483)(113,255,515,322,222,266,299,160,264)
(115,131,123,316,328,253,482,195,486)(125,149,218,318,137,179,520,237,311)
(134,263,155)(167,498,258,302,481,288,213,425,429)(177,400,403,410,238,245,
217,261,380)]],
[4,1572480,0,"2",[[63,1],[72,1],[168,1],[216,1]],1,
"L2,64#520.4",["L",[2,64],1],
[(1,172,43,252,100,407,16,311,372,420,229,499,191,516,78,261,6,351)
(2,399,44,369,349,426,412,340,276,266,449,141,233,377,206,180,128,394)
(3,319,39,508,317,450,158,148,150,480,293,388,75,341,24,421,98,406)
(4,211,41,414,489,125,380,23,490,445,162,74,207,26,237,101,105,31)
(5,398,42,441,221,518,318,347,103,225,72,511,223,116,136,13,93,187)
(7,133,45,22,302,216,200,83,411)(8,12,40,96,405,60,363,513,357,
166,458,241,199,215,230,378,113,80)(9,410,28,295,167,487,476,481,471,
314,468,430,153,364,198,459,111,286)(10,358,469,214,467,427,249,131,339)
(11,203,464,431,344,79,348,53,287,90,370,57,228,343,183,256,134,401)
(14,328,312,384,432,336,512,502,365,192,334,462,226,106,270,55,124,254)
(15,255,222,301,297,383,132,395,35,189,142,306,227,368,350,239,84,404)
(17,385,269,143,446,179,323,264,479,514,281,171,220,423,477,274,107,397)
(18,473,313,389,121,186,59,329,224,331,279,474,73,307,47,470,97,245)
(19,77,403,38,117,99,71,64,452,181,330,440,235,517,501,210,110,393)
(20,51,437,288,92,238,32,137,305,387,483,515,209,154,433,156,122,129)
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(40,440,414,310,250,456)(42,348,131,96,181,406)(46,290,178,228,474,112,
513,249,334,127,65,136,142,409,306,330,78,436)(47,455,82,259,379,280)
(48,193,292,447,329,229,169,469,466,308,168,518,322,133,284,340,159,173)
(58,411,268,231,445,253,364,503,358,62,114,86,90,314,317,425,187,158)
(60,505,177,183,157,215,460,341,338,150,470,103,129,270,296,218,182,137)
(69,117,234,301,475,219,167,248,519,242,138,318,395,487,305,281,370,99)
(76,464,326,493,192,377,407,123,194,495,287,361,467,428,186,146,100,418)
(79,210,87,498,400,345)(85,285,499,153,387,224,227,176,510,94,251,351,
217,357,195,320,189,446)(89,450,271,286,160,184)(93,303,430,206,135,404)
(111,170,288,200,256,274,465,375,316,501,240,126,382,371,412,512,324,482)
(122,261,258)(185,252,500)]],
[8,Factorial(520)/2,1,"2",[[519,1]],518,"A_n",["A",520,1],520],
[9,Factorial(520),0,"2",[[519,1]],520,"S_n",["A",520,1],520]];
PRIMGRP[521]:=
[[1,Factorial(521)/2,1,"2",[[520,1]],519,"A_n",["A",521,1],521],
[2,Factorial(521),0,"2",[[520,1]],521,"S_n",["A",521,1],521]];
PRIMGRP[522]:=
[[1,70710120,1,"2",[[521,1]],2,"L2,521 on projective points.1",
["L",[2,521],1],
[(3,521,519,517,515,513,511,509,507,505,503,501,499,497,495,493,491,489,487,
485,483,481,479,477,475,473,471,469,467,465,463,461,459,457,455,453,451,
449,447,445,443,441,439,437,435,433,431,429,427,425,423,421,419,417,415,
413,411,409,407,405,403,401,399,397,395,393,391,389,387,385,383,381,379,
377,375,373,371,369,367,365,363,361,359,357,355,353,351,349,347,345,343,
341,339,337,335,333,331,329,327,325,323,321,319,317,315,313,311,309,307,
305,303,301,299,297,295,293,291,289,287,285,283,281,279,277,275,273,271,
269,267,265,263,261,259,257,255,253,251,249,247,245,243,241,239,237,235,
233,231,229,227,225,223,221,219,217,215,213,211,209,207,205,203,201,199,
197,195,193,191,189,187,185,183,181,179,177,175,173,171,169,167,165,163,
161,159,157,155,153,151,149,147,145,143,141,139,137,135,133,131,129,127,
125,123,121,119,117,115,113,111,109,107,105,103,101,99,97,95,93,91,
89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,
53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,
17,15,13,11,9,7,5)(4,522,520,518,516,514,512,510,508,506,504,
502,500,498,496,494,492,490,488,486,484,482,480,478,476,474,472,470,468,
466,464,462,460,458,456,454,452,450,448,446,444,442,440,438,436,434,432,
430,428,426,424,422,420,418,416,414,412,410,408,406,404,402,400,398,396,
394,392,390,388,386,384,382,380,378,376,374,372,370,368,366,364,362,360,
358,356,354,352,350,348,346,344,342,340,338,336,334,332,330,328,326,324,
322,320,318,316,314,312,310,308,306,304,302,300,298,296,294,292,290,288,
286,284,282,280,278,276,274,272,270,268,266,264,262,260,258,256,254,252,
250,248,246,244,242,240,238,236,234,232,230,228,226,224,222,220,218,216,
214,212,210,208,206,204,202,200,198,196,194,192,190,188,186,184,182,180,
178,176,174,172,170,168,166,164,162,160,158,156,154,152,150,148,146,144,
142,140,138,136,134,132,130,128,126,124,122,120,118,116,114,112,110,108,
106,104,102,100,98,96,94,92,90,88,86,84,82,80,78,76,74,72,
70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,
34,32,30,28,26,24,22,20,18,16,14,12,10,8,6),
(1,2,263)(3,465,61)(4,147,378)(5,413,111)(6,136,387)(7,122,400)
(8,22,499)(9,314,206)(10,55,464)(11,281,237)(12,33,484)
(13,414,102)(14,349,166)(15,167,347)(16,435,78)(17,242,270)
(18,185,326)(19,316,194)(20,53,456)(21,123,385)(23,267,239)
(24,374,131)(25,361,143)(26,215,288)(27,504,518)(28,386,115)
(29,425,75)(30,418,81)(31,442,56)(32,201,296)(34,457,38)
(35,409,85)(36,154,339)(37,406,86)(39,207,283)(40,90,399)
(41,153,335)(42,493,514)(43,183,303)(44,157,328)(45,178,306)
(46,384,99)(47,312,170)(48,151,330)(49,104,376)(50,222,257)
(51,274,204)(52,236,241)(54,350,125)(57,248,224)(58,162,309)
(59,254,216)(60,264,205)(62,471,516)(63,336,130)(64,371,94)
(65,295,169)(66,145,318)(67,313,149)(68,128,333)(69,492,488)
(70,473,506)(71,226,232)(72,229,228)(73,180,276)(74,367,88)
(76,218,235)(77,121,331)(79,340,110)(80,362,87)(82,301,146)
(83,197,249)(84,495,470)(89,175,265)(91,510,448)(92,114,323)
(93,202,234)(95,260,174)(96,244,189)(97,133,299)(98,160,271)
(100,124,305)(101,497,451)(103,317,109)(105,280,144)(106,137,286)
(107,171,251)(108,496,445)(112,513,424)(113,521,415)(116,134,279)
(117,491,441)(118,253,158)(119,211,199)(120,489,440)(126,404,519)
(127,436,486)(129,132,268)(135,233,161)(138,219,172)(139,390,520)
(140,498,411)(141,403,505)(142,480,427)(148,379,522)(150,422,477)
(152,502,395)(155,462,432)(156,181,192)(159,452,438)(163,182,184)
(164,446,439)(165,501,383)(168,188,173)(176,472,401)(177,512,360)
(179,359,511)(186,447,416)(187,372,490)(190,463,396)(191,373,485)
(193,398,458)(195,405,449)(196,375,478)(198,369,482)(200,341,508)
(203,412,434)(208,381,460)(209,423,417)(210,507,332)(212,517,320)
(213,459,377)(214,479,356)(217,364,468)(220,348,481)(221,402,426)
(223,343,483)(225,444,380)(227,393,429)(230,325,494)(231,461,357)
(238,311,500)(240,389,420)(243,319,487)(245,515,289)(246,421,382)
(247,392,410)(250,346,453)(252,475,322)(255,366,428)(256,284,509)
(258,394,397)(259,503,287)(261,351,437)(262,466,321)(266,431,352)
(269,304,476)(272,467,310)(273,408,368)(275,355,419)(277,329,443)
(278,469,302)(282,430,337)(285,290,474)(291,308,450)(292,324,433)
(293,391,365)(294,300,455)(297,454,298)(307,388,354)(315,407,327)
(334,345,370)(338,358,353)(342,344,363)]],
[2,141420240,0,"2",[[521,1]],3,"L2,521 on projective points.2",
["L",[2,521],1],
[(1,180,207,309,343,184,347,261,313,353,86,455,92,479,418,102,74,35,153,
494,171,272,41,333,93,46,201,327,450,397,363,150,380,205,318,415,14,
503,170,147,47,406,222,465,460,478,396,209,38,160,13,299,161,27,271,
53,127,323,338,334,135,45,178,495,188)(2,141,354,151,284,194,515,511,
6,202,276,58,302,168,30,316,169,291,120,453,371,389,384,107,443,282,
182,159,346,315,434,11,124,469,179,486,452,399,522,128,283,236,516,288,
57,158,355,176,294,255,227,431,370,237,394,243,496,16,68,502,145,506,
20,122,149)(3,186,37,324,22,407,444,233,56,118,468,457,420,262,374,
267,25,395,489,101,325,504,235,247,250,167,174,198,379,445,73,148,18,
75,467,117,356,409,208,448,113,441,314,306,361,305,91,95,285,278,69,
463,78,320,90,71,417,348,126,48,217,388,142,221,132)(4,228,360,454,
304,62,475,67,429,392,381,211,273,96,405,442,307,5,292,143,326,197,
108,187,461,112,281,203,501,432,258,239,9,251,386,260,51,44,234,238,
24,488,23,15,408,216,401,121,440,493,212,382,254,311,181,256,404,470,
131,155,162,79,82,94,345)(7,111,144,439,219,373,509,195,100,447,136,
514,137,31,480,183,81,437,59,252,28,498,483,54,85,293,87,154,240,
241,436,422,157,114,165,414,39,129,393,26,140,213,372,430,428,449,105,
245,362,133,130,12,337,474,438,364,109,481,266,424,484,332,29,492,416)
(8,458,319,246,226,177,308,349,377,138,125,459,34,385,341,33,259,521,
331,119,519,507,115,376,55,139,462,352,482,329,383,403,17,231,336,510,
60,279,19,426,471,61,263,286,277,42,451,99,297,491,490,344,223,156,
65,280,163,123,499,289,104,265,249,232,76)(10,391,321,253,97,80,64,
225,40,350,206,166,49,264,173,106,505,359,358,32,230,398,287,52,43,
66,268,378,423,310,50,269,339,513,98,312,446,466,520,367,497,387,190,
274,473,214,342,330,210,518,328,70,296,508,464,295,390,204,191,472,500,
21,152,103,83)(36,244,275,366,351,301,77,270,412,248,146,369,298,192,
335,193,402,229,134,340,476,110,410,185,218,322,433,357,300,517,365,425,
63,368,220,485,411,375,512,317,199,196,487,84,224,400,421,419,477,116,
189,303,456,200,290,435,164,215,172,427,413,88,89,175,242),
(1,383,373,232,11,75,90,120,242,399,140,149,316,508,144,4,99,299,89,
284,315,452,146,464,257,460,363,145,387,494,297,427,158,322,392,308,147,
8,20,62,474,344,13,67,275,95,352,227,369,389,396,117,465,266,511,
240,84,65,263,125,47,96,18,400,78,59,423,152,397,198,26,267,274,
294,436,311,48,388,76,130,319,189,81,123,135,516,355,271,341,505,236,
366,169,276,518,300,203,406,199,517,211,348,379,54,364,44,139,519,155,
347,514,3,264,421,23,53,68,132,431,290,280,2,106,141,409,244,317,
438,349,360,288,50,215,374,237,154,45,338,521,501,377,126,269,101,446,
381,238,234,470,328,63,487,420,5,367,161,7,339,32,333,119,463,252,
226,121,265,323,486,480,157,293,159,167,113,418,235,228,205,285,156,482,
218,190,124,60,29,439,467,503,402,61,208,456,251,163,444,386,258,66,
326,249,357,332,253,221,471,320,278,273,350,69,39,216,43,195,182,493,
476,433,310,150,376,416,466,49,260,434,395,79,255,15,131,14,175,164,
248,450,515,97,356,21,351,9,342,283,451,231,185,58,462,186,475,105,
109,33,174,305,361,56,329,345,336,112,204,71,210,194,354,88,86,304,
422,510,171,25,191,220,133,483,401,178,490,495,206,165,92,143,184,6,
441,372,223,292,298,16,250,214,497,91,368,36,256,281,233,424,362,384,
417,484,259,27,209,28,41,491,70,202,35,272,151,40,270,393,103,512,
391,108,461,73,172,102,115,454,116,404,179,246,279,301,239,430,382,407,
107,295,52,166,449,413,127,365,371,440,291,222,137,479,520,51,498,457,
168,173,485,262,180,10,443,472,118,492,153,241,359,57,55,309,469,453,
72,459,31,327,318,334,87,302,358,489,110,34,38,188,477,201,85,478,
432,212,380,321,134,312,122,307,46,148,213,415,499,488,129,12,128,408,
64,268,229,403,94,197,247,287,513,353,230,187,170,481,468,100,447,104,
74,313,390,385,343,192,442,410,331,306,414,337,77,405,277,219,500,412,
207,455,82,261,160,196,224,114,83,19,473,445,181,507,378,458,435,428,
245,30,496,504,370,506,183,177,340,398,22,437,411,200,24,330,111,324,
136,502,296,138,243,176,80,335,193,429,425,282,217,42,394,17,286,162,
142,325,98,509,426,289,448,93,375,303,314,225,346,419,254,522,37)]],
[3,Factorial(522)/2,1,"2",[[521,1]],520,"A_n",["A",522,1],522],
[4,Factorial(522),0,"2",[[521,1]],522,"S_n",["A",522,1],522]];
PRIMGRP[523]:=
[[1,Factorial(523)/2,1,"2",[[522,1]],521,"A_n",["A",523,1],523],
[2,Factorial(523),0,"2",[[522,1]],523,"S_n",["A",523,1],523]];
PRIMGRP[524]:=
[[1,71527572,1,"2",[[523,1]],2,"L2,523 on projective points.1",
["L",[2,523],1],
[(3,523,521,519,517,515,513,511,509,507,505,503,501,499,497,495,493,491,489,
487,485,483,481,479,477,475,473,471,469,467,465,463,461,459,457,455,453,
451,449,447,445,443,441,439,437,435,433,431,429,427,425,423,421,419,417,
415,413,411,409,407,405,403,401,399,397,395,393,391,389,387,385,383,381,
379,377,375,373,371,369,367,365,363,361,359,357,355,353,351,349,347,345,
343,341,339,337,335,333,331,329,327,325,323,321,319,317,315,313,311,309,
307,305,303,301,299,297,295,293,291,289,287,285,283,281,279,277,275,273,
271,269,267,265,263,261,259,257,255,253,251,249,247,245,243,241,239,237,
235,233,231,229,227,225,223,221,219,217,215,213,211,209,207,205,203,201,
199,197,195,193,191,189,187,185,183,181,179,177,175,173,171,169,167,165,
163,161,159,157,155,153,151,149,147,145,143,141,139,137,135,133,131,129,
127,125,123,121,119,117,115,113,111,109,107,105,103,101,99,97,95,93,
91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,
55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,
19,17,15,13,11,9,7,5)(4,524,522,520,518,516,514,512,510,508,
506,504,502,500,498,496,494,492,490,488,486,484,482,480,478,476,474,472,
470,468,466,464,462,460,458,456,454,452,450,448,446,444,442,440,438,436,
434,432,430,428,426,424,422,420,418,416,414,412,410,408,406,404,402,400,
398,396,394,392,390,388,386,384,382,380,378,376,374,372,370,368,366,364,
362,360,358,356,354,352,350,348,346,344,342,340,338,336,334,332,330,328,
326,324,322,320,318,316,314,312,310,308,306,304,302,300,298,296,294,292,
290,288,286,284,282,280,278,276,274,272,270,268,266,264,262,260,258,256,
254,252,250,248,246,244,242,240,238,236,234,232,230,228,226,224,222,220,
218,216,214,212,210,208,206,204,202,200,198,196,194,192,190,188,186,184,
182,180,178,176,174,172,170,168,166,164,162,160,158,156,154,152,150,148,
146,144,142,140,138,136,134,132,130,128,126,124,122,120,118,116,114,112,
110,108,106,104,102,100,98,96,94,92,90,88,86,84,82,80,78,76,
74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,
38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6),
(1,2,264)(3,263,265)(4,489,38)(5,215,311)(6,192,333)(7,366,158)
(8,219,304)(9,231,291)(10,399,122)(11,454,66)(12,475,44)
(13,100,418)(14,435,82)(15,40,476)(16,299,216)(17,172,342)
(18,402,111)(19,119,393)(20,424,87)(21,350,160)(22,345,164)
(23,60,448)(24,127,380)(25,372,134)(26,184,321)(27,425,79)
(28,247,256)(29,437,65)(30,405,96)(31,114,386)(32,124,375)
(33,357,141)(34,81,416)(35,284,212)(36,218,277)(37,266,228)
(39,524,490)(41,255,235)(42,115,374)(43,236,252)(45,201,285)
(46,85,400)(47,88,396)(48,365,118)(49,283,199)(50,194,287)
(51,137,343)(52,488,513)(53,516,484)(54,361,116)(55,198,278)
(56,120,355)(57,248,226)(58,239,234)(59,332,140)(61,155,315)
(62,303,166)(63,318,150)(64,359,108)(67,145,319)(68,175,288)
(69,360,102)(70,203,258)(71,170,290)(72,369,90)(73,282,176)
(74,517,462)(75,214,242)(76,322,133)(77,83,371)(78,354,99)
(80,468,505)(84,268,179)(86,257,188)(89,337,105)(91,499,463)
(92,144,295)(93,514,446)(94,301,136)(95,298,138)(97,202,232)
(98,222,211)(101,279,151)(103,501,449)(104,508,441)(106,220,205)
(107,259,165)(109,117,305)(110,428,515)(112,447,494)(113,275,143)
(121,189,221)(123,498,432)(125,152,254)(126,510,417)(128,443,482)
(129,518,406)(130,193,208)(131,261,139)(132,440,481)(135,409,509)
(142,414,497)(146,204,181)(147,197,187)(148,401,504)(149,182,200)
(153,404,496)(154,413,486)(156,503,394)(157,445,451)(159,456,438)
(161,180,190)(162,521,370)(163,480,410)(167,474,412)(168,459,426)
(169,464,420)(171,495,387)(173,408,472)(174,450,429)(178,507,368)
(183,506,364)(185,391,477)(186,356,511)(191,439,423)(195,336,522)
(196,469,388)(206,452,395)(207,344,502)(209,383,461)(210,465,378)
(213,373,467)(217,313,523)(223,411,419)(224,309,520)(225,466,362)
(227,434,392)(229,512,312)(230,433,390)(233,384,436)(237,297,519)
(238,358,457)(240,353,460)(241,334,478)(243,327,483)(244,493,316)
(245,479,329)(246,455,352)(249,427,377)(250,330,473)(251,310,492)
(253,415,385)(260,444,349)(262,491,300)(267,397,389)(269,421,363)
(270,325,458)(271,442,340)(272,281,500)(273,487,293)(274,376,403)
(276,292,485)(280,471,302)(286,314,453)(289,470,294)(296,326,431)
(306,430,317)(307,339,407)(308,422,323)(320,335,398)(324,382,347)
(328,346,379)(331,381,341)(338,348,367)]],
[2,143055144,0,"2",[[523,1]],3,"L2,523 on projective points.2",
["L",[2,523],1],
[(1,122,59,356,262,507,411,479,497,142,302,196,27,344,246,198,201,503,462,
123,470,461,76,174,271,60,114,43,311,150,243,433,14,8,284,168,375,
185,296,484,229,341,440,333,255,99,9,343,483,203,219,305,106,227,251,
454,107,214,172,183,481,448,187,206,412,378,487,190,400,475,155,208,120,
147,17,82,58,116,270,422,193,133,438,97,191,98,328,519,415,79,24,
515,62,140,358,200,349,437,402,417,63,298,231,372,421,480,489,346,493,
252,281,89,498,451,318,159,103,374,317,506,322,468,128,501,508,396,350,
242,119,144,414,179,463,384,397,225,308,105,391,392,15,408,313,85,127,
228,64,264,238,353,222,303,245,156,20,517,332,6,49,364,472,388,511,
188,177,312,450,373,469,474,70,366,326,66)(2,44,306,266,40,158,163,
259,182,320,455,444,121,244,160,268,61,104,300,115,90,476,387,329,410,
279,394,368,46,404,505,25,319,224,95,240,241,5,324,407,235,248,169,
453,218,488,513,390,282,236,124,131,504,164,310,126,315,258,7,473,314,
181,134,21,351,380,139,286,143,152,211,260,401,334,47,215,230,195,283,
432,274,492,48,117,86,31,217,113,304,12,441,13,194,499,439,210,362,
516,52,28,93,485,512,424,477,157,232,442,145,254,220,426,445,184,151,
449,460,418,3,178,381,405,4,327,413,429,149,289,101,11,377,299,192,
291,403,148,336,447,257,464,348,102,96,199,389,482,321,67,518,50,361,
458,34,171,162,509,170,129,431,434,386,288,83,436,330,490,135,153,221,
125,370,276,51,510)(10,382,189,359,53,109,130,261,430,465,295,77,249,
275,379,166,409,486,212,216,290,23,471,297,294,452,35,423,467,36,395,
32,55,78,237,74,165,209,75,180,338,335,161,87,342,416,420,146,223,
466,253,357,383,33,337,167,202,371,502,523,57,273,443,250,100,301,309,
94,367,91,176,213,425,239,521,88,175,354,385,68,292,520,137,478,360,
398,307,491,39,280,204,267,72,524,138,69,277,496,56,29,369,269,197,
522,30,173,18,293,256,233,205,186,406,37,84,118,132,45,345,316,287,
65,500,514,26,73,226,446,427,399,376,339,92,459,80,110,435,363,263,
81,54,136,355,41,494,108,38,365,428,352,71,141,325,234,272,154,495,
112,340,42,247,278,457,22,111,393,207,419,456,19,265,16,323,331),
(1,457,22,138,165,442,193,452,420,98,91,418,275,421,205,333,103,21,395,
171,347,308,167,42,401,524,248,249,450,389,469,315,371,461,204,449,228,
198,290,28,26,488,419,307,89,112,40,362,128,271,155,276,378,330,519,
317,332,279,97,443,134,160,432,66,180,405,244,322,175,118,441,15,9,
456,358,225,494,202,502,409,254,406,132,283,76,153,465,201,289,386,207,
370,266,369,487,380,346,269,504,169,314,220,56,161,168,397,351,104,496,
226,3,120,166,44,4,521,334,117,93,497,284,140,382,268,162,234,505,
87,194,247,281,459,216,331,251,501,63,238,65,407,448,481,438,253,515,
92,110,186,367,27,295,433,164,25,363,125,172,306,479,181,263,57,60,
51,116,43,184,417,83,402,100,294,353,250,130,190,261,50,262,426,221,
270,287,325,518,33,69,252,115,94,30,233,61,187,516,24,338,462,377,
144,291,293,241,88,368,476,463,227,327,336,108,239,47,31,229,286,200,
126,321,451,203,177,278,348,345,149,210,303,232,411,473,185,16,80,277,
388,396,435,489,17,255,106,445,219,191,102,385,460,349,82,464,422,387,
96,357,424,324,258,400,154,8)(2,231,85,361,503,437,337,404,143,374,
339,297,157,412,301,376,137,48,20,316,133,506,222,272,326,365,373,484,
159,223,54,288,350,7,458,29,90,416,413,483,62,36,310,440,113,39,
475,10,208,192,522,131,425,434,12,298,285,393,151,520,468,470,95,384,
299,423,215,245,52,178,6,209,145,124,509,170,206,243,436,474,491,18,
335,499,189,500,49,109,511,408,467,139,359,156,344,55,196,123,188,179,
182,498,58,282,455,67,114,398,214,75,328,466,212,394,53,129,147,246,
508,323,280,313,354,174,523,176,260,510,430,23,302,480,514,45,152,256,
5,77,493,379,99,477,264,146,122,427,240,235,195,73,119,236,13,265,
135,410,364,71,78,183,19,447,70,257,492,415,381,274,392,495,391,32,
375,472,38,296,86,163,478,107,355,507,352,259,37,267,14,403,305,230,
224,320,121,64,439,517,356,59,173,329,79,105,318,142,482,429,444,242,
431,383,485,84,490,111,399,199,127,150,454,342,273,213,211,471,41,11,
312,35,300,390,446,292,372,311,512,513,237,360,197,72,453,414,68,366,
218,136,428,34,340,486,343,148,141,341,309,46,319,74,101,217,304)]],
[3,Factorial(524)/2,1,"2",[[523,1]],522,"A_n",["A",524,1],524],
[4,Factorial(524),0,"2",[[523,1]],524,"S_n",["A",524,1],524]];
PRIMGRP[525]:=
[[1,126000,1,"2",[[20,1],[48,3],[120,3]],1,"U3,5 on non-isotropic\
 projective points.1",["2A",[2,5],1],
[(2,18,3,23,4,8,5,13)(6,19,11,24,16,9,21,14)
(7,20,12,25,17,10,22,15)(26,32,27,37,28,42,29,47)
(30,33,35,38,40,43,45,48)(31,34,36,39,41,44,46,49)
(50,107,88,69)(51,111,90,77,53,119,92,85)(52,116,91,82,54,124,
89,74)(55,112,96,78,62,120,103,86)(56,113,97,79,63,121,104,87)
(57,114,98,80,64,122,105,72)(58,115,99,81,65,123,106,73)
(59,117,100,83,66,125,93,75)(60,109,101,71,67,108,94,70)
(61,118,102,84,68,110,95,76)(126,426,326,226)(127,432,327,236,128,439,
328,243)(129,433,333,237,137,440,341,244)(130,428,334,229,138,430,342,227)
(131,434,335,238,139,441,343,231)(132,435,336,239,140,442,344,232)
(133,436,337,240,141,443,329,233)(134,437,338,241,142,444,330,234)
(135,429,339,230,143,427,331,228)(136,438,340,242,144,431,332,235)
(145,445,345,245)(146,449,347,253,148,457,349,261)(147,454,348,258,149,462,
346,250)(150,450,353,254,157,458,360,262)(151,451,354,255,158,459,361,263)
(152,452,355,256,159,460,362,248)(153,453,356,257,160,461,363,249)
(154,455,357,259,161,463,350,251)(155,447,358,247,162,446,351,246)
(156,456,359,260,163,448,352,252)(164,470,365,275,166,480,367,285)
(165,475,366,280,167,485,364,270)(168,471,373,276,178,481,383,286)
(169,472,374,277,179,482,384,287)(170,465,375,266,180,467,385,264)
(171,473,376,278,181,483,386,268)(172,474,377,279,182,484,387,269)
(173,476,378,281,183,486,368,271)(174,477,379,282,184,487,369,272)
(175,466,380,267,185,464,370,265)(176,478,381,283,186,468,371,273)
(177,479,382,284,187,469,372,274)(188,488,388,288)(189,494,389,298,190,501,
390,305)(191,495,395,299,199,502,403,306)(192,490,396,291,200,492,404,289)
(193,496,397,300,201,503,405,293)(194,497,398,301,202,504,406,294)
(195,498,399,302,203,505,391,295)(196,499,400,303,204,506,392,296)
(197,491,401,292,205,489,393,290)(198,500,402,304,206,493,394,297)
(207,507,407,307)(208,513,408,317,209,520,409,324)(210,514,414,318,218,521,
422,325)(211,509,415,310,219,511,423,308)(212,515,416,319,220,522,424,312)
(213,516,417,320,221,523,425,313)(214,517,418,321,222,524,410,314)
(215,518,419,322,223,525,411,315)(216,510,420,311,224,508,412,309)
(217,519,421,323,225,512,413,316),
(1,26,354,149,2)(3,28,426,413,489)(4,29,299,310,126)
(5,27,470,400,365)(6,45,523,198,216)(7,47,398,444,111)
(8,48,195,290,341)(9,33,128,50,434)(10,49,451,254,462)
(11,42,262,23,40)(12,34,100,116,274)(13,44,371,220,81)
(14,37,228,495,200)(15,32,120,515,482)(16,31,328,337,314)
(17,35,418,227,231)(18,41,85,142,406)(19,30,219,182,181)
(20,38,55,368,304)(21,43,282,286,512)(22,46,155,460,356)
(24,39,493,469,58)(25,36,183,74,98)(51,315,382,476,409)
(52,361,80,117,147)(53,288,201,190,488)(54,485,309,425,364)
(56,256,396,298,75)(57,179,436,381,177)(59,415,127,90,302)
(60,524,124,186,463)(61,122,503,399,248)(62,65,330,448,241)
(63,94,68,215,520)(64,490,92,441,316)(66,281,472,130,273)
(67,457,287,82,222)(69,306,131,260,366)(70,322,499,173,492)
(71,357,313,229,145)(72,344,267,129,324)(73,197,379,519,395)
(76,458,432,336,78)(77,150,473,355,486)(79,513,420,289,249)
(83,261,296,487,433)(84,265,175,121,202)(86,367,91,307,453)
(87,166,188,285,118)(88,350,174,268,148)(89,480,115,447,407)
(93,384,134,204,258)(95,452,97,140,435)(96,187,516,294,404)
(99,278,374,373,334)(101,331,297,500,244)(102,156,235,347,217)
(103,233,474,478,184)(104,509,154,332,359)(105,255,196,437,468)
(106,391,497,224,271)(107,475,252,439,491)(108,295,284,303,408)
(109,345,329,412,146)(110,247,505,320,223)(112,393,211,483,191)
(113,123,239,139,450)(114,143,376,506,259)(119,372,152,369,360)
(125,411,427,185,232)(132,236,192,168,136)(133,210,392,514,428)
(135,169,424,464,502)(137,521,218,429,388)(138,477,340,394,339)
(141,419,264,417,446)(144,343,165,385,250)(151,321,362,403,467)
(153,277,349,193,325)(157,501,352,517,171)(158,160,351,348,245)
(159,410,346,375,401)(161,176,358,414,189)(162,206,363,240,342)
(163,300,353,272,214)(164,333,522,251,422)(167,213,319,327,257)
(170,317,430,461,311)(172,291,207,370,234)(178,479,455,301,293)
(180,389,405,266,445)(194,390,421,308,397)(199,456,205,481,387)
(203,335,442,431,279)(208,225,496,377,423)(209,326,221,454,484)
(212,230,275,318,253)(226,518,383,459,510)(237,402,242,386,443)
(238,416,508,270,246)(243,438,263,465,280)(269,494,504,449,378)
(276,338,466,507,498)(283,440,292,380,312)(305,511,525,323,471)]],
[2,252000,0,"2",[[20,1],[48,1],[96,1],[120,3]],1,
"U3,5 on non-isotropic projective points.2",["2A",[2,5],1],
[(1,416,471,171,88,17,30,190)(2,288,452,178,394,58,254,110)
(3,257,97,172,196,418,105,495)(4,136,11,180,256,179,284,380)
(5,203,423,174,450,432,441,243)(6,486,150,173,306,84,224,40)
(7,331,71,186,241,244,398,259)(8,399,236,165,37,277,472,443)
(9,458,512,177,430,27,367,484)(10,282,442,167,489,447,363,211)
(12,54,61,176,509,245,126,396)(13,95,139,184,74,93,192,419)
(14,216,213,164,338,506,73,328)(15,23,309,182,183,124,333,147)
(16,75,270,166,348,349,519,315)(18,146,119,187)(19,435,364,168,225,298,
238,76)(20,229,345,169,151,142,65,517)(21,525,405,170,377,316,321,264)
(22,496,336,181,133,521,454,453)(24,369,500,175,312,391,297,294)
(25,123,45,185,481,221,491,359)(26,220,487,96,402,308,524,106)
(28,346,465,144,248,39,301,477)(29,451,483,324,204,414,251,371)
(31,114,466,351,319,492,370,395)(32,253,480,455,116,379,219,513)
(33,232,482,278,141,205,411,317)(34,329,464,289,387,444,266,350)
(35,66,476,239,158,326,118,459)(36,138,479,390,217,280,149,235)
(38,406,467,188,424,109,352,51)(41,70,473,375,330,260,404,163)
(42,48,478,469,82,234,461,502)(43,503,485,113,511,140,327,279)
(44,154,475,523,274,72,322,296)(46,307,470,490,428,59,436,80)
(47,94,474,341)(49,514,468,64,299,155,189,407)(50,498,311,77)
(52,335,209,354,388,381,240,378)(53,355,198,412,445,152,262,313)
(55,376,303,401,488,222,143,501)(56,397,103,342,426,332,99,518)
(57,318,134,117,226,191,413,302)(60,98,386,372,107,104,438,121)
(62,156,431,102,145,267,273,100)(63,237,281,325,207,320,383,462)
(67,78,258,214,69,510,358,283)(68,276,449,268,507,290,223,343)
(79,403,85,129,269,300,111,120)(81,433,400,515,427,499,206,421)
(83,201,410,439,295,272,389,457)(86,446,92,125,137,374,91,347)
(87,365,522,162,382,130,227,132)(89,275,263,159,90,231,494,304)
(108,392,287,497,252,460,261,265)(112,215,230,249,508,195,425,242)
(115,286,334,135,429,361,128,353)(122,305,310,356,161,218,437,210)
(127,314,344,339,323,246,199,420)(131,456,208,160,463,194,415,393)
(148,360,385,255,505,516,504,153)(157,293,247,292,440,250,340,368)
(193,422,285,212,384,197,409,337)(200,408,493,233,520,366,362,434)
(202,417,373,271)(228,291,357,448),
(1,505,84,194,416,20,335,51,422,375,14,175,420,146,390,21,409,132,258,
443)(2,260,362,71,289,24,227,254,105,82,8,401,475,397,113,19,451,
328,275,341)(3,136,269,466,188,7,107,94,169,150,17,293,442,494,239,
13,63,366,361,455)(4,31,217,301,351,18,513,445,117,523,16,104,231,
207,28,15,266,320,312,469)(5,471,33,67,144,6,225,206,371,96,10,
434,496,463,324,22,162,305,515,171)(11,202,159,40,278,25,378,509,240,
64,23,321,121,428,490,12,347,178,140,221)(26,487,411,304,481,138,414,
393,190,265,413,224,161,330,421,122,112,209,412,62)(27,109,149,119,377,
402,249,386,75,50,238,331,299,222,210,181,242,298,164,100)
(29,338,461,103,256,68,79,148,89,359,276,345,431,501,52,396,268,32,
153,322)(30,415,88,285,241,419,267,168,295,418,255,325,81,425,440,488,
376,417,35,290)(34,46,352,327,151,183,429,506,482,449,208,56,114,137,
384,42,192,404,458,348)(36,134,474,59,196,97,154,516,115,235)
(37,247,524,78)(38,521,370,263,306,77,309,223,373,476,467,160,229,185,
253,244,80,350,57,167)(39,364,236,128,450,288,200,292,392,49,448,251,
186,74,333,357,141,237,323,205)(41,232,189,214,430,499,211,280,261,405,
69,484,272,433,498,329,91,483,106,135)(43,395,219,226,394,365,143,332,
129,203,340,193,460,519,464,319,187,264,277,457)(44,98,436,495,284,218,
116,454,444,491,139,511,92,195,313,246,262,86,85,111)(45,180,118,391,
133,108,172,201,179,342,380,283,389,99,95,372,446,382,326,525)
(47,426,502,427,489,152,468,228,358,520,406,400,65,296,234,473,336,337,
441,503)(48,83,177,477,124,318,300,307,145,131,317,381,191,110,287,54,
465,438,500,252)(53,439,493,399,233,512,315,270,102,344,170,522,142,147,
273,204,508,291,303,385)(55,158,198,126)(58,93,507,334,485,360,470,368,
367,314,346,123,257,163,87,101,310,398,176,173)(60,212,259,286,73,230,
387,157,156,250,486,76,281,155,66,61,462,165,311,447)(70,383,294,279,
517,282,127,130,356,197,199,480,184,388,349,220,472,510,248,343)
(72,456,452,410,355,379,120,423,479,216,518,408,514,437,492,407,182,363,
245,424)(90,459,478,302)(125,353,243,271)(166,369,432,504)
(174,215,316,435,497,354,297,453,274,374)(213,403,308,339)]],
[3,378000,0,"2",[[20,1],[120,3],[144,1]],1,
"U3,5 on non-isotropic projective points.3",["2A",[2,5],1],
[(1,109,340,82,483,364,461,223,464,426,420,266,482,15,239,388,471,247,315,
48,470,290,203,356)(2,6,360,116,458,438,169,394,317,361,112,279,283,
507,455,490,442,97,68,102,398,493,316,126)(3,485,98,8,132,473,217,
488,261,480,521,271,93,478,278,220,309,469,180,61,183,479,448,262)
(4,323,87,47,312,103,106,446,383,306,463,273,80,191,144,332,345,108,
363,107,195,517,344,304)(5,335,137,88,516,196,268,342,409,28,259,270,
318,252,375,155,45,218,462,12,219,386,234,200)(7,167,520,428,32,407,
53,303,156,381,72,269,357,115,324,189,256,333,403,242,451,99,495,216)
(9,425,190,402,337,525,418,166,44,406,13,286,435,387,171,233,139,206,
431,327,228,287,60,58)(10,56,212,204,298,339,197,70,343,254,54,267,
164,130,351,124,213,152,154,258,354,123,509,181)(11,77,289,274)
(14,452,240,511,350,120,250,249,231,21,145,284,424,209,221,353,119,138,
410,310,282,194,184,341)(16,297,27,158,86,66,226,368,399,127,176,275,
255,502,96,313,423,429,202,222,328,450,358,111)(17,432,55,346,114,149,
23,95,170,173,104,276,147,355,113,62,405,285,33,305,523,129,71,365)
(18,389,251,141,52,456,311,63,519,211,441,281,457,151,188,29,336,499,
494,199,371,326,163,314)(19,508,320,319,237,362,122,422,447,459,143,277,
504,400,416,291,182,288,69,172,85,238,437,489)(20,377,492,299,404,393,
81,25,201,162,330,264,293,433,443,79,500,34,265,133,26,64,376,512)
(22,40,24,248,417,491,382,39,497,230,214,272,370,280,390,105,150,513,
236,419,128,160,100,434)(30,454,178,246,295,378,59,76,245,90,207,301,
51,42,75,215,175,325,380,308,518,503,131,460)(31,384,359,118)
(35,193,472,338,385,379,465,415,510,65,474,352,117,498,477,505,347,110,
484,67,135,235,476,46)(36,522,401,445,396,373,414,348,121,244,37,436,
307,440,142,369,260,185,453,413,229,322,168,210)(38,227,146,243,165,367,
205,50,331,43,186,411,148,421,366,140,321,296,294,92,84,78,449,514)
(41,349,125,374,94,372,444,257,161,177,506,524,292,253,225,74,136,501,
187,159,208,392,49,101)(57,408,91,241)(73,515,486,395,174,427,467,134,
300,412,466,83,430,157,475,192,89,334,468,153,391,302,481,232)
(179,198,496,329)(224,263,397,439),
(1,480,41,461,411,288,95,63,421,276,362,330,420,160,242,7,410,252,205,
507,424,389,175,374)(2,21,459,155,171,83,40,335,401,285,284,447,117,
510,336,501,509,142,295,208,158,299,114,400)(3,327,520,399,223,503,452,
293,157,279,129,375,487,76,154,322,427,435,317,332,82,364,484,143)
(4,112,194,492,156,148,377,471,92,283,436,10,203,368,465,329,339,219,
104,123,274,324,134,315)(5,500,441,326,258,115,323,202,348,277,164,57,
35,106,376,469,153,396,524,85,458,137,231,292)(6,162,343,280,296,442,
239,505,187,267,49,226,340,138,141,161,345,165,14,28,217,359,429,518)
(8,272,56,260)(9,426,264,414,489,391,360,409,454,273,71,413,174,319,
37,418,86,20,406,408,234,460,224,425)(11,516,314,512,373,476,297,321,
301,275,257,70,430,124,221,395,259,64,448,495,116,431,78,55)
(12,381,481,17,62,144,109,136,249,286,378,473,271,228,404,61,216,446,
69,392,491,255,463,346)(13,77,107,72,287,102,167,347,33,268,215,318,
385,467,440,387,474,325,496,25,173,229,39,197)(15,211,300,59,320,170,
201,31,139,270,402,191,89,449,16,127,185,94,36,311,248,513,490,278)
(18,93,19,306,349,379,485,227,508,266,198,282,488,302,262,438,91,356,
238,199,428,65,511,207)(22,254,498,140,90,195,132,225,58,281,334,101,
73,184,515,43,122,125,183,298,47,81,193,152)(23,230,97,308,120,52,
145,434,222,269,514,363,135,397,80,291,455,338,380,468,204,186,251,44)
(24,361,393,444,405,450,432,451,237,265,111,163,220,188,192,243,371,483,
351,98,88,506,331,119)(26,382,472,365,466,177,210,30,394,146,206,456,
522,196,316,310,99,305,403,100,337,457,181,504)(27,497,307,218,182,344,
42,353,523,247,328,200,253,304,87,519,51,105,150,67,294,241,179,151)
(29,289,290,419,357,213,128,417,383,482,121,423,118,367,486,422,131,502,
233,416,521,517,172,407)(32,169,462,34,250,133,333,439,494,384,475,60,
74,84,246,369,470,209,437,149,130,54,166,398)(38,433,178,108)
(45,48,53,499,68,235,313,390,232,110,445,366,477,388,113,352,453,309,
355,263,212,261,168,176)(46,147,103,240,214,386,464,256,245,236,159,75,
342,358,50,66,372,478,493,350,189,341,180,443)(79,96,415,190)
(126,354,312,244)(303,370,479,525)]],
[4,756000,0,"2",[[20,1],[120,3],[144,1]],1,
"U3,5 on non-isotropic projective points.4",["2A",[2,5],1],
[(1,103,115,342,431,367,291,348,435,81,171,51,426,152,464,411,442,521,240,
48,438,256,142,494)(2,414,502,100,54,314,308,163,493,91,82,22,211,
400,522,266,263,145,50,344,281,351,392,203)(3,154,387,74,396,283,186,
321,131,508,113,210,62,496,98,461,350,228,423,245,466,41,339,303)
(4,309,58,140,42,120,269,415,68,375,188,500,93,207,30,149,72,279,
128,373,121,153,318,12)(5,357,191,363,372,157,412,390,460,254,278,285,
327,449,405,84,67,34,525,216,512,17,371,26)(6,267,151,295,208,174,
135,257,111,399,341,155,459,55,250,404,141,330,110,484,193,227,63,286)
(7,241,252,369,181,326,80,299,519,453,490,101,162,197,132,352,108,310,
467,270,391,422,49,66)(8,445,15,429,305,505,97,432,397,45,221,428,
28,315,381,436,202,370,389,441,504,92,238,440)(9,46,77,242,319,236,
380,463,35,293,324,297,410,374,19,524,507,420,192,402,222,76,345,349)
(10,79,130,388,122,417,23,200,280,477,523,476,230,518,70,322,416,356,
306,165,354,177,273,214)(11,506,105,38,473,53,52,223,366,232,469,133,
272,119,179,301,43,196,156,159,180,365,492,106)(13,249,355,253,329,509,
338,20,172,184,150,244,361,44,233,189,212,289,382,516,292,60,474,472)
(14,468,340,311,488,96,514,127,481,125,144,166,112,346,501,88,325,259,
175,24,335,209,201,246)(16,116,433,264,78,75,434,465,248,195,443,331,
406,260,430,219,334,176,439,413,408,271,427,129)(18,64,409,173,425,294,
251,497,104,332,239,87,480,86,148,25,300,478,215,450,446,204,185,243)
(21,143,455,118)(27,169,32,393,403,383,479,376,424,137,147,114,454,225,
421,485,178,83,206,448,138,61,124,71)(29,261,520,353,337,386,268,458,
482,359,224,470,401,503,95,489,94,395,183,199,510,182,447,275)
(31,456,167,486,462,379,317,85,220,161,284,226,237,168,498,90,475,290,
288,274,59,190,418,312)(33,364,333,258)(36,362,487,499,102,368,213,277,
194,37,491,99,187,511,384,136,231,109,513,398,360,139,298,117)
(39,407,451,69,377,385,57,164,255,65,73,343,198,313,287,320,217,247,
419,160,336,471,146,40)(47,276,495,89,265,378,358,323,457,229,126,205,
123,262,234,296,328,134,218,107,302,452,316,515)(56,158,347,517)
(170,394,483,307)(235,282,304,444),
(1,365,149,491,4)(2,364,126,5,367)(3,366,489,407,147)
(6,381,81,393,519,10,374,262,339,105)(7,382,512,221,363,14,378,98,
456,441)(8,371,40,77,254,18,384,482,261,73)(9,377,406,293,65,22,
373,341,315,238)(11,379,58,120,224,15,386,231,196,454)(12,376,304,233,
119,19,369,314,66,192)(13,387,200,39,333,23,383,111,473,398)
(16,372,274,103,30,20,368,181,525,472)(17,380,434,362,284,24,370,356,
438,171)(21,375,462,276,321,25,385,216,169,297)(26,288,400,313,78,464,
307,343,299,249)(27,97,310,215,417,465,521,291,458,414)(28,68,413,347,
392,466,239,410,428,335)(29,285,354,144,252,467,175,440,141,79)
(31,138,182,92,100,476,130,278,511,524)(32,461,142,397,167,480,212,131,
330,267)(33,183,227,507,235,484,287,51,88,64)(34,469,337,205,471,468,
38,402,116,46)(35,318,515,452,62,477,294,99,217,241)(36,513,495,250,
159,481,101,504,82,154)(37,218,220,427,207,485,459,453,346,445)
(41,108,50,303,268,486,189,226,319,172)(42,419,290,475,348,470,424,309,
47,429)(43,247,444,277,135,474,71,360,173,143)(44,152,198,55,503,478,
161,114,234,506)(45,206,74,75,457,487,122,258,248,211)(48,499,460,163,
443,479,496,225,158,357)(49,240,286,112,322,483,59,179,204,300)
(52,280,447,251,421,228,170,209,72,418)(53,353,415,70,57,229,437,423,
246,242)(54,61,86,140,432,230,232,257,137,358)(56,162,332,214,501,237,
155,391,455,494)(60,334,520,197,279,243,404,94,124,186)(63,463,95,516,
399,244,222,523,102,340)(67,323,500,281,150,236,295,505,174,153)
(69,104,260,298,308,245,514,87,324,289)(76,166,121,416,265,255,266,199,
411,165)(80,110,129,320,430,259,194,132,306,349)(83,502,396,160,178,256,
497,342,157,282)(84,338,336,164,388,263,405,395,264,326)(85,518,355,213,
331,253,96,431,448,401)(89,345,117,201,361,508,426,195,115,433)
(90,296,190,517,420,509,312,109,93,412)(91,275,425,327,125,510,185,422,
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180,351,202,208)(113,403,139,451,311,191,344,134,210,292)(123,328,450,305,
133,193,390,223,317,136)(127,488,492,146,145)(128,148,409,408,490)
(168,271,273,301,219,272,184,177,325,449)(176,329,350,359,316,269,394,436,
435,302)]],
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(16,29,53,92,160)(18,33,54,94,24)(22,40,71,122,30)
(26,47,81,140,230)(28,51,89,155,231)(32,58,102,176,79)
(34,61,106,180,278)(36,46,80,138,226)(37,66,88,153,224)
(39,69,118,150,243)(41,73,126,57,100)(43,55,96,167,264)
(44,77,72,124,206)(48,83,144,233,332)(50,87,151,136,189)
(52,91,158,250,234)(59,103,110,185,284)(60,104,177,275,314)
(62,108,183,282,148)(64,111,187,286,383)(65,112,188,259,363)
(67,114,192,291,389)(68,116,194,225,115)(70,120,200,299,393)
(74,128,213,84,145)(76,132,173,273,377)(78,135,193,292,179)
(82,142,207,308,403)(86,149,241,344,438)(90,157,251,105,109)
(93,162,258,277,197)(95,165,260,365,143)(97,166,262,368,222)
(99,171,270,123,204)(101,174,236,336,428)(107,181,279,134,221)
(113,190,288,137,209)(117,195,293,268,170)(119,198,297,391,384)
(121,201,301,396,437)(125,208,309,210,311)(127,211,182,281,172)
(129,214,316,406,280)(131,217,319,356,447)(133,219,322,412,263)
(139,228,331,392,416)(141,232,305,202,164)(146,238,338,372,448)
(152,246,350,390,420)(154,247,351,203,303)(156,249,354,444,296)
(159,254,252,357,355)(161,256,248,353,445)(163,237,337,168,265)
(169,267,371,212,313)(175,255,361,450,333)(178,276,379,235,334)
(184,283,285,196,295)(186,266,242,345,440)(191,290,388,205,306)
(199,298,257,274,378)(215,317,407,483,339)(216,239,340,433,318)
(218,320,408,485,401)(220,324,415,484,335)(223,328,421,492,516)
(227,330,364,323,413)(229,329,422,493,369)(240,342,409,486,446)
(244,343,436,500,358)(245,348,423,346,441)(253,359,429,312,404)
(261,366,455,510,294)(269,373,461,431,452)(271,375,464,508,430)
(272,374,462,426,494)(287,385,370,458,476)(289,387,470,398,414)
(300,321,410,487,424)(302,397,411,352,443)(304,399,478,482,517)
(307,402,481,395,475)(310,360,451,507,439)(315,405,466,381,367)
(325,417,382,468,472)(326,418,490,520,512)(327,419,491,506,488)
(341,434,454,349,442)(347,386,469,459,477)(362,453,509,522,501)
(376,465,503,449,505)(380,460,513,463,425)(394,474,473,400,480)
(427,495,502,432,496)(435,498,467,456,511)(457,497,515,524,499)
(471,514,523,525,518)(479,489,519,504,521),
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(12,22,41,74,129,215,318)(14,26,48,84,146,130,216)(17,32,59,89,
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(25,46,80,139,229,114,193)(27,50,88,154,69,119,199)(29,54,95,166,
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(47,82,143,235,335,427,487)(49,86,150,244,347,417,58)(53,93,163,73,
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(63,110,186,273,361,428,180)(66,113,191,128,171,271,340)(71,123,205,307,
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(81,141,233,333,425,493,162)(83,144,236,313,165,261,367)(85,148,240,343,
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(94,164,259,364,454,422,379)(96,168,266,370,459,410,488)(98,170,269,374,
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(108,184,190,289,256,230,292)(118,197,194,208,310,251,356)(120,185,285,359,
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(157,252,358,449,500,445,365)(167,226,187,287,386,451,508)(177,204,305,401,
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(56,98,144,322,271,340,490,269,356,476,190,121)(58,459,425,169,467,129,
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(60,368,410,451,76,175)(61,391,466,218)(65,377,485,235,323,196,328,209,
394,321,222,230)(72,216,484,141,495,481,153,128,261,513,159,200)
(73,301,194,474,431,293,401,315,140,79,406,364)(74,404,428,134,133,361,
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(87,275,277,149)(88,273,152,385)(89,329,219,353,447,416)(95,135,259,375,
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327,165,359,136)(117,512,204,162,127,419,389,468,501,453,446,237)
(122,310,381,390,436,418,369,402,503,408,457,146)(123,166,472,392,338,181,
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(176,243,525,343,420,231)(195,398,314,456),
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(4,202,374,8,469,269,19,102,358,284,212,291,264,238)(5,442,174,70,
317,363,276,53,117,430,30,270,237,106)(6,360,93,127,85,132,337,130,
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(10,513,138,307,460,79,65,182,413,196,486,415,343,183)(11,332,277,119,
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129,326,423,144,309,69)(14,39,416,256,250,320,180,494,197,484,55,173,
300,33)(15,369,288,296,379,511,209,452,315,491,292,241,371,247)
(16,142,498,418,172,246,64,305,118,304,361,421,46,306)(17,171,509,35,
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111,431,376,32,382,272)(21,280,331,240,54,454,465,440,245,489,221,114,
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(23,191,496,25,448,350,218,75,186,214,476,325,121,328)(24,446,198,162,
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287,215,438,168,139,222)(29,500,433,213,187,72,341,322,303,253,387,279,
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(34,386,391,409,468,150,403,523,402,133,327,480,521,165)(38,461,120,473,
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514,105,362,417,396,294)(44,467,519,390,445,249,156)(45,462,110,289,525,
419,115,356,108,98,263,504,359,310)(47,104,381,508,179,334,148,51,160,
60,78,206,357,131)(48,432,434,367,352,456,464)(50,242,177,412,375,58,
170,411,140,378,195,164,146,107)(52,368,518,443,92,274,257)
(56,68,323,169,441,94,261,436,286,184,258,428,151,333)(59,354,157,298,
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(74,224,199,233,515,243,380,348,490,335,266,275,116,239)(84,282,435,458,
200,219,481,400,488,520,385,397,217,340)(101,204,192,346,293,414,231,404,
410,324,470,159,429,190)(112,225,319,383,321,297,455,450,153,463,373,188,
394,453)(134,475,392,312,232,422,398,408,474,203,260,478,399,308)]],
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[8,Factorial(525),0,"2",[[524,1]],525,"S_n",["A",525,1],525]];
PRIMGRP[526]:=
[[1,Factorial(526)/2,1,"2",[[525,1]],524,"A_n",["A",526,1],526],
[2,Factorial(526),0,"2",[[525,1]],526,"S_n",["A",526,1],526]];
PRIMGRP[527]:=
[[1,23499295948800,1,"2",[[256,1],[270,1]],1,"O10+,2#527.1",
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(2,489,214,324,323,161,491,31,393,3,479,135,500,122,413,513,222,511,
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313,165,396,399,138,81,167,432,405,425,85,52,112,96,144)
(4,236,269,498,8,195,464,482,297,87,525,182,372,451,160,5,217,94,
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PRIMGRP[529]:=
[[1,208119169843200,0,"4c",[[44,1],[484,1]],1,"m23^2#529.1",
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(48,322,262,352,57,483,255,306,55,368,264,467)(50,207,271,375)
(53,69,276,260)(58,529,275,99,65,437,265,513,68,115,272,421)
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(117,312,124,358,126,473)(119,197,133,381)(186,317,377,349,195,478,370,303,
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52,165,134,194,293,514)(48,163,117,186,278,508)(57,172,126,195,287,517)
(62,177,131,200,292,522)(67,182,136,205,297,527)(346,352,357,367,365,350,
360,359,363,348,358,354,368,351,349,364,355,362,353)]],
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[[44,1],[484,1]],1,"A23 on 1-sets^2.2",["A",23,2],
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295,350,47,146,489,10,299,364,51,139,491,6,286,368,65,143,484,8,
282,355,69,157,488)(2,288,362,59,159,503)(3,291,356,53,152,487,16,
298,354,49,153,494,7,290,349,62,160,492)(4,292,367,55,141,498,11,
283,359,50,154,505,9,279,360,57,145,497)(12,293,358,67,158,485)
(13,297,365,48,150,500)(14,280,361,68,147,486,15,287,352,60,142,499,
22,285,348,61,149,490)(17,289,366,66,140,495)(18,294,363,64,156,501)
(20,278,357,63,151,504)(21,296,347,58,155,496)(24,399,443,263,115,433,
120,461,77,236,332,184,226,28,392,445,259,102,437,134,465,70,238,328,
171,230,42,396,438,261,98,424,138,479,74,231,330,167,217,46,410,442,
254,100,420,125,483,88,235,323,169,213,33,414,456,258,93,422,121,470,
92,249,327,162,215,29,401,460,272,97,415,123,466,79,253,341,166,208,
31,397,447,276,111,419,116,468,75,240,345,180,212)(25,403,454,266,113,
434,117,472,86,243,343,181,209,35,408,450,274,112,416,127,477,82,251,
342,163,219,40,404,458,273,94,426,132,473,90,250,324,173,224,36,412,
457,255,104,431,128,481,89,232,334,178,220,44,411,439,265,109,427,136,
480,71,242,339,174,228,43,393,449,270,105,435,135,462,81,247,335,182,227
)(26,406,448,260,106,418,131,482,78,233,337,172,214,37,395,453,275,101,
417,130,471,76,244,326,177,229,32,394,452,264,99,428,119,476,91,239,
325,176,218,30,405,441,269,114,423,118,475,80,237,336,165,223,45,400,
440,268,103,421,129,464,85,252,331,164,222,34,398,451,257,108,436,124,
463,84,241,329,175,211,39,413,446,256,107,425,122,474,73,246,344,170,
210,38,402,444,267,96,430,137,469,72,245,333,168,221,27,407,459,262,
95,429,126,467,83,234,338,183,216)(41,409,455,271,110,432,133,478,87,
248,340,179,225)(185,192,190,194,207,203,189)(186,196,201,197,205,204)
(187,199,195,191,198,188,200,206,193)(300,514,374,309,529,387,304,507,376,
305,516,391,318,511,369,307,512,378,322,525,373)(301,518,385,312,527,388)
(302,521,379,306,520,372,315,528,377)(303,522,390,308,509,383,310,513,382)
(311,523,381,320,526,370)(313,510,384,321,515,371,314,517,375)
(316,519,389,319,508,380)(317,524,386),
(1,308,336,185,316,428,199,109,421,15,101,329)(2,377,341,116,319,244,206,
454,437,176,104,214,13,400,330,70,317,497,186,385,433,130,112,237,22,
446,345,162,311,221,197,408,422,84,110,490)(3,354,332,254,310,37,205,
155,419,61,108,467)(4,285,326,277,303,290,188,293,418,291,96,283)
(5,55,338,461,302,359,194,270,425,38,113,145)(6,515,328,507,305,520,
190,523,420,521,98,513)(7,9,331,323,300,313,198,201,431,429,107,99)
(8,78,340,484,301,382,203,132,434,245,114,444,23,170,334,208,312,405,
192,86,432,498,94,375,19,124,342,231,321,451,207,178,426,222,105,398)
(10,262,333,24,320,152,189,63,430,475,95,352)(11,32,343,139,304,60,
200,477,417,360,102,260)(12,216,335,392,307,83,202,500,416,383,111,122,
20,239,344,438,322,175,196,224,427,406,100,76,18,492,324,369,318,129,
204,247,436,452,115,168)(14,193,339,415,314,106,191,17,423,337,93,306)
(16,469,325,346,309,267,195,40,435,153,97,53)(21,147,327,47,315,474,
187,362,424,268,103,30)(25,389,157,120,66,246,482,440,368,171,265,218,
36,412,146,74,64,499,462,371,364,125,273,241,45,458,161,166,58,223,
473,394,353,79,271,494)(26,366,148,258,57,39,481,141,350,56,269,471)
(27,297,142,281,50,292,464,279,349,286,257,287)(28,67,154,465,49,361,
470,256,356,33,274,149)(29,527,144,511,52,522,466,509,351,516,259,517)
(31,90,156,488,48,384,479,118,365,240,275,448,46,182,150,212,59,407,
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(34,44,159,143,51,62,476,463,348,355,263,264)(35,228,151,396,54,85,
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41,504,140,373,65,131,480,233,367,447,276,172)(71,386,502,117,388,249,
137,457,253,183,449,230,174,403,215,82,409,491)(73,294,487,278,372,295,
119,296,234,298,441,299,165,288,211,289,395,284)(75,524,489,508,374,525,
121,526,236,528,443,529,167,518,213,519,397,514)(77,87,501,485,370,387,
134,135,250,252,459,460,184,173,219,220,404,399)(81,225,496,393,376,88,
133,503,232,390,456,138,181,242,229,450,414,169)(89,248,505,439,391,180,
127,227,243,413,445,92,179,495,209,381,410,123)(91,455,506,163,380,226,
128,411,238)(282,510)]],
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[[44,1],[484,1]],1,"A23 on 1-sets^2.3",["A",23,2],
[(1,166,70,184,346,171,185,173)(2,235,82,115,347,240,197,104)
(3,143,77,414,360,516,191,265,21,120,91,230,356,447,204,495)
(4,419,75,69,363,470,201,380,14,327,78,322,364,33,188,426,6,51,
87,483,362,378,198,334,9,304,88,46,349,424,190,58,18,465,86,391,
359,332,193,311,19,28,73,437,351,56,202,472,17,373,83,345,354,309,
203,35)(5,74,92,368,355,194,196,12)(7,258,90,138,367,217,195,449,
20,488,72,161,353,401,199,518)(8,396,84,529,352,263,205,127,22,212,
80,460,365,493,187,150)(10,189,81,23,350,79,207,357)(11,442,89,506,
348,148,192,403,15,511,76,276,366,125,206,219)(13,97,71,253,358,102,
186,242)(16,281,85,299,361,286,200,288)(24,165,415,167,47,179,461,178,
369,175,323,170,300,180)(25,234,427,98,48,248,473,109,370,244,335,101,
301,249,36,96,416,236,59,110,462,247,381,106,324,239,312,111)
(26,142,422,397,61,524,467,270,389,129,344,216,310,456,43,487,417,144,
54,409,475,523,375,267,343,124,321,226,34,441,434,489,49,156,468,408,
383,520,329,262,320,134,45,211,425,443,66,501,463,155,376,405,337,515,
306,272,44,119,436,213,57,455,480,500,371,152,330,400,314,525,30,257,
435,121,68,225,471,454,388,497,325,147,307,410,38,510,421,259,67,133,
482,224,379,451,342,492,302,157,31,395,429,512,53,271,481,132,390,221,
333,446,319,502)(27,418,420,52,64,478,477,385,382,336,331,308,318,42)
(29,50,432,466,63,386,474,339,377,313,341,32,303,433)(37,326,423,305,
65,41,464,431,374,60,340,469,316,387)(39,280,430,282,62,294,476,293,
384,290,338,285,315,295)(40,372,428,328,55,317,479)(93,163,231,174)
(94,232,243,105)(95,140,238,404,107,508,237,266,113,117,252,220,103,439,
250,496)(99,255,251,128,114,209,241,450,112,485,233,151,100,393,245,519)
(108,278,246,289)(116,183,208,172,438,181,484,164,139,169,392,176,507,168,
254,182)(118,160,215,402,452,526,490,256,159,123,413,222,517,444,273,504)
(122,275,228,126,459,227,494,440,158,491,394,153,514,398,268,527)
(130,528,214,264,458,135,505,210,149,445,411,498,509,145,261,412)
(131,298,223,287,453,296,499,279,154,284,407,291,522,283,269,297)
(136,137,229,218,448,457,503,486,141,146,399,406,521,513,260,274)(177,277),
(1,188,35,316,443,369,186,288,322,236,376,163,285,437,244,261,172,400,427,
336,263,471,413,220,341,516,480,367,223,502,524,89,360,131,488,64,72,
153,122,5,50,26,155,444)(2,280,46,247,445,162,193,426,313,259,379,
393,289,345,240,468,183,216,433,520,273,356,407,496,340,79,475,137,212,
65,509,158,352,16,487,41,86,452,116,189,58,302,144,375)
(3,142,30,17,441,24,201,449,300,190,380,301,282,391,232,284,184,239,
422,175,262,425,405,266,333,401,473,344,217,479,528,227,364,522,503,363,
85,498,133,74,61,118,143,53)(4,27,40,454,438,185,196,311,305,374,
370,278,299,253,238,169,170,423,428,267,264,402,404,335,332,470,482,229,
226,525,526,365,361,499,501,87,84,130,120,51,49,141,145,7)
(6,372,25,293,460,231,192,173,308,420,382,255,287,414,243,330,171,469,
436,221,272,517,411,358,338,493,478,91,222,134,511,66,348,154,490,18,
73,38,132,442,47,187,150,306)(8,165,32,431,451,254,195,403,312,328,
378,462,298,230,249,514,181,354,430,497,271,80,406,128,327,56,463,160,
214,19,510,43,362,453,484,202,81,314,121,373,48,279,161,237)
(9,418,37,270,448,392,197,334,309,466,390,209,295,529,250,353,177,492,
432,83,268,126,396,59,325,148,467,22,211,42,523,457,346,200,495,317,
75,383,117,281,69,233,146,168)(10,464,45,224,456,507,204,357,315,489,
386,71,291,138,235,54,164,147,421,14,257,34,408,450,323,194,472,321,
213,387,508,296,368,246,491,179,78,429,129,258,57,394,151,329)
(11,395,36,339,447,461,206,219,318,512,388,347,292,506,248,77,176,124,
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92,245,123,166,55,417,152,260)(12,303,29,385,439,277,207,242,307,167,
377,416,290,276,241,399,174,331,424,474,275,218,410,519,342,355,476,505,
225,88,521,135,350,62,486,156,76,15,119,28,63,440,139,191)
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415,198,265,310,397,381,324,286,483,252,215,180,515,434,359,269,494,409,
82,337,125,465,68,210,157,513)(21,96,44,109,458,93,205,104,320,98,
389,94,297,115,251,100,182,101,435,106,274,103,412,105,343,102,481,114,
228,111,527,112,366,108,504,110,90,107,136,97,67,95,159,99)]],
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[[44,1],[484,1]],1,"A23 on 1-sets^2.4",["A",23,2],
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175,368,525,103,373,209,270)(2,266,415,55,202,75,451,366,180,115,511,
218,385)(3,36,424,308,206,397,440,44,171,322,528,402,371,25,263,300,
68,409,72,37,355,318,114,396,210,40,10,312,436,400,187,29,447,320,
183,414,509,34,378,301,275,392,49,41,79,313,367,410,95,28,217,316,
22,404,417,32,194,305,459,412,164,46,516,310,390,393,256,24,56,317,
91,405,348,42,102,304,229,408)(4,243,422,124,196,466,457,159,177,299,
510,241,376,117,265,461,66,156,85,290,349,249,100,120,219,477,20,151,
430,285,188,236,445,136,173,483,526,149,384,278,257,231,54,133,81,474,
365,157,108,281,211,247,8,128,426,469,204,144,453,297,165,253,514,126,
380,462,273,139,62,294,73,244,353,134,104,465,227,155,16,289,418,239,
192,121,449,481,181,161,522,287,372,232,261,116,58,478,89,152,361,295,
96,235,215,132,12,473,434,147,200,282,441,251,169,138,518,471,388,140,
269,277,50,248,77,129,357,479,112,143,223,293)(5,220,431,9,197,420,
446,205,167,460,527,172,391,508,264,369,48,271,70,60,363,88,106,350,
226,109)(6,450,435,170,207,512,448,389,163,276,507,57,386,71,267,346,
65,110,74,221,362,19,105,419,216,201)(7,496,421,492,191,489,444,504,
168,506,513,494,375,485,260,484,53,501,76,497,352,502,99,488,214,500)
(13,427,423,193,190,443,458,182,184,529,517,379,370,255,254,47,64,87,
83,359,364,111,97,212,224,17)(14,358,433,101,189,213,454,21,174,437,
515,195,374,439,274,162,69,524,80,382,347,272,93,51,225,86)
(15,335,429,331,199,328,452,343,176,345,521,333,383,324,268,323,61,340,
84,336,360,341,107,327,222,339)(18,82,428,354,203,98,442,228,178,23,
519,425,377,186,259,438,67,179,92,520,356,387,94,258,208,63)
(26,33,309,321,413,394)(27,240,307,137,403,463,43,148,315,298,395,233,
31,125,311,482,411,141,39,286,303,252,399,118,35,470,319,160,407,279)
(30,493,306,505,398,486)(38,332,314,344,406,325)(45,401,302)
(119,242,468,135,150,476,296,142,246,284)(122,495,467,503,145,499,283,487,
237,491)(123,127,472,480,158,154,292,280,234,238)(130,334,475,342,153,338,
291,326,245,330)(131,288,464,250,146)(329,498),
(1,173,203,352,110,142,394,82,373,476,121,56,428,342,514,232,291,17,183,
205,368,103,139,403,88,375,478,119,49,427,327,522,236,286,14,181,192,
347,107,155,413,90,391,471,116,58,433,329,524,234,279,13,166,200,351,
102,152,411,77,370,475,132,68,435,345,517,231,288,19,168,202,349,95,
151,396,85,374,470,129,66,422,324,521,247,298,21,184,195,346,104,157,
398,87,372,463,128,51,430,328,516,244,296,8,163,199,362,114,159,414,
80,369,472,134,53,432,326,509,243,281,16,167,194,359,112,146,393,84,
385,482,136,69,425,323,518,249,283,18,165,187,358,97,154,397,79,382,
480,123,48,429,339,528,251,299,11,162,196,364,99,156,395,72,381,465,
131,52,424,336,526,238,278,15,178,206,366,115,149,392,81,387,467,133,
50,417,335,511,246,282,10,175,204,353,94,153,408,91,389,483,126,47,
426,341,513,248,280,3,174,189,361,98,148,405,89,376,462,130,63,436,
343,529,241,277,12,180,191,363,96,141,404,74,384,466,125,60,434,330,
508,245,293,22,182,207,356,93,150,410,76,386,464,118,59,419,338,512,
240,290,20,169,186,360,109,160,412,92,379,461,127,65,421,340,510,233,
289,5,177,190,355,106,158,399,71,383,477,137,67,437,333,507,242,295,
7,179,188,348,105,143,407,75,378,474,135,54,416,337,523,252,297,23,
172,185,357,111,145,409,73,371,473,120,62,420,332,520,250,284,2,176,
201,367,113,161,402,70,380,479,122,64,418,325,519,235,292,6,171,198,
365,100,140,406,86,390,481,138,57,415,334,525,237,294,4,164,197,350,
108,144,401,83,388,468,117,61,431,344,527,253,287)(9,170,193,354,101,
147,400,78,377,469,124,55,423,331,515,239,285)(24,265,456,490,317,27,
256,450,488,315,29,263,451,503,307,25,268,454,505,320,46,264,438,495,
318,30,271,441,486,312,28,269,443,493,313,43,261,439,498,316,45,274,
460,494,300,35,272,444,501,303,26,266,442,499,305,33,267,457,491,301,
38,270,459,504,322,34,254,449,502,306,41,257,440,496,304,39,259,447,
497,319,31,255,452,500,321,44,276,448,484,311,42,260,455,487,302,36,
258,453,489,309,37,273,445,485,314,40,275,458,506,310)(32,262,446,492,
308)(208,219,226,214,225,211,210,220,212,223,213,217,221,227,215,209,222,
224,229,228,230,218)]],
[6,Factorial(529)/2,1,"2",[[528,1]],527,"A_n",["A",529,1],529],
[7,Factorial(529),0,"2",[[528,1]],529,"S_n",["A",529,1],529]];
PRIMGRP[530]:=
[[1,74017680,1,"2",[[529,1]],2,"L2,529 on projective points.1",
["L",[2,529],1],
[(3,529,527,525,523,521,519,517,515,513,511,509,24,506,504,502,500,498,496,
494,492,490,488,486,23,483,481,479,477,475,473,471,469,467,465,463,22,
460,458,456,454,452,450,448,446,444,442,440,21,437,435,433,431,429,427,
425,423,421,419,417,20,414,412,410,408,406,404,402,400,398,396,394,19,
391,389,387,385,383,381,379,377,375,373,371,18,368,366,364,362,360,358,
356,354,352,350,348,17,345,343,341,339,337,335,333,331,329,327,325,16,
322,320,318,316,314,312,310,308,306,304,302,15,299,297,295,293,291,289,
287,285,283,281,279,14,276,274,272,270,268,266,264,262,260,258,256,13,
253,251,249,247,245,243,241,239,237,235,233,12,230,228,226,224,222,220,
218,216,214,212,210,11,207,205,203,201,199,197,195,193,191,189,187,10,
184,182,180,178,176,174,172,170,168,166,164,9,161,159,157,155,153,151,
149,147,145,143,141,8,138,136,134,132,130,128,126,124,122,120,118,7,
115,113,111,109,107,105,103,101,99,97,95,6,92,90,88,86,84,82,
80,78,76,74,72,5,69,67,65,63,61,59,57,55,53,51,49,4,
46,44,42,40,38,36,34,32,30,28,26)(25,530,528,526,524,522,520,
518,516,514,512,510,508,507,505,503,501,499,497,495,493,491,489,487,485,
484,482,480,478,476,474,472,470,468,466,464,462,461,459,457,455,453,451,
449,447,445,443,441,439,438,436,434,432,430,428,426,424,422,420,418,416,
415,413,411,409,407,405,403,401,399,397,395,393,392,390,388,386,384,382,
380,378,376,374,372,370,369,367,365,363,361,359,357,355,353,351,349,347,
346,344,342,340,338,336,334,332,330,328,326,324,323,321,319,317,315,313,
311,309,307,305,303,301,300,298,296,294,292,290,288,286,284,282,280,278,
277,275,273,271,269,267,265,263,261,259,257,255,254,252,250,248,246,244,
242,240,238,236,234,232,231,229,227,225,223,221,219,217,215,213,211,209,
208,206,204,202,200,198,196,194,192,190,188,186,185,183,181,179,177,175,
173,171,169,167,165,163,162,160,158,156,154,152,150,148,146,144,142,140,
139,137,135,133,131,129,127,125,123,121,119,117,116,114,112,110,108,106,
104,102,100,98,96,94,93,91,89,87,85,83,81,79,77,75,73,71,
70,68,66,64,62,60,58,56,54,52,50,48,47,45,43,41,39,37,
35,33,31,29,27),(1,2,14)(3,12,16)(4,18,9)(5,20,6)
(7,13,11)(8,23,22)(10,24,19)(15,21,17)(25,145,409)
(26,462,91)(27,69,484)(28,510,41)(29,416,134)(30,454,95)
(31,512,36)(32,75,472)(33,92,455)(34,235,310)(35,385,160)
(37,187,355)(38,247,295)(39,311,230)(40,353,186)(42,117,420)
(43,524,519)(44,386,150)(45,527,514)(46,232,301)(47,272,261)
(48,476,55)(49,307,223)(50,431,98)(51,419,109)(52,447,80)
(53,236,290)(54,178,347)(56,228,296)(57,62,461)(58,180,342)
(59,194,326)(60,221,299)(61,128,391)(63,453,64)(65,363,152)
(66,89,425)(67,118,394)(68,399,113)(70,286,224)(71,486,528)
(72,273,234)(73,209,297)(74,279,226)(76,350,153)(77,172,330)
(78,168,333)(79,507,500)(81,349,149)(82,316,182)(83,480,523)
(84,104,392)(85,306,188)(86,253,241)(87,371,121)(88,280,211)
(90,173,317)(93,529,464)(94,493,498)(96,267,216)(97,335,147)
(99,159,322)(100,463,522)(101,525,460)(102,492,491)(103,345,132)
(105,175,300)(106,197,277)(107,120,352)(108,503,475)(110,328,141)
(111,129,340)(112,289,179)(114,262,204)(115,167,298)(116,177,287)
(119,337,123)(122,154,303)(124,505,457)(125,240,214)(126,271,183)
(127,148,304)(130,466,489)(131,291,158)(133,292,155)(135,438,513)
(136,504,446)(137,231,212)(138,157,285)(139,526,421)(140,250,189)
(142,242,195)(143,190,246)(144,274,162)(146,410,530)(151,191,237)
(156,487,442)(161,437,488)(163,451,471)(164,427,494)(165,171,243)
(166,217,196)(169,511,405)(170,520,395)(174,199,207)(176,185,219)
(181,198,201)(184,468,434)(192,490,403)(200,368,518)(202,515,369)
(203,435,448)(205,479,402)(206,474,406)(208,377,501)(210,452,423)
(213,375,497)(215,426,444)(218,436,432)(220,458,408)(222,387,477)
(225,383,478)(227,445,414)(229,361,496)(233,396,456)(238,382,465)
(239,473,373)(244,516,325)(245,320,521)(248,506,332)(249,470,367)
(251,407,428)(252,401,433)(254,323,509)(255,380,450)(256,334,495)
(257,388,440)(258,346,482)(259,327,499)(260,308,517)(263,422,400)
(264,424,397)(265,319,502)(266,443,376)(268,378,439)(269,485,331)
(270,398,417)(275,467,344)(276,481,329)(278,358,449)(281,411,393)
(282,483,321)(283,508,294)(284,429,372)(288,459,339)(293,441,351)
(302,469,314)(305,415,366)(309,365,412)(312,384,390)(313,413,360)
(315,430,341)(318,364,404)(324,418,343)(336,370,379)(338,389,359)
(348,356,381)(354,357,374)]],
[2,148035360,0,"2",[[529,1]],3,"L2,529 on projective points.2",
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[(1,145,525,456,492,461,465,521,377,112,99,323,479,276,421,289,65,254,409,
301,512,383,231,511,279,488,165,143,298,207,397,89,528,495,86,420,467,
233,157,41,109,408,22,131,212,94,236,146,453,259,258,329,265)
(2,382,318,389,388,194,501,411,47,435,516,10,239,32,100,490,414,180,
227,55,152,119,52,250,440,349,504,482,159,368,136,416,264,135,346,238,
393,76,358,226,371,168,324,42,29,270,126,182,186,155,191,122,502)
(3,381,378,8,308,54,130,315,348,373,451,459,473,243,302,138,317,129,
98,61,267,84,344,426,213,200,260,79,341,314,268,208,204,147,45,385,
209,161,37,187,436,497,401,322,36,494,484,283,244,295,189,228,343)
(4,327,148,478,462,108,422,123,210,446,334,354,164,27,370,450,398,5,
249,197,277,114,483,293,313,201,437,524,225,33,185,169,499,320,6,82,
471,115,74,372,237,529,134,192,455,513,118,410,275,67,26,176,59)
(7,304,419,458,352,403,364,163,153,105,325,246,150,211,460,104,486,438,
262,96,500,443,439,379,333,306,62,387,447,434,221,303,57,380,80,43,
518,330,509,345,404,174,188,196,274,299,332,517,87,339,24,269,266)
(9,466,83,507,448,18,21,222,514,337,463,470,53,16,88,177,184,310,
133,425,11,14,199,140,58,181,23,287,34,472,338,273,44,366,206,375,
125,111,316,69,72,331,30,522,272,441,281,97,374,309,175,107,360)
(12,257,183,432,220,418,154,167,445,491,106,336,449,139,25,406,137,120,
469,321,193,242,71,300,294,284,234,351,132,429,13,144,223,235,121,219,
498,261,356,481,40,224,340,312,520,282,240,523,232,151,75,288,252)
(15,444,48,433,173,350,263,46,63,216,142,117,230,172,506,171,280,90,
247,245,255,248,38,292,110,452,179,56,477,271,113,49,68,285,369,457,
394,290,256,286,487,39,519,489,328,305,396,77,217,162,205,50,81)
(17,60,91,442,485,430,64,251,342,319,158,128,102,160,361,391,357,253,
190,278,362,73,92,28,376,170,85,468,195,31,355,103,399,392,402,400,
51,367,476,141,475,417,530,505,431,78,95,384,297,474,214,93,203)
(19,218,515,296,413,363,353,347,70,405,454,326,178,527,510,241,116,508,
198,311,35,156,202,480,493,229,427,215,464,390,20,395,359,66,496,415,
124,407,365,127,335,307,423,101,166,291,386,149,428,526,412,424,503),
(1,166,49,119,439,435,211,41,223,363,215,72,353,173,238,317,329,93,312,
379,348,35,440,103,468,117,217,169,163,339,506,251,290,291,432,398,247,
27,294,331,174,484,47,134,209,319,270,464,311,54,75,287,405,362,255,
129,18,306,114,204,138,488,105,233,397,422,133,141,360,373,445,7,241,
470,295,505,297,56,480,107,82,466,385,407,8,167,269,64,164,433,512,
279,226,155,61,84,100,342,88,32,59,253,415,73,406,109,304,302,29,
127,392,503,128,419,131,490,361,256,349,175,459,473,198,224,366,350,21,
190,387,427,91,395,145,113,318,448,132,479,13,177,402,399,428,219,201,
516,377,507,367,171,478,345,364,320,369,202,273,34,334,275,112,327,160,
206,23,207,346,94,43,526,176,178,110,280,244,416,359,76,52,38,245,
301,184,502,246,303,368,375,213,77,66,483,411,193,236,314,79,457,284,
390,351,396,185,11,335,99,130,289,196,322,328,441,90,25,511,474,214,
15,123,53,283,5,424,104,189,22,341,525,529,384,486,218,40,436,465,
36,135,197,394,3,249,475,530,471,118,508,156,97,152,378,96,232,430,
492,85,162,191,81,409,140,243,98,102,286,165,438,523,203,50,344,68,
504,326,413,153,116,95,31,10,299,305,431,338,497,528,292,418,442,231,
276,237,343,170,42,313,391,434,216,144,55,44,414,252,259,16,381,125,
443,325,382,83,69,45,268,210,383,17,517,449,451,101,78,26,281,420,
142,421,467,300,515,352,293,87,354,425,258,307,263,282,149,456,260,120,
250,111,426,408,199,228,225,450,372,148,495,179,309,514,482,12,30,200,
240,437,188,277,261,403,429,154,168,452,14,370,266,137,496,208,499,124,
235,500,92,324,323,518,221,4,212,374,62,89,33,285,527,37,60,472,
401,347,115,194,462,57,358,460,487,220,242,161,39,520,147,65,330,122,
332,157,386,510,182,254,267,485,494,205,230,393,522,139,489,423,513,321,
257,498,371,265,222,340,46,67,316,9,357,308,417,493,74,143,453,296,
333,6,380,229,195,336,337,376,121,288,463,458,410,509,159,524,186,86,
278,248,315,28,298,310,389,454,274,48,412,264,404,80,20,192,187,24,
71,461,2,355,521,481,262,227,271,181,455,151,234,150,469,239,447,501,
491,51,63,183,108,519,444,58,70,136,126,180,388,158,477,19,476,172,
446,356,400,365,146,106,272)]],
[3,148035360,0,"2",[[529,1]],2,"L2,529 on projective points.3",
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[(1,366,356,75,479,289)(2,522,145,282,268,340)(3,131,10,327,406,293)
(4,409,190,180,34,466)(5,418,84,91,434,358)(6,51,218,398,21,202)
(7,456,519,116,45,453)(8,487,279,156,135,31)(9,334,159)
(11,494,350,140,419,515)(12,300,513,337,446,348)(13,134,463,301,482,379)
(14,413,380,339,451,452)(15,403,270)(16,185,221,455,354,375)
(17,114,173,369,244,509)(18,158,142,444,161,215)(19,182,178,436,111,310)
(20,506,205,410,274,153)(22,264,290,437,465,320)(23,411,489,400,345,328)
(24,316,73,69,105,216)(25,371,344,317,201,263)(26,253,383,361,42,307)
(27,79,206,110,266,174)(28,172,483,285,65,211)(29,330,329,374,248,72)
(30,238,445,333,122,430)(32,454,151,370,448,207)(33,97,516,230,154,183)
(35,203,235,401,61,119)(36,399,228,321,457,405)(37,338,438,322,355,229)
(38,157,100,68,492,257)(39,291,450,386,514,194)(40,499,476,472,281,70)
(41,498,196,332,385,378)(43,169,258,439,335,249)(44,176,265,473,247,86)
(46,416,250,127,294,133)(47,103,210,298,56,189)(48,113,152,261,125,184)
(49,313,308,431,408,433)(50,352,467,481,367,474)(52,469,59,121,66,299)
(53,342,141,102,90,284)(54,277,420,393,486,443)(55,395,95,302,233,286)
(57,83,389)(58,170,404,417,353,254)(60,193,271,311,220,191)
(62,262,414,518,71,163)(63,188,391,442,529,314)(64,260,138,447,204,164)
(67,192,422,349,226,112)(74,269,377,186,359,81)(76,278,241,365,92,242)
(77,471,239,214,428,118)(78,435,343,326,148,521)(80,212,132,525,524,165)
(82,390,167,117,396,397)(85,225,470,219,108,303)(87,488,468,166,137,124)
(88,179,502)(89,421,376,505,295,223)(93,143,423,272,280,150)
(94,209,372,520,429,501)(96,129,381,309,426,146)(98,251,341,144,477,120)
(99,130,412,109,459,484)(101,384,222,496,336,357)(104,364,415,460,123,177)
(106,461,362)(107,236,200,387,305,197)(115,187,255,360,510,304)
(126,394,246,527,292,441)(128,287,240,324,267,276)(136,227,500,507,458,234)
(139,425,217,273,306,149)(147,508,283,168,526,171)(155,331,325,297,503,493)
(160,323,232,490,462,245)(162,407,392,485,464,318)(175,231,449,347,312,181)
(195,530,252)(198,480,243,373,528,504)(199,351,475)(208,511,491,440,497,363)
(213,382,296,259,224,346)(237,402,388,523,427,288)(256,368)(275,512,432)
(315,319,495,424,478,517),(1,380,447,271,288,353,241,59,119,525,484,106,
87,99,159,280,51,123,256,342,404,84,19,344,45,518,180,282,260,379,270,
501,498,245,207,312,117,398,158,226,62,388,492,34)(2,446,494,93,418,
13,323,82,363,168,274,235,488,485,210,101,220,198,15,468,436,137,88,
396,76,139,224,357,429,200,322,381,393,374,503,22,361,421,239,127,192,
209,33,100)(3,309,190,112,304,305,143,135,502,96,395,114,157,214,264,
487,24,148,286,5,243,426,56,155,110,517,64,77,520,91,57,306,299,
422,411,435,73,129,36,297,276,425,227,495)(4,221,121,292,43,212,368,
310,373,48,527,163,53,307,511,284,378,316,185,335,177,131,283,397,400,
7,476,218,20,151,371,480,451,377,138,365,401,193,49,442,526,86,300,412
)(6,387,265,78,165,147,89,251,360,269,17,31,291,523,428,459,146,228,
440,505,457,382,41,439,98,530,482,40,253,334,528,52,463,189,449,134,
211,120,230,392,333,315,402,215)(8,328,203,132,72,21,302,277,240,204,
178,42,408,348,14,152,341,415,258,279,405,338,44,263,183,71,406,464,
458,249,493,12,529,522,74,409,298,217,437,142,75,201,222,66)
(9,35,162,327,352,473,118,246,366,97,294,289,419,199,336,521,301,355,
512,167,202,524,350,149,67,470,208,252,330,453,187,133,172,391,376,339,
471,321,25,497,10,161,375,242)(11,213,509,37,26,225,169,506,324,136,
18,32,124,413,386,504,232,478,285,314,257,206,247,452,467,399,261,50,
434,514,340,358,60,417,154,441,490,92,108,95,500,354,250,450)
(16,367,85,384,23,346,337,175,176,369,290,171,456,491,254,55,205,184,
444,351,407,46,70,58,182,174,423,390,466,403,416,469,370,325,424,54,
237,410,194,332,479,499,216,266)(27,150,229,273,516,414,331,130,462,278,
313,474,125,179,465,144,281,61,191,186,383,115,234,362,513,128,153,319,
445,318,238,105,320,295,489,455,160,515,141,104,90,308,347,293)
(28,233,275,223,166,195,508,248,483,94,68,356,448,111,345,156,481,311,
255,454,443,477,267,272,30,231,126,486,385,372,389,496,39,326,63,420,
122,140,472,47,430,219,81,519)(29,507,109,329,65,262,510,364,80,83,
197,349,303,145,296,164,102,196,475,173,427,317,460,432,107,170,113,268,
438,188,359,259,433,69,181,394,461,38,431,287,79,116,343,103)]],
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[(1,13,136,266,485,380,519,448,509,169,190,173,227,60,490,126,311,282,235,
171,506,468,241,94,408,451,369,424,456,163,31,76,294,179,429,3,15,
318,336,88,147,397,407,216,367,400,493,248)(2,91,368,129,494,121,454,
335,208,423,525,486,54,239,432,399,61,428,16,483,405,199,492,110,453,
298,114,302,355,243,119,391,44,389,370,98,128,441,164,363,351,326,342,
337,375,284,219,527)(4,115,53,220,353,50,215,125,32,499,345,457,515,
85,73,168,9,261,133,79,341,373,495,280,224,442,436,99,155,43,406,
427,521,124,67,101,502,416,414,440,30,491,225,462,228,417,344,322)
(5,287,524,372,28,48,498,29,419,102,256,7,472,496,470,103,112,505,
52,23,57,160,245,187,156,449,378,371,433,514,22,309,116,426,374,358,
438,476,526,165,233,25,226,445,264,466,334,315)(6,331,186,232,270,293,
404,247,362,465,230,38,304,242,135,392,240,297,33,174,443,159,398,450,
18,146,420,377,444,80,254,221,231,41,434,478,312,117,255,403,418,77,
74,382,487,327,276,507)(8,357,24,384,301,39,307,308,517,141,127,218,
130,49,324,482,447,70,359,290,288,291,340,185,455,310,200,153,425,150,
131,508,366,175,520,209,222,69,192,51,281,97,346,321,516,207,323,262)
(10,234,413,386,481,166,89,109,100,183,107,149,461,258,139,296,463,63,
267,467,37,347,330,265,176,144,278,381,191,271,437,140,410,259,260,390,
19,364,184,272,72,518,229,421,295,319,182,211)(11,361,411,162,196,333,
181,198,58,194,469,82,113,402,317,350,395,274,108,300,62,529,122,431,
530,158,354,474,27,251,479,388,14,56,458,501,237,269,383,105,314,87,
134,460,275,178,484,511)(12,504,415,93,201,148,142,34,21,257,204,303,
328,286,464,145,249,180,236,352,338,205,66,202,244,45,409,170,217,64,
279,65,42,285,152,379,71,305,263,137,132,213,522,47,277,316,348,477)
(17,528,489,193,412,500,167,349,195,177,376,401,356,268,252,250,365,86,
238,360,253,299,325,473,306,104,488,387,68,197,40,430,394,332,20,55,
329,81,189,510,385,459,503,273,435,161,46,157)(26,210,151,90,422,513,
212,393,154,292,446,59,123,96,512,206,78,172,339,246,223,188,92,475,
283,120,203,143,313,36,75,439,138,343,452,83,111,497,289,471,523,95,
118,214,106,84,396,480)(35,320),
(1,279,6,10,51,357,165,254,251,408,126,237,399,39,69,271,411,276,263,
72,164,162,186,148,213,34,499,155,277,149,248,30,295,311,267,459,454,
101,58,56,243,161,490,11)(2,467,139,50,386,353,65,358,175,84,362,
392,334,221,381,375,352,272,130,443,20,349,442,420,464,468,366,67,218,
528,54,170,230,318,503,93,378,480,463,474,71,89,29,481)
(3,229,268,523,368,360,449,250,191,12,332,75,196,316,53,303,393,21,
339,521,60,233,314,394,436,496,17,265,249,451,462,327,355,526,46,173,
143,489,37,427,78,258,201,377)(4,274,397,166,379,380,269,282,106,193,
400,315,252,63,370,290,202,235,8,70,456,433,103,297,301,438,178,180,
364,261,133,361,234,98,395,428,108,45,190,86,325,485,313,77)
(5,38,41,184,455,142,57,509,383,317,418,336,176,90,55,228,372,328,
512,406,35,27,14,446,80,450,236,305,329,298,413,92,373,187,398,36,
396,491,81,100,217,64,447,129)(7,529,256,138,68,87,453,441,210,31,
246,331,66,16,174,179,82,183,52,95,182,223,412,15,42,401,232,33,
231,293,255,312,216,119,300,486,19,445,43,85,351,500,88,59)
(9,405,23,25,461,479,209,283,206,409,302,114,291,205,215,169,416,465,
437,508,96,294,319,457,208,448,113,203,354,402,487,511,61,382,131,145,
200,204,434,435,253,238,284,262)(13,494,287,259,24,524,493,431,40,257,
264,333,522,525,79,306,430,239,510,159,518,134,245,167,222,102,140,156,
469,99,385,270,321,507,188,458,415,91,369,240,497,47,94,211)
(18,407,135,384,417,111,76,118,389,199,32,44,171,107,122,365,359,83,
530,136,473,121,527,342,22,374,495,28,470,132,390,260,323,214,104,440,
296,308,371,244,198,160,105,488)(26,391,192,194,212,425,414,484,338,247,
326,117,423,227,419,426,168,181,144,172,466,335,345,120,376,163,195,460,
429,424,498,515,62,220,141,346,275,150,516,97,421,224,310,367)
(48,363,123,513,151,197,241,128,519,517,280,444,73,422,288,514,157,356,
225,278,471,219,109,337,475,137,146,320,340,304,477,322,387,127,504,189,
153,452,347,285,403,343,482,299)(49,502,348,307,110,324,388,309,478,492,
506,292,74,410,147,350,226,273,281,115,476,207,125,185,242,112,152,501,
289,432,483,116,154,266,520,330,158,286,404,344,472,177,341,439)]],
[5,296070720,0,"2",[[529,1]],3,"L2,529 on projective points.5",
["L",[2,529],1],
[(1,83,295,159)(2,407,182,525)(3,173,470,184)(4,56,445,428)
(5,335,201,447)(6,78,392,111)(7,157,204,425)(8,272,25,378)
(9,89,245,449)(10,403,104,72)(11,436,292,379)(12,220,314,435)
(13,279,180,394)(14,451,251,337)(15,511,234,327)(16,486,261,145)
(17,212,301,313)(18,55,50,237)(19,319,518,368)(20,437,194,334)
(21,41,316,97)(22,414,484,384)(23,85,246,383)(24,409,250,315)
(26,67,396,441)(27,129,388,88)(28,494,443,300)(29,400,141,431)
(30,183,460,501)(31,186,429,210)(32,166,36,59)(33,359,448,207)
(34,105,304,281)(35,364,410,381)(37,206,311,221)(38,218,161,60)
(39,276,322,406)(40,352,142,126)(42,363,256,324)(43,147,307,483)
(44,323,160,254)(45,377,507,121)(46,222,76,297)(47,374,356,189)
(48,102,420,287)(49,223,354,154)(51,450,320,80)(52,209,262,257)
(53,185,132,268)(54,227,325,475)(57,473,459,468)(58,393,413,318)
(61,333,282,497)(62,491,71,238)(63,516,93,244)(64,192,418,529)
(65,492,115,480)(66,376,513,487)(68,472,162,260)(69,137,174,217)
(70,118,458,75)(73,417,404,310)(74,522,230,349)(77,266,86,290)
(79,135,343,390)(81,242,463,176)(82,357,197,229)(84,412,464,362)
(87,231,342,498)(90,462,453,148)(91,259,351,340)(92,200,106,252)
(94,195,108,371)(95,133,113,504)(96,248,198,119)(98,355,205,99)
(100,224,495,341)(101,193,515,187)(103,474,228,243)(107,155,426,438)
(109,353,158,274)(110,524,236,419)(112,114,298,152)(116,505,144,131)
(117,452,270,512)(120,523,430,446)(122,439,427,165)(123,263,203,493)
(124,305,350,208)(125,280,386,338)(127,253,461,136)(128,267,241,219)
(130,434,175,169)(134,167,397,309)(139,214,196,424)(140,284,517,454)
(143,385,485,370)(146,303,326,293)(149,502,471,188)(150,361,330,332)
(151,423,422,345)(153,317,215,433)(156,213,306,489)(163,278,264,380)
(164,178,477,457)(168,302,455,408)(170,508,321,233)(171,372,269,291)
(172,255,442,271)(177,369,488,382)(179,346,365,478)(181,202,527,286)
(190,367,275,240)(191,375,265,467)(199,405,226,415)(211,328,285,520)
(216,299,510,526)(225,528,277,308)(232,239,466,421)(235,283,348,289)
(247,296,402,456)(249,258,373,416)(273,514,360,509)(288,490,481,503)
(294,411,482,469)(312,395,506,519)(329,336,500,465)(331,347,496,389)
(344,399,479,391)(358,521,401,499)(366,432,398,476)(387,444,530,440),
(1,405,42,433,189,112,343,348,55,254,269,165,178,185,378,48,498,54,471,
294,528,111)(2,131,20,344,472,412,445,277,59,50,259,257,168,66,382,
419,94,375,248,268,395,385)(3,242,267,511,417,181,102,451,22,518,229)
(4,394,106,77,107,255,311,158,350,289,71,484,307,507,337,391,105,431,
414,201,304,60)(5,432,136,195,486,11,504,482,82,335,438,526,250,170,
139,413,474,425,104,492,237,256)(6,475,306,424,52,426,169,83,62,34,
524,69,371,204,180,264,387,401,161,98,25,245)(7,313,243,220,435,23,
39,239,465,79,281,219,477,505,523,147,481,191,476,286,41,114)
(8,202,514,213,384,193,24,222,491,249,262,75,342,9,295,12,149,90,
72,166,500,340)(10,238,368,228,140,115,407,320,522,186,359,88,381,129,
284,315,434,502,196,427,164,338)(13,67,226,386,171,35,167,363,319,163,
212,292,356,334,231,423,18,318,351,447,38,416)(14,206,449,275,353,362,
450,188,29,215,283,244,336,224,232,235,409,97,73,271,46,347)
(15,49,214,317,515,327,470,291,260,127,499,525,31,455,422,265,113,57,
410,415,296,263)(16,100,151,130,246,366,290,87,21,126,218,330,358,331,
198,390,459,133,217,530,124,332)(17,446,322,440,282,152,64,400,513,483,
162,305,300,109,135,108,393,85,125,357,123,63)(19,377,190,236,278,512,
489,47,261,437,485,460,208,148,258,279,210,182,376,360,341,43)
(27,456,324,501,521,345,406,463,444,309,177,372,473,361,428,379,223,203,
137,448,141,33)(28,138,205,276,101,430,154,373,408,155,493,116,84,91,
494,314,160,312,392,44,364,302)(30,457,297,301,70,367,252,200,273,333,
241,469,509,299,153,187,56,506,78,355,421,439)(32,92,326,453,143,197,
383,479,389,280,253,316,272,303,184,144,89,216,325,397,510,287)
(36,328,173,132,233,461,369,37,403,285,354,503,517,497,519,374,468,80,
192,352,339,329)(40,211,221,183,293,399,134,86,121,68,157,207,464,81,
240,225,490,118,346,270,150,266)(45,74,96,402,61,51,227,370,179,527,
230,496,458,119,176,520,454,103,159,145,247,274)(53,418,429,310,298,146,
443,110,365,120,288,388,142,174,95,529,175,380,452,172,436,488)
(58,516,76,441,65,122,128,308,480,349,93,251,442,117,487,323,404,209,
495,199,234,99)(156,396,478,467,398,462,508,420,194,466,321)]],
[6,Factorial(530)/2,1,"2",[[529,1]],528,"A_n",["A",530,1],530],
[7,Factorial(530),0,"2",[[529,1]],530,"S_n",["A",530,1],530]];
PRIMGRP[531]:=
[[1,Factorial(531)/2,1,"2",[[530,1]],529,"A_n",["A",531,1],531],
[2,Factorial(531),0,"2",[[530,1]],531,"S_n",["A",531,1],531]];
PRIMGRP[532]:=
[[1,Factorial(532)/2,1,"2",[[531,1]],530,"A_n",["A",532,1],532],
[2,Factorial(532),0,"2",[[531,1]],532,"S_n",["A",532,1],532]];
PRIMGRP[533]:=
[[1,Factorial(533)/2,1,"2",[[532,1]],531,"A_n",["A",533,1],533],
[2,Factorial(533),0,"2",[[532,1]],533,"S_n",["A",533,1],533]];
PRIMGRP[534]:=
[[1,Factorial(534)/2,1,"2",[[533,1]],532,"A_n",["A",534,1],534],
[2,Factorial(534),0,"2",[[533,1]],534,"S_n",["A",534,1],534]];
PRIMGRP[535]:=
[[1,Factorial(535)/2,1,"2",[[534,1]],533,"A_n",["A",535,1],535],
[2,Factorial(535),0,"2",[[534,1]],535,"S_n",["A",535,1],535]];
PRIMGRP[536]:=
[[1,Factorial(536)/2,1,"2",[[535,1]],534,"A_n",["A",536,1],536],
[2,Factorial(536),0,"2",[[535,1]],536,"S_n",["A",536,1],536]];
PRIMGRP[537]:=
[[1,Factorial(537)/2,1,"2",[[536,1]],535,"A_n",["A",537,1],537],
[2,Factorial(537),0,"2",[[536,1]],537,"S_n",["A",537,1],537]];
PRIMGRP[538]:=
[[1,Factorial(538)/2,1,"2",[[537,1]],536,"A_n",["A",538,1],538],
[2,Factorial(538),0,"2",[[537,1]],538,"S_n",["A",538,1],538]];
PRIMGRP[539]:=
[[1,Factorial(539)/2,1,"2",[[538,1]],537,"A_n",["A",539,1],539],
[2,Factorial(539),0,"2",[[538,1]],539,"S_n",["A",539,1],539]];
PRIMGRP[540]:=
[[1,3265920,1,"2",[[63,1],[224,1],[252,1]],1,"U4,3 on non-isotrop\
ic projective points.1",["2A",[3,3],1],
[(1,2)(3,5)(4,6)(7,44,13,26)(8,43,14,25)(9,47,15,29)
(10,48,16,30)(11,45,17,27)(12,46,18,28)(19,50,37,32)
(20,49,38,31)(21,53,39,35)(22,54,40,36)(23,51,41,33)
(24,52,42,34)(55,77,62,92)(56,74,61,95)(57,78,65,93)
(58,73,66,94)(59,75,63,96)(60,76,64,91)(67,83,86,99)
(68,81,85,101)(69,84,89,100)(70,79,90,98)(71,82,87,102)
(72,80,88,97)(103,160)(104,167,105,164)(106,168,109,165)(107,161,110,162
)(108,163,111,166)(112,187,118,205)(113,192,119,209)(114,188,123,207)
(115,190,120,210)(116,189,121,206)(117,191,122,208)(124,193,142,211)
(125,196,143,215)(126,194,146,212)(127,195,147,214)(128,197,144,216)
(129,198,145,213)(130,175,148,169)(131,179,150,172)(132,177,149,174)
(133,180,152,173)(134,176,153,170)(135,178,151,171)(136,199,154,181)
(137,201,155,185)(138,204,159,184)(139,202,156,186)(140,200,157,182)
(141,203,158,183)(217,379)(218,386,219,383)(220,387,223,384)(221,380,224,381
)(222,382,225,385)(226,406,232,424)(227,410,233,429)(228,411,235,427)
(229,407,236,426)(230,409,237,428)(231,408,234,425)(238,412,256,430)
(239,416,257,433)(240,417,260,434)(241,414,261,435)(242,413,258,431)
(243,415,259,432)(244,394,262,388)(245,399,264,390)(246,397,263,392)
(247,396,267,391)(248,398,265,393)(249,395,266,389)(250,418,268,400)
(251,422,269,402)(252,423,271,403)(253,419,272,401)(254,420,273,404)
(255,421,270,405)(274,458,281,473)(275,455,280,476)(276,459,284,474)
(277,454,285,475)(278,456,282,477)(279,457,283,472)(286,464,305,480)
(287,462,304,482)(288,465,308,481)(289,460,309,479)(290,463,306,483)
(291,461,307,478)(292,447,313,439)(293,442,314,437)(294,444,315,440)
(295,445,310,441)(296,443,311,436)(297,446,312,438)(298,471,317,451)
(299,469,316,453)(300,466,320,449)(301,468,321,452)(302,467,318,448)
(303,470,319,450)(322,484)(323,491,324,488)(325,492,328,489)(326,485,329,486
)(327,487,330,490)(331,511,337,529)(332,515,338,534)(333,516,340,532)
(334,512,341,531)(335,514,342,533)(336,513,339,530)(343,517,361,535)
(344,521,362,538)(345,522,365,539)(346,519,366,540)(347,518,363,536)
(348,520,364,537)(349,499,367,493)(350,504,369,495)(351,502,368,497)
(352,501,372,496)(353,503,370,498)(354,500,371,494)(355,523,373,505)
(356,527,374,507)(357,528,376,508)(358,524,377,506)(359,525,378,509)
(360,526,375,510),(1,110,89,316,371,522,287,49,105)(2,164,84,286,
429,260,317,20,162)(3,225,70,298,532,120,275,42,486)(4,325,58,280,
152,377,305,11,381)(5,384,63,274,210,402,299,16,324)(6,490,101,304,
265,173,281,33,219)(7,103,74,357,226,133,115,430,513)(8,167,87,333,
440,433,139,155,369)(9,223,97,370,170,43,109,102,449)(10,327,66,345,
495,255,159,214,212)(12,485,94,375,393,510,128,480,137)(13,107,82,398,
447,347,204,182,426)(14,160,77,421,499,190,180,343,246)(15,218,96,403,
340,271,216,453,200)(17,382,59,434,236,528,186,129,125)(18,492,67,427,
119,44,168,71,479)(19,106,55,209,518,47,386,88,461)(21,217,75,177,
412,354,422,142,408)(22,323,91,172,254,397,416,468,332)(23,387,72,201,
462,197,399,524,264)(24,488,81,196,198,156,392,364,500)(25,108,62)
(26,163,56)(27,221,80)(28,330,68)(29,385,98)(30,491,86)
(31,111,69,496,432,390,252,231,362)(32,161,92,520,157,138,228,441,506)
(34,322,76,540,211,516,240,493,132)(35,383,79,533,374,45,220,57,437)
(36,487,60,509,481,235,270,389,207)(37,104,95,261,185,202,503,446,269)
(38,166,100,237,346,341,526,502,413)(39,222,65,273,450,498,508,338,150)
(40,329,85,267,401,48,489,64,443)(41,379,78,243,124,248,539,232,189)
(46,326,83,467,50,165,61,153,257)(51,224,90,146,147,184,339,414,227)
(52,328,99,140,471,144,334,251,531)(53,380,93,123,525,336,363,463,395)
(54,484,73,116,361,410,358,193,351)(112,130,297,238,244,296,418,406,292)
(113,205,456,179,523,407,475,373,514)(114,250,350,477,400,247,176,148,454)
(117,505,249,420,331,135,242,199,409)(118,192,419,262,457,537,388,131,474)
(121,417,290,483,451,300,194,530,312)(122,442,151)(126,302,469,465,288,494,
206,315,405)(127,342,348)(134,356,529,459,241,337,188,472,169)
(136,352,178,268,515,359,394,191,538)(141,289,301,396,277,284,272,308,318)
(143,263,310,174,365,321,452,482,309)(145,504,527)(149,313,376,215,307,464,
470,319,233)(154,512,476,256,411,239,424,455,360)(158,234,415)(171,436,208)
(175,187,295,535,511,293,355,349,294)(181,245,473,517,353,536,367,458,423)
(183,497,366)(195,229,253)(203,320,306,335,282,279,507,303,291)(213,391,435)
(230,283,445,444,278,431,368,311,519)(258,460,534)(259,501,276,438,439,285,
344,425,314)(266,521,466)(372,404,478)(378,448,428)]],
[2,6531840,0,"2",[[63,1],[224,1],[252,1]],1,
"U4,3 on non-isotropic projective points.2",["2A",[3,3],1],
[(1,299,519,501,432,152,89,403,398,218)(2,225,381,184,290,159,243,196,53,
278)(3,59,15,461,474,109,317,333,356,481)(4,364,95,143,187,139,380,
29,111,205)(5,455,178,262,30,115,36,280,493,90)(6,181,158,31,492,
128,193,110,451,351)(7,400,394,55,367)(8,61,313,118,237)
(9,293,485,14,391,10,496,43,370,309)(11,215,213,247,450,12,330,464,
162,513)(13,176,98,452,230,375,502,429,303,189)(16,101,103,76,328,345,
27,124,287,288)(17,505,194,260,179,325,244,495,312,342)(18,259,282,360,
525,357,170,340,276,434)(19,440,41,421,186,227,279,417,537,69)
(20,320,508,350,418,219,415,60,479,424)(21,387,57,174,63,246,40,168,
378,180)(22,238,470,484,437,264,523,321,268,323)(23,338,167,252,248,257,
443,372,99,319)(24,515,369,129,534,269,188,510,155,527)(25,145,327,315,
446,83,140,407,457,285)(26,134,144,305,163,72,157,133,71,471)
(28,137,389,302,102,77,125,352,428,539)(32,202,478,382,150,462,49,272,
263,132)(33,377,341,516,135,473,258,234,332,104)(34,410,301,439,127,469,
465,255,463,146)(35,80,200,239,154,480,392,222,409,148)(37,74,441,329,
86,411,220,433,221,422)(38,518,66,42,482,423,454,503,393,183)
(39,233,141,425,217,405,396,149,346,529)(44,472,355,84,334,494,486,322,
489,100)(45,208,435,361,201,524,453,291,349,408)(46,310,500,401,397,536,
376,444,172,447)(47,265,173,236,92,512,81,52,442,240)(48,91,67,532,
507,530,204,79,96,161)(50,343,231,476,75,190,331,448,195,358)
(51,526,256,64,347,197,78,517,339,253)(54,413,223,388,540,165,164,277,
379,300)(56,82,271,97,209,416,363,294,85,426)(58,528,107,106,359,371,
324,114,138,431)(62,488,266,483,402,399,182,354,383,459)(65,216,490,522,
123,281,73,307,374,122)(68,226,250,212,88,386,535,511,241,228)
(70,198,207,384,365,270,304,254,487,306)(87,430,185,468,249,210,406,366,
506,466)(93,274,404,395,298,326,214,314,177,191)(94,251,116,199,131,275,
420,151,211,117)(105,261,337,373,284)(108,497,348,353,414,153,491,192,292,
245)(112,335,206,390,362,136,419,538,477,498)(113,273,436,438,308,147,267,
242,531,295)(119,175,126,156,169)(120,504,412,456,121)(130,160,142,521,445)
(166,475,449,533,336,316,297,344,289,229)(171,499,385,224,427,458,232,296,
460,514)(203,368,520,235,509,286,467,311,283,318),
(1,470,137,283,15,126,62)(2,465,325,150,109,369,61)(3,439,319,488,
234,26,63)(4,482,179,34,349,409,65)(5,451,428,375,310,193,64)
(6,444,35,84,437,278,66)(7,368,75,479,164,435,399)(8,425,338,39,
396,16,501)(9,263,393,529,279,69,443)(10,206,250,106,376,305,232)
(11,149,156,254,143,172,342)(12,530,314,176,49,244,284)(13,417,267,412,
268,331,237)(14,365,353,387,207,270,341)(17,230,161,397,29,203,499)
(18,215,112,434,411,92,442)(19,507,171,323,129,79,445)(20,173,367,88,
448,400,119)(21,324,131,508,181,318,504)(22,89,483,169,345,533,280)
(23,406,83,477,506,192,178)(24,303,398,44,289,366,337)(25,320,536,91,
456,225,502)(27,522,520,524,427,328,121)(28,219,531,287,327,103,339)
(30,130,492,217,526,386,177)(31,120,48,260,87,468,118)(32,272,359,198,
74,436,285)(33,308,224,540,97,459,235)(36,381,214,128,94,449,395)
(37,162,379,186,281,53,282)(38,511,374,316,493,146,175)(40,277,59,462,
372,60,447)(41,377,297,142,191,212,123)(42,70,460,332,218,519,503)
(43,58,471,114,391,513,340)(45,187,199,518,487,231,180)(46,141,304,273,
362,344,500)(47,486,259,67,480,208,233)(50,105,336,240,261,76,446)
(51,101,472,498,132,523,394)(52,402,108,364,334,253,122)(54,335,246,311,
213,155,236)(55,450,384,174,358,163,407)(56,481,200,495,158,226,196)
(57,440,288,333,262,401,124)(68,438,309,239,222,512,371)(71,458,241,251,
134,521,535)(72,475,490,245,317,509,194)(73,464,360,185,296,113,408)
(77,473,534,294,140,293,127)(78,454,269,370,95,476,537)(80,453,423,312,
190,209,258)(81,466,110,357,210,247,274)(82,455,266,385,160,392,539)
(85,461,373,301,430,383,195)(86,457,256,102,463,347,538)(90,474,517,515,
330,138,275)(93,441,300,415,255,154,257)(96,469,151,125,99,478,197)
(98,467,144,167,421,299,410)(100,452,433,404,147,182,276)(104,322,159,265,
432,388,496)(107,348,489,271,326,145,216)(111,350,416,242,238,249,292)
(115,424,352,403,157,221,497)(116,422,295,133,514,361,329)(117,380,188,168,
405,152,153)(135,494,148,136,291,356,211)(139,315,166,414,220,484,252)
(165,426,363,378,290,343,505)(170,351,389,485,264,429,355)(183,298,382,202,
532,307,229)(184,313,201,491,243,228,189)(204,525,413,227,205,223,510)
(248,302,419,286,354,418,306)(321,516,346,528,390,527,420)]],
[3,6531840,0,"2",[[63,1],[224,1],[252,1]],1,
"U4,3 on non-isotropic projective points.3",["2A",[3,3],1],
[(1,89,433,477,320,35,468,149,285,462,511,208)(2,163,448,492,289,361,501,
51,278,495,423,249)(3,532,52,342,277,210,375,75,288,371,122,390)
(4,50,262,60,303,440,91,420,309,70,209,323)(5,124,168,261,308,432,
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(15,201,69,111)(16,286,340,237,238,302,525,71,494,293,185,199)
(17,25,517,417,135,128,454,537,329,334,402,436)(18,384,29,315,481,483,
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(20,61,313,147,355,386,310,385,143,358,314,226)(21,242,464,267,155,161,
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(32,451,133,273)(33,460,159,459,175,215,252,260,431,114,392,373)
(34,476,110,129,389,368,438,217,181,266,203,435)(37,229,382,66)
(41,179,291,330,338,466,306,499,154,126,284,198)(42,425,255,498,112,534,
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(53,81,333,516)(54,422,174,102,182,55,519,136,388,326,376,496)
(56,137,531,467,500,443,369,219,132,162,207,332)(59,193,419,504)
(62,227,189)(64,380,379,230,505,65,145,360,146,359,231,478)
(67,256,151,160,109,456,475,497,539,377,206,364)(68,317,401,212,413,275,
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(90,248,343,113)(105,281,518,461,200,305,170,486,437,287,374,395)
(108,530,130,283,412,428,197,295,236,474,453,274)(140,166,493,239)
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(260,530,420,416)(262,488,517,313)(268,450,484,431)(279,292,390,363)
(288,323,326,338)(291,332,451,441)(293,449,300,490)(296,512,455,429)
(315,426,433,401)(324,378,477,539)(330,351,489,447)(342,386,503,536)
(346,461,415,540)(348,494,508,392)(359,520,428,443),
(1,177,305,498,327,41,140)(2,269,490,495,356,136,364)(3,491,154,496,
366,350,411)(4,303,458,493,343,482,313)(5,75,414,494,333,221,19)
(6,143,66,497,354,275,161)(7,213,198,90,297,211,278)(8,103,101,376,
385,231,486)(9,423,18,412,461,417,23)(10,508,525,266,38,363,359)
(11,263,401,135,206,13,182)(12,341,108,286,523,472,234)(14,516,186,130,
310,324,123)(15,92,504,289,173,314,346)(16,325,319,89,521,195,229)
(17,281,406,377,457,419,513)(20,34,232,176,45,316,295)(21,37,162,378,
290,30,531)(22,24,26,291,132,267,146)(25,197,444,374,255,300,500)
(27,349,259,179,514,106,253)(28,157,71,131,474,388,387)(29,468,386,87,
49,192,116)(31,210,218,175,215,260,405)(32,460,466,288,483,428,194)
(33,125,79,264,268,440,110)(35,383,431,415,158,159,284)(36,292,512,88,
432,166,335)(39,445,345,133,429,538,308)(40,407,322,413,220,485,188)
(42,102,365,373,115,511,518)(43,199,505,134,148,442,352)(44,63,52,86,
227,180,393)(46,476,141,375,203,119,506)(47,348,398,262,492,282,258)
(48,222,270,178,448,397,153)(50,427,276,416,187,455,69)(51,252,441,85,
104,200,57)(53,535,391,287,242,367,91)(54,451,169,265,301,251,73)
(55,279,507,174,96,100,328)(56,196,430,59,64,285,274)(58,257,436,226,
74,246,77)(60,409,362,334,72,527,532)(61,420,138,332,189,381,517)
(62,155,223,437,183,399,426)(65,219,402,170,205,421,216)(67,82,93,113,
389,114,307)(68,396,312,336,418,233,488)(70,172,151,230,403,83,209)
(76,321,109,117,236,273,271)(78,164,357,392,254,484,225)(80,534,467,112,
137,337,181)(81,149,519,277,118,168,347)(84,315,342,228,144,536,452)
(94,201,249,438,294,449,479)(95,382,447,331,280,129,528)(97,340,296,390,
501,459,190)(98,353,126,171,530,122,471)(99,360,237,439,522,256,299)
(105,454,465,121,245,298,384)(107,503,380,184,243,371,150)(111,379,293,309,
217,145,193)(124,238,370,477,450,524,424)(127,395,473,304,462,247,147)
(128,480,152,185,481,475,212)(139,323,163,351,537,214,540)(142,410,358,306,
283,539,235)(156,191,250,272,404,394,208)(160,338,443,329,510,478,533)
(165,361,330,469,502,499,202)(167,326,244,400,526,207,464)(204,318,435,470,
456,224,302)(239,372,529,320,520,408,344)(240,369,425,261,487,422,453)
(241,368,311,355,515,434,509)(248,489,463,317,446,339,433)]],
[7,13063680,0,"2",[[63,1],[224,1],[252,1]],1,
"U4,3 on non-isotropic projective points.7",["2A",[3,3],1],
[(1,252,527,153,255,415,380,403,226,300,237,467)(2,161,421,323,427,457,244,
41,416,50,139,396)(3,377,256,211,538,65,157,276,501,423,20,47)
(4,477,468,292,19,308,178,89,36,118,511,231)(5,395,307,46,90,490,
453,224,74,347,212,198)(6,32,362,404,331,159,279,207,366,208,448,352)
(7,344,456,379,482,369,242,94,220,328,486,15)(8,238,386,353,293,105,
144,512,335,95,483,410)(9,452,502,83,265,227,284,330,471,280,122,142)
(10,507,98,35,391,443,60,114,516,117,71,465)(11,405,112,472,492,518,
349,282,435,258,262,333)(12,291,288,304,364,86,426,38,311,412,363,504)
(13,529,316,197,306,249,87,134,253,25,52,322)(14,444,389,346,84,341,
446,170,484,180,209,385)(16,299,131,145,473,429,104,398,320,128,143,165)
(17,383,218,434,26,497,433,372,45,79,82,107)(18,214,61,93,354,302,
185,524,445,334,246,225)(21,150,162,263,173,355,498,37,111,70,240,177)
(22,171,181,417,519,217,531,310,148,146,375,535)(23,430,195,289,313,523,
525,189,123,160,106,476)(24,358,172,130,378,406,485,384,138,48,91,34)
(27,285,29,420,76,188,463,530,301,39,199,440)(28,155,277,223,204,113,
254,348,339,149,474,132)(30,219,464,462,325,233,359,59,496,243,522,205)
(31,480,42,436,108,168,340,40,235,236,97,64)(33,487,156,278,140,147,
72,121,373,367,461,77)(43,56,228,321,411,469,318,536,259,505,428,215)
(44,102,408,357,438,266,393,272,66,520,400,388)(49,179,137,515,55,58,
441,342,273,407,184,152)(51,229,296,510,466,312,187,200,390,191,78,270)
(53,425,508,491,245,503,264,494,532,297,338,526)(54,528,271,537,368,327,
99,126,167,458,154,275)(57,336,387,210,521,499,455,175,350,319,370,203)
(62,176,222,239,247,402,493,324,186,269,371,432)(63,381,500,109,376,193,
314,343,419,241,450,479)(67,75,413,248,351,286,294,422,201,332,451,141)
(68,329,133,163,506,234,488,92,401,169,232,135)(69,533,290,317,257,418,
119,250,442,439,213,129)(73,447,116,399,315,268,260,103,251,151,514,495)
(80,459,517,136,166,81,509,183,345,110,513,437)(85,100,540,125,475,356,
230,287,303,470,309,449)(88,182,190,431,127,374,124,397,281,534,305,382)
(96,206,158,274,481,261,337,192,326,360,392,414)(101,194,283,460,202,174,
424,267,115,164,216,409)(120,394,295,454,361,221)(196,298,489,365,478,539),
(1,450,51,462,286,518,126,532,310,385,367,432)(2,12,238,194,299,419,200,
372,297,213,75,539)(3,535,95,255,295,43,249,473,301,258,179,378)
(4,251,105,302,306,164,342,314,316,68,16,320)(5,123,466,137,321,77,
427,206,305,534,492,480)(6,191,390,414,312,148,494,150,290,442,437,271)
(7,15,308,360,141,382,292,485,351,176,287,181)(8,481,73,254,183,499,
434,70,425,401,326,163)(9,135,221,460,374,99,89,118,147,490,210,203)
(10,172,116,519,533,115,231,364,241,441,392,177)(11,524,506,417,247,24,
107,25,520,270,79,189)(13,277,350,413,489,274,207,523,235,279,502,445)
(14,282,329,358,223,311,242,36,503,294,464,130)(17,289,370,521,161,317,
65,453,396,280,408,386)(18,303,361,197,330,284,157,61,119,307,50,261)
(19,387,185,140,340,244,236,504,108,156,101,90)(20,328,530,461)
(21,167,438,357,205,146,114,186,402,476,173,484)(22,487,136,196,410,39,
403,406,193,233,219,42)(23,222,248,298,467,208,366,319,102,88,451,315)
(26,112,435,83,538,57,121,422,256,498,243,341)(27,338,212,82)
(28,37,155,80,250,430,94,38,515,201,517,459)(29,409,318,81,120,260,
288,111,323,125,283,509)(30,471,482,84,452,491,224,211,93,429,354,265)
(31,363,384,522)(32,416,463,415,398,272,76,190,166,153,45,53)
(33,228,526,300,528,169,348,304,269,60,188,281)(34,128,127,359,478,62,
536,98,87,537,66,424)(35,216,58,252,371,104,170,397,124,456,226,145)
(40,447,152,412,346,525)(41,355)(44,182,275,138,149,132,276,217,345,469,
278,405)(46,418,144,465,180,263,162,239,381,109,475,327)(47,440,160,198,
505,495,512,257,266,393,376,63)(48,375,71,253)(49,175,493,195,472,158,
59,540,67,449,113,369)(52,352,134,139)(54,389,264,356,500,230,421,470,
225,117,103,232)(55,426,220,399,391,131,479,72,331,234,353,377)
(56,336,159,74,335,174,245,324,388,497,379,431)(64,334,322,458,368,227,
202,110,411,436,531,215)(69,192,529,343,142,347,204,444,516,527,325,273)
(78,122,199,433)(85,332,510,133,349,496,339,488,404,171,214,100)
(86,428,483,97)(91,448,246,154)(92,187,454,446,380,443,337,344,362,151,
267,268)(96,333,407,513,365,439,129,165,383,229,259,373)(106,507,262,457)
(143,395,168,511)(184,218,486,501)(209,468,400,237)(285,477,508,291,293,394,
455,296,313,514,420,309)]],
[8,26127360,0,"2",[[63,1],[224,1],[252,1]],1,
"U4,3 on non-isotropic projective points.8",["2A",[3,3],1],
[(1,248,22,199,72,425,433,479,86,49,252,340)(2,102,207,434,68,78,363,
250,90,60,439,43)(3,525,283,329,69,445,507,104,88,271,132,222)
(4,110,436,279,67,223,209,348,89,326,361,417)(5,334,505,10,70,50,
134,308,87,501,280,448)(6,474,432,119,71,116,253,36,85,419,42,174)
(7,218,169,190,355,325,122,40,539,105,23,148)(8,13,241,296,172,171,
178,240,120,121,292,175)(9,464,482,513,249,409,338,214,426,142,202,388)
(11,421,372,454,503,472,237,521,331,115,141,256)(12,156,395,349)
(14,429,459,32,359,17,522,245,535,246,261,428)(15,59,514,282,499,101,
212,506,335,74,389,131)(16,350,352,471)(18,24,406,387,304,151,143,168,
452,187,462,492)(19,226,530,194)(20,484,333,442,309,386,31,272,449,163,
502,526)(21,373,257,113,360,313,457,418,536,401,517,473)(25,258,220,180,
149,458,328,297,191,520,108,243)(26,183,61,371,430,264,91,235,254,316,
80,140)(28,415,204,489,247,277,483,381,424,345,342,164)(29,478,317,299,
306,337,184,124,451,201,266,496)(30,330,392,270,500,111,511,524,336,225,
213,443)(33,129,322,480,150,498,106,341,192,303,224,203)(34,46,310,232,
357,504,400,139,538,332,377,369)(35,166,58,153,435,486,97,189,251,379,
77,53)(37,267,145,215,305,321,461,391,453,186,410,515)(38,470,154,227)
(39,383,117,412,173,160,423,276,118,485,477,347)(41,73,123,366,356,55,
52,441,540,98,170,210)(44,274,491,103,152,346,384,221,188,416,161,323)
(45,294,182,259,307,239,262,455,450,179,318,518)(47,291,468,397)
(48,300,427,497,244,128)(51,206,94,96,431,362,82,84,255,438,63,66)
(54,509,404,81,358,130,375,62,537,281,312,93)(56,380,508,528,99,162,
133,447,75,487,284,273)(57,339,205,494,100,200,365,302,76,481,437,127)
(64,407,440,367,95,146,208,236,79,463,364,138)(65,260,510,476,92,456,
135,112,83,519,285,420)(107,319,413,211,219,185,278,390,327,263,343,512)
(109,382,444,446,217,165,268,269,324,490,527,523)(114,298,378,125,422,126,
315,495,475,493,405,301)(136,411,320,137,368,147,181,370,234,465,265,233)
(144,176,516,403,460,293,216,374,408,238,393,311)(155,531,198,354)
(157,287,286,229)(158,351,228,398)(159,467,534,193)(167,314,344,242,488,402,
414,177,385,376,275,295)(195,396,399,533)(196,466,290,532)(197,529)
(230,288,394,469)(289,353),
(1,478,188,16,494,206,105,386,195,241,201,336,535,301,401,491,106,135,117,
39,96,423,25,499,63,439,443,502)(2,486,417,70,131,271,249,426,121,
429,483,220,166,324,419,296,394,292,476,89,210,412,67,382,44,12,284,23
)(3,40,153,500,85,469,523,430,484,350,302,126,93,156,416,72,257,190,
355,242,315,383,363,99,373,273,501,77)(4,293,278,434,263,18,29,411,
364,59,424,33,305,234,379,482,496,408,294,512,372,427,265,115,422,488,
232,213)(5,392,24,245,176,342,477)(6,193,346,360,286,409,197,403,264,
522,128,82,402,53,433,123,318,457,537,384,267,407,489,200,533,142,399,361
)(7,139,506,177,410,481,157,311,214,97,17,413,69,54,528,308,349,256,
421,262,337,252,452,49,354,387,485,314)(8,76,91,189,152,38,371,327,
159,111,300,509,321,138,289,340,377,471,178,517,449,143,255,238,104,260,
222,511)(9,540,335,203,34,322,221)(10,470,140,181,285,280,462,453,376,
45,338,161,455,351,212,94,368,526,358,124,100,516,191,306,310,529,168,180
)(11,385,295,163,231,92,495,270,435,198,127,58,43,277,359,404,365,86,
112,187,174,162,428,490,30,332,110,333)(13,88,20,268,19,225,146,147,
160,136,129,64,202,447,244,459,236,530,473,61,539,445,356,451,164,316,
320,323)(14,179,116,460,125,75,56,524,150,169,28,31,21,229,73,102,
276,151,357,186,497,341,32,441,258,283,154,436)(15,130,518,288,209,46,
216,87,519,343,246,329,282,369,456,204,134,205,536,532,514,281,224,472,
81,287,269,304)(22,254,405,297,48,107,531,374,339,395,479,465,243,50,
298,182,420,120,175,468,454,103,41,425,194,508,51,165)(26,145,513,493,
114,370,319)(27,464,290,113,223,251,291,521,510,328,498,520,185,52,62,
352,446,170,475,78,79,348,149,248,228,65,312,444)(35,398,266,467,317,
226,83,239,414,68,303,347,172,144,375,406,122,42,474,57,326,192,431,
366,95,217,275,247)(36,101,253,344,432,390,487,538,259,158,199,381,388,
362,84,505,527,47,418,393,118,325,461,183,219,397,389,480)
(37,207,313,299,240,353,133)(55,137,345,504,80,450,279,173,515,218,378,
208,237,334,438,215,66,108,442,309,437,331,233,132,466,330,367,230)
(60,458,415,71,534,274,503)(74,90,272,148,307,109,211)(98,167,525,171,
250,507,227)(119,141,448,396,492,440,380)(155,235,261,463,400,196,184)]],
[9,Factorial(540)/2,1,"2",[[539,1]],538,"A_n",["A",540,1],540],
[10,Factorial(540),0,"2",[[539,1]],540,"S_n",["A",540,1],540]];
PRIMGRP[541]:=
[[1,Factorial(541)/2,1,"2",[[540,1]],539,"A_n",["A",541,1],541],
[2,Factorial(541),0,"2",[[540,1]],541,"S_n",["A",541,1],541]];
PRIMGRP[542]:=
[[1,79169940,1,"2",[[541,1]],2,"L2,541 on projective points.1",
["L",[2,541],1],
[(3,541,539,537,535,533,531,529,527,525,523,521,519,517,515,513,511,509,507,
505,503,501,499,497,495,493,491,489,487,485,483,481,479,477,475,473,471,
469,467,465,463,461,459,457,455,453,451,449,447,445,443,441,439,437,435,
433,431,429,427,425,423,421,419,417,415,413,411,409,407,405,403,401,399,
397,395,393,391,389,387,385,383,381,379,377,375,373,371,369,367,365,363,
361,359,357,355,353,351,349,347,345,343,341,339,337,335,333,331,329,327,
325,323,321,319,317,315,313,311,309,307,305,303,301,299,297,295,293,291,
289,287,285,283,281,279,277,275,273,271,269,267,265,263,261,259,257,255,
253,251,249,247,245,243,241,239,237,235,233,231,229,227,225,223,221,219,
217,215,213,211,209,207,205,203,201,199,197,195,193,191,189,187,185,183,
181,179,177,175,173,171,169,167,165,163,161,159,157,155,153,151,149,147,
145,143,141,139,137,135,133,131,129,127,125,123,121,119,117,115,113,111,
109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,
73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,
37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5)
(4,542,540,538,536,534,532,530,528,526,524,522,520,518,516,514,512,510,
508,506,504,502,500,498,496,494,492,490,488,486,484,482,480,478,476,474,
472,470,468,466,464,462,460,458,456,454,452,450,448,446,444,442,440,438,
436,434,432,430,428,426,424,422,420,418,416,414,412,410,408,406,404,402,
400,398,396,394,392,390,388,386,384,382,380,378,376,374,372,370,368,366,
364,362,360,358,356,354,352,350,348,346,344,342,340,338,336,334,332,330,
328,326,324,322,320,318,316,314,312,310,308,306,304,302,300,298,296,294,
292,290,288,286,284,282,280,278,276,274,272,270,268,266,264,262,260,258,
256,254,252,250,248,246,244,242,240,238,236,234,232,230,228,226,224,222,
220,218,216,214,212,210,208,206,204,202,200,198,196,194,192,190,188,186,
184,182,180,178,176,174,172,170,168,166,164,162,160,158,156,154,152,150,
148,146,144,142,140,138,136,134,132,130,128,126,124,122,120,118,116,114,
112,110,108,106,104,102,100,98,96,94,92,90,88,86,84,82,80,78,
76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,
40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6),
(1,2,273)(3,272,274)(4,169,376)(5,317,227)(6,65,478)(7,174,368)
(8,414,127)(9,184,356)(10,93,446)(11,232,306)(12,283,254)
(13,221,315)(14,399,136)(15,426,108)(16,35,498)(17,427,105)
(18,261,270)(19,53,477)(20,349,180)(21,479,49)(22,211,316)
(23,456,70)(24,321,204)(25,442,82)(26,287,236)(27,336,186)
(28,46,475)(29,181,339)(30,467,52)(31,160,358)(32,373,144)
(33,98,418)(34,126,389)(36,291,222)(37,311,201)(38,296,215)
(39,80,430)(40,322,187)(41,252,256)(42,328,179)(43,357,149)
(44,92,413)(45,409,95)(47,124,378)(48,511,530)(50,96,403)
(51,407,91)(54,293,202)(55,282,212)(56,392,101)(57,431,61)
(58,196,295)(59,387,103)(60,88,401)(62,175,312)(63,269,217)
(64,383,102)(66,223,260)(67,525,497)(68,481,540)(69,493,527)
(71,500,518)(72,394,83)(73,400,76)(74,262,213)(75,258,216)
(77,193,279)(78,110,361)(79,516,494)(81,351,117)(84,298,167)
(85,165,299)(86,99,364)(87,243,219)(89,203,257)(90,523,476)
(94,326,129)(97,302,150)(100,453,536)(104,521,464)(106,318,125)
(107,271,171)(109,140,300)(111,297,141)(112,238,199)(113,158,278)
(114,304,131)(115,489,485)(116,466,507)(118,237,194)(119,529,441)
(120,531,438)(121,305,123)(122,162,265)(128,448,513)(130,266,153)
(132,538,419)(133,454,502)(134,176,239)(135,214,200)(137,501,451)
(138,205,206)(139,495,455)(142,198,209)(143,450,496)(145,458,486)
(146,473,470)(147,532,410)(148,156,245)(151,226,172)(152,474,463)
(154,490,445)(155,161,233)(157,420,512)(159,487,443)(163,482,444)
(164,208,177)(166,192,191)(168,422,499)(170,377,542)(173,514,402)
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],[3,Factorial(542)/2,1,"2",[[541,1]],540,"A_n",["A",542,1],542
],[4,Factorial(542),0,"2",[[541,1]],542,"S_n",["A",542,1],542]
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PRIMGRP[549]:=
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PRIMGRP[550]:=
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PRIMGRP[551]:=
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PRIMGRP[552]:=
[[1,Factorial(552)/2,1,"2",[[551,1]],550,"A_n",["A",552,1],552],
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PRIMGRP[553]:=
[[1,78156525216,1,"2",[[552,1]],2,"L3,23 on projective points.1",
["L",[3,23],1],
[(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24)(26,46,44,42,40,38,36,34,32,30,28)(27,47,45,43,
41,39,37,35,33,31,29)(48,531,508,485,462,439,416,393,370,347,324,
301,278,255,232,209,186,163,140,117,94,71)(49,552,527,502,477,452,427,
402,377,352,327,302,299,274,249,224,199,174,149,124,99,74)
(50,553,528,503,478,453,428,403,378,353,328,303,300,275,250,225,200,175,
150,125,100,75)(51,532,529,504,479,454,429,404,379,354,329,304,279,276,
251,226,201,176,151,126,101,76)(52,533,530,505,480,455,430,405,380,355,
330,305,280,277,252,227,202,177,152,127,102,77)(53,534,509,506,481,456,
431,406,381,356,331,306,281,256,253,228,203,178,153,128,103,78)
(54,535,510,507,482,457,432,407,382,357,332,307,282,257,254,229,204,179,
154,129,104,79)(55,536,511,486,483,458,433,408,383,358,333,308,283,258,
233,230,205,180,155,130,105,80)(56,537,512,487,484,459,434,409,384,359,
334,309,284,259,234,231,206,181,156,131,106,81)(57,538,513,488,463,460,
435,410,385,360,335,310,285,260,235,210,207,182,157,132,107,82)
(58,539,514,489,464,461,436,411,386,361,336,311,286,261,236,211,208,183,
158,133,108,83)(59,540,515,490,465,440,437,412,387,362,337,312,287,262,
237,212,187,184,159,134,109,84)(60,541,516,491,466,441,438,413,388,363,
338,313,288,263,238,213,188,185,160,135,110,85)(61,542,517,492,467,442,
417,414,389,364,339,314,289,264,239,214,189,164,161,136,111,86)
(62,543,518,493,468,443,418,415,390,365,340,315,290,265,240,215,190,165,
162,137,112,87)(63,544,519,494,469,444,419,394,391,366,341,316,291,266,
241,216,191,166,141,138,113,88)(64,545,520,495,470,445,420,395,392,367,
342,317,292,267,242,217,192,167,142,139,114,89)(65,546,521,496,471,446,
421,396,371,368,343,318,293,268,243,218,193,168,143,118,115,90)
(66,547,522,497,472,447,422,397,372,369,344,319,294,269,244,219,194,169,
144,119,116,91)(67,548,523,498,473,448,423,398,373,348,345,320,295,270,
245,220,195,170,145,120,95,92)(68,549,524,499,474,449,424,399,374,349,
346,321,296,271,246,221,196,171,146,121,96,93)(69,550,525,500,475,450,
425,400,375,350,325,322,297,272,247,222,197,172,147,122,97,72)
(70,551,526,501,476,451,426,401,376,351,326,323,298,273,248,223,198,173,
148,123,98,73),(1,2,25,301,313,3,26,255,311,361,51,446,79,543,
15,38,462,320,385,340,194,548,227,139,425,150,354,75,109,328,98,110,206,
164,259,95,256,263,551,179,187,260,287,144,112,134,231,429,464,394,269,
69,494,153,474,18,41,186,308,73,399,511,444,295,216,91,181,137,183,
185,427,246,68,180,211,405,21,44,370,316,337,482,176,475,466,104,352,
291,480,128,233,262,93,423,78,85,61,470,538,83,13,36,232,310,145,
282,96,400,77,519,250,118,257,407,53,300,432,198,8,31,508,322,505,
177,65,228,381,244,6,29,94,304,457,127,353,509,274,383,484,418,414,
487,395,413,173,355,533,397,101,86,327,458,391,486,273,119,401,535,107,
472,368,507,419,440,271,191,284,528,178,331,74,447,537,517,154,64,204,
138,497,17,40,324,314,481,392,436,174,235,454,343,386,196,356,147,88,
229,165,403,365,123,521,468,514,516,540,155,330,530,420,102,544,469,80,
157,210,261,527,372,412,389,388,124,87,205,380,364,219,357,363,195,162,
426,366,387,220,237,286,552,493,539,541,349,411,125,545,59,252,166,451,
19,42,209,309,553,421,294,192,524,202,188,404,245,478,200,66,132,329,
290,4,27,393,317,193,90,375,292,70,422,512,106,12,35,347,315,49,
276,503,129,11,34,140,306,289,240,550,373,460,489,105,254,430,54,518,
348,267,5,28,439,319,121,111,230,501,201,332,532,275,167,113,376,510,
396,461,417,270,335,242,358,243,238,526,130,473,248,190,114,182,379,148,
546,325,266,239,92,495,369,435,390,172,161,498,467,296,120,449,367,171,
547,203,212,453,55,84,471,152,10,33,531,323,433,222,477,344,170,89,
133,207,500,345,506,491,515,82,253,502,225,189,452,465,442,441,415,437,
488,443,103,158,136,377,76,279,264,143,450,247,334,362,339,338,50,398,
293,336,24,47,416,318,217,549,131,63,326,410,221,7,30,278,312,241,
142,402,149,160,184,499,57,156,208,428,20,43,117,305,97,448,151,234,
406,463,272,215,525,226,213,115,496,249,214,285,72,277,431,342,122,281,
456,223,67,374,100,520,16,39,48,302,265,359,23,46,485,321,169,523,
346,434,126,159,378,534,445,513,298,168,283,288,360,483,490,297,384,52,
108,62,60,14,37)(9,32,71,303,409,197,236,116,424,536,299,504,371,
268,479,224,333,146,522,58,350,459,175)(22,45,163,307,529,492,81,351,
99,280,408,341,218,141,258,455,199,476,56,542,251,382)]],
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[3,Factorial(553),0,"2",[[552,1]],553,"S_n",["A",553,1],553]];
PRIMGRP[554]:=
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[2,Factorial(554),0,"2",[[553,1]],554,"S_n",["A",554,1],554]];
PRIMGRP[555]:=
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