#############################################################################
##
#A  prim10.grp                 GAP group library             Heiko Theissen
#A                                                          John Dixon
#A                                                          Brian Mortimer
#A                                                          Charles Sims
##
#A  @(#)$Id: prim10.grp,v 1.2 2000/01/18 15:59:26 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.prim10_grp:=
"@(#)$Id: prim10.grp,v 1.2 2000/01/18 15:59:26 ahulpke Exp $";

PRIMGRP[380]:=
[[1,27219780,1,"2",[[379,1]],2,"L2,379 on projective points.1",
["L",[2,379],1],
[(3,379,377,375,373,371,369,367,365,363,361,359,357,355,353,351,349,347,345,
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)(4,380,378,376,374,372,370,368,366,364,
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),
(1,2,192)(3,191,193)(4,55,328)(5,48,334)(6,296,85)(7,77,303)
(8,216,163)(9,113,265)(10,326,51)(11,16,360)(12,305,70)
(13,222,152)(14,197,176)(15,104,268)(17,350,20)(18,127,242)
(19,99,269)(21,184,182)(22,214,151)(23,124,240)(24,368,373)
(25,161,201)(26,283,78)(27,52,308)(28,247,112)(29,228,130)
(30,108,249)(31,236,120)(32,89,266)(33,274,80)(34,367,364)
(35,316,36)(37,209,141)(38,203,146)(39,210,138)(40,158,189)
(41,262,84)(42,248,97)(43,167,177)(44,102,241)(45,267,75)
(46,106,235)(47,63,277)(49,199,139)(50,336,379)(53,114,220)
(54,186,147)(56,329,380)(57,140,190)(58,374,333)(59,205,123)
(60,263,64)(61,154,172)(62,86,239)(65,72,250)(66,92,229)
(67,95,225)(68,349,348)(69,224,94)(71,213,103)(73,87,227)
(74,133,180)(76,332,357)(79,372,314)(81,307,377)(82,215,90)
(83,173,131)(88,378,299)(91,196,100)(93,166,128)(96,126,165)
(98,111,178)(101,358,306)(105,150,132)(107,321,337)(109,153,125)
(110,351,304)(115,285,365)(116,280,369)(117,339,309)(118,295,352)
(119,271,375)(121,324,320)(122,343,300)(134,312,319)(135,276,354)
(136,342,287)(137,356,272)(142,257,366)(143,282,340)(144,260,361)
(145,298,322)(148,353,264)(149,278,338)(155,292,318)(156,355,254)
(157,297,311)(159,289,317)(160,315,290)(162,371,232)(164,270,331)
(168,376,221)(169,302,294)(170,362,233)(171,313,281)(174,345,246)
(175,347,243)(179,325,261)(181,346,238)(183,223,359)(185,335,245)
(187,370,208)(188,293,284)(194,244,327)(195,226,344)(198,330,237)
(200,363,202)(204,251,310)(206,273,286)(207,217,341)(211,301,253)
(212,230,323)(218,291,256)(219,258,288)(231,275,259)(234,279,252)]],
[2,54439560,0,"2",[[379,1]],3,"L2,379 on projective points.2",
["L",[2,379],1],
[(1,151,8,85,138,380,251,82,162,261,302,257,168,92,83,247,200,121,4,
297,245,137,317,111,161,145,193,5,113,45,356,97,231,160,190,195,256,
215,266,43,355,372,244,175,328,179,358,260,235,321,99,16,65,3,186,
106,379,107,88,287,21,326,363,30,34,136,32,135,144,13,269,7,125,
182,226,101,373,329,153,234,324,158,246,172,313,249,206,285,59,44,209,
319,81,152,253,80,295,301,264,62,220,170,54,369,66,310,298,262,108,
57,130,221,167,205,237,198,323,288,286,71,67,87,169,42,142,242,115,
197,217,213,376,374,339,86,47,79,117,63,154,227,176,22,364,352,218,
293,230,114,64,222,20,361,367,204,31,132,203,343,75,240,225,377,78,
35,349,112,38,126,338,50,131,333,289,183,58,102,159,277,15,271,140,
149,252,148,250,254,299,336,263,375,196,177,283,178,98,281,219,268,185,
341,49,24,304,105,334,109,40,290,307,241,18,69,28,89,94,124,53,
187,306,239,171,279,91,139,123,173,345,147,39,365,280,163,84,37,201,
192,116,27,360,23,122,202,33,282,146,199,276,133,2,340,294,346,73,
194,189,70,366,19,11,181,327,300,141,371,76,6,46,359,248,258,274,
164,348,25,207,233,93,156,155,350,157,229,12,110,344,330,309,292,29,
9,357,210,354,118,61,48,104,72,378,232,325,270,150,216,320,347,56,
165,184,351,41,188,224,331,60,96,243,311,100,119,228,315,342,68,134,
14,337,52,284,212,180,236,223,166,308,74,305,275,255,370,353,332,318,
174,272,55,127,312,129,128,191,51,77,259,314,120,10,26,36,303,238,
278,208,291,143,362,335,103,273,265,296,214,95,90,211,316,368,322),
(1,227,237,296,251,375,35,114,209,178,147,242,321,359,105,60,119,129,2,
7,125,330,34,220,206,187,50,117,82,94,378,276,347,353,282,248,46,
307,309,84,23,95,232,78,58,313,141,367,215,43,298,278,124,261,333,
272,47,49,310,108,74,3,9,80,356,262,274,239,306,169,150,136,322,
26,231,349)(4,357,122,350,72,15,101,260,244,235,89,198,90,39,127,
18,140,5,380,294,287,16,211,113,376,111,19,193,202,265,252,320,345,
192,68,241,316,246,156,208,20,256,142,86,106,277,273,286,166,54,305,
365,236,291,184,325,57,314,223,271,222,92,374,143,146,230,188,311,224,
344,149,363,324,71,13,332)(6,234,377,352,24,343,285,32,371,207,12,
132,45,168,126,210,213,360,264,134,85,133,42,299,31,172,65,120,369,
51,302,190,70,83,79,250,270,214,100,336,148,200,110,40,115,288,164,
11,36,104,91,154,163,337,245,358,243,145,340,69,62,354,351,216,338,
229,317,266,158,267,121,112,96,255,341,284)(8,238,61,107,27,22,176,
44,73,212,76,269,56,161,346,189,240,173,247,263,191,218,368,194,228,
342,290,301,233,254,268,21,362,67,197,182,361,152,319,323,297,186,205,
326,293,77,139,196,364,25,181,48,226,292,29,221,257,355,179,203,81,
41,201,339,38,258,28,219,131,259,103,199,171,303,281,52)
(10,195,300,87,280,144,283,312,180,334,329,249,295,118,348,304,75,53,
185,157,253,97,225,137,328,98,318,17,155,315,275,153,177,379,99,135,
327,64,130,308,175,331,370,160,217,279,63,30,151,170,59,33,37,204,
373,174,159,289,372,335,88,102,123,55,66,14,128,162,366,138,165,93,
109,183,116,167)]],
[3,Factorial(380)/2,1,"2",[[379,1]],378,"A_n",["A",380,1],380],
[4,Factorial(380),0,"2",[[379,1]],380,"S_n",["A",380,1],380]];
PRIMGRP[381]:=
[[1,5644682640,1,"2",[[380,1]],2,"L3,19 on projective points.1",
["L",[3,19],1],
[(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)
(22,38,36,34,32,30,28,26,24)(23,39,37,35,33,31,29,27,25)
(40,363,344,325,306,287,268,249,230,211,192,173,154,135,116,97,78,59)
(41,380,359,338,317,296,275,254,233,212,209,188,167,146,125,104,83,62)
(42,381,360,339,318,297,276,255,234,213,210,189,168,147,126,105,84,63)
(43,364,361,340,319,298,277,256,235,214,193,190,169,148,127,106,85,64)
(44,365,362,341,320,299,278,257,236,215,194,191,170,149,128,107,86,65)
(45,366,345,342,321,300,279,258,237,216,195,174,171,150,129,108,87,66)
(46,367,346,343,322,301,280,259,238,217,196,175,172,151,130,109,88,67)
(47,368,347,326,323,302,281,260,239,218,197,176,155,152,131,110,89,68)
(48,369,348,327,324,303,282,261,240,219,198,177,156,153,132,111,90,69)
(49,370,349,328,307,304,283,262,241,220,199,178,157,136,133,112,91,70)
(50,371,350,329,308,305,284,263,242,221,200,179,158,137,134,113,92,71)
(51,372,351,330,309,288,285,264,243,222,201,180,159,138,117,114,93,72)
(52,373,352,331,310,289,286,265,244,223,202,181,160,139,118,115,94,73)
(53,374,353,332,311,290,269,266,245,224,203,182,161,140,119,98,95,74)
(54,375,354,333,312,291,270,267,246,225,204,183,162,141,120,99,96,75)
(55,376,355,334,313,292,271,250,247,226,205,184,163,142,121,100,79,76)
(56,377,356,335,314,293,272,251,248,227,206,185,164,143,122,101,80,77)
(57,378,357,336,315,294,273,252,231,228,207,186,165,144,123,102,81,60)
(58,379,358,337,316,295,274,253,232,229,208,187,166,145,124,103,82,61),
(1,2,21,211,221,3,22,192,220,241,42,312,86,354,14,33,135,217,81,
254,365,311,368,371,351,168,178,379,129,276,346,310,66,171,298,45,372,
231,202,4,23,306,226,101,73,191,339,187,179,79,194,320,186,279,44,
70,51,50,12,31)(5,24,249,223,141,95,294,165,56,130,176,259,19,
38,287,225,181,359,108,53,272,64,373,13,32,40,212,201,240,20,39,
325,227,121,376,271,264,103,93,112,113,133,296,245,102,375,149,177,77,
333,349,370,169,98,195,260,43,252,263,183)(6,25,59,213,321,106,235,
364,209,300,285,304,305,327,309,266,303,125,236,82,72,273,366,251,323,
288,205,280,144,237,162,358,188,99,315,246,122,94,132,134,336,47,170,
118,316,16,35,173,219,361,290,265,123,156,318,146,55,110,275,164)
(7,26,363,229,341,127,54,190,299,145)(8,27,78,214,261,143,357,270,
324,328,267,343,329,67,353,248,342,289,307,206,180,159,378,109,153,337,
147,137,317,46,90,152,297,17,36,97,215,61,313,166,138,257,345,208,
120,74,111,175,319,286,326,207,100,255,83,374,49,232,322,126)
(9,28,154,218,161,158,76,293,85,172,338,269,204,140,377,189,119,256,
163,238,362,330,369,89,52,150,115,335,15,34,268,224,281,284,124,356,
148,277,244,182,239,242,142,157,258,243,282,184,57,292,367,69,11,30,
230,222,41,210,340,107)(10,29,344,228,301,185,139,75,131,114,295,347,
250,203,58,332,167,278,18,37,116,216,381,331,87,234,62,253,63,71,
151,117,196,60,193,200,360,128,136,197,380,291,65,91,274,84,92,174,
199,160,96,334,247,302,105,355,48,352,350,88)(68,233,262,283,104,155,
198,80,314,348)]],
[2,16934047920,0,"2",[[380,1]],2,"L3,19 on projective points.2",
["L",[3,19],1],
[(1,53,372,152,51,128,34,71,224,322,245,231,379,202,298,100,230,192,234,
187,250,150,268,364,116,165,351,198,335,8,359,80,380,55,222,365,253,
260,206,140,352,341,258,122,255,175,62,204,319,274,195,350,155,294,101,
14,327,149,247,50,347,229,131,354,363,270,279,37,156,161,85,271,177,
278,172,142,168,218,212,200,24,125,13,214,259,228,52,338,188,191,367,
331,355,145,189,35,183,232,6,16,121,342,57,40,3,193,11,76,44,
323,56,151,328,273,301,112,170,370,360,127,77,326,307,251,343,221,25,
288,102,136,27,93,207,377,381,70,184,321,119,378,29,374,296,108,82,
362,7,147,205,209,42,31,282,333,210,163,199,134,246,83,33,357,348,
26,211,138,61,346,314,345,68,244,308,292,99,185,129,287,107,340,63,
366,309,146,254,10,248,290,114,43,92,65,21,311,88,126,197,265,291,
105,69,144,316,67,84,315,337,300,98,358,299,110,267,276,118,87,158,
237,36,141,375,243,336,325,86,216,277,78,339,157,332,242,72,124,310,
201,181,135,220,305,109,281,240,261,167,28,5,263,344,190,46,235,120,
213,236,153,96,249,75,18,306,39,38,58,179,295,111,30,252,22,329,
132,280,148,19,160,275,266,45,169,256,373,79,241,217,73,284,312,215,
154,123,143,302,106,368,178,203,269,223,186,159,66,64,324,320,20,272,
74,304,2,104,317,171,47,289,97,293,113,219,15,182,227,361,54,196,
90,91,137,117,176,4,94,174,95,48,257,239,353,283,17,371,166)
(9,32,238,285,49,60,164,313,173,356,262,81,303,115,194,226,330,369)
(12,297,103,133,41,286,349,233,162,180,334,23,208,59,264,318,376,225,89
),(1,110,255,268,65,322,217,260,27,145,274,67,179,193,160,123,122,
358,331,290,103,334,236,156,369,381,141,57,350,33,312,13,293,226,198,235
)(2,61,85,240,80,208,86,256,96,367,81,102,91,323,79,55,92,155,
78,219,83,186,88,353,82,147,90,130,87,10,95,39,89,298,94,271)
(3,174,318,150,176,113,363,261,352,165,159,338,269,62,108,14,58,273,
72,49,303,320,266,247,327,348,131,29,215,211,149,297,202,134,237,365)
(4,371,301,128,212,246,42,259,139,17,336,152,368,281,75,329,258,220,
347,98,183,157,109,292,34,36,248,175,116,203,207,313,275,59,171,54)
(5,242,232,213,337,170,354,263,51,125,188,279,73,344,286,60,136,25,
380,321,163,153,192,7,218,48,309,107,37,178,262,328,105,209,291,294)
(6,119,100,115,359,227,133,249,316,185,372,41,229,296,333,373,241,308,
35,282,63,26,167,200,52,332,197,148,142,169,288,355,173,234,270,76)
(8,206,379,161,253,189,305,267,168,245,137,315,306,330,129,299,190,143,
238,23,43,114,222,364,201,278,66,214,112,120,335,40,22,11,349,357)
(9,154,182,38,132,151,250,254,205,225,28,356,50,378,361,195,97,47,
146,343,223,272,77,126,311,300,158,317,233,99,276,68,377,181,340,20)
(12,310,196,345,370,341,32,257,117,285,71,210,342,180,187,216,319,374,
221,15,283,69,295,135,360,239,251,302,45,53,230,118,172,24,106,166)
(16,144,127,44,162,284,74,264,375,21,287,366,101,244,194,184,351,304,
277,64,243,346,140,224,191,18,31,326,339,324,56,204,252,104,307,124)
(19,265)(30,199)(46,177)(70,280)(93,325)(111,138)(121,376)(164,228)
(231,289)(314,362)]],
[3,Factorial(381)/2,1,"2",[[380,1]],379,"A_n",["A",381,1],381],
[4,Factorial(381),0,"2",[[380,1]],381,"S_n",["A",381,1],381]];
PRIMGRP[382]:=
[[1,Factorial(382)/2,1,"2",[[381,1]],380,"A_n",["A",382,1],382],
[2,Factorial(382),0,"2",[[381,1]],382,"S_n",["A",382,1],382]];
PRIMGRP[383]:=
[[1,Factorial(383)/2,1,"2",[[382,1]],381,"A_n",["A",383,1],383],
[2,Factorial(383),0,"2",[[382,1]],383,"S_n",["A",383,1],383]];
PRIMGRP[384]:=
[[1,28090752,1,"2",[[383,1]],2,"L2,383 on projective points.1",
["L",[2,383],1],
[(3,383,381,379,377,375,373,371,369,367,365,363,361,359,357,355,353,351,349,
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)(4,384,382,380,378,376,374,372,
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),(1,2,194)(3,60,328)(4,234,153)(5,205,181)
(6,210,175)(7,300,84)(8,28,355)(9,252,130)(10,43,338)
(11,95,285)(12,129,250)(13,257,121)(14,323,54)(15,151,225)
(16,201,174)(17,58,316)(18,127,246)(19,61,311)(20,251,120)
(21,53,317)(22,340,29)(23,160,208)(24,87,280)(25,198,168)
(26,206,159)(27,125,239)(30,67,294)(31,319,41)(32,248,111)
(33,360,380)(34,275,82)(35,288,68)(36,245,110)(37,59,295)
(38,196,157)(39,256,96)(40,139,212)(42,123,226)(44,219,128)
(45,122,224)(46,227,118)(47,102,242)(48,366,359)(49,291,51)
(50,345,378)(52,253,86)(55,81,255)(56,62,273)(57,218,116)
(63,204,124)(64,156,171)(65,374,334)(66,173,152)(69,357,347)
(70,209,112)(71,335,367)(72,330,371)(73,75,243)(74,150,167)
(76,92,223)(77,327,369)(78,172,141)(79,195,117)(80,177,134)
(83,203,105)(85,109,197)(88,381,304)(89,147,155)(90,200,101)
(91,114,186)(93,329,351)(94,321,358)(97,339,337)(98,189,104)
(99,144,148)(100,353,320)(103,293,377)(106,119,166)(107,158,126)
(108,301,364)(113,354,306)(115,326,332)(131,375,267)(132,349,292)
(133,307,333)(135,336,302)(136,379,258)(137,368,268)(138,259,376)
(140,356,277)(142,261,370)(143,352,278)(145,313,315)(146,286,341)
(149,263,361)(154,384,235)(161,342,270)(162,265,346)(163,237,373)
(164,266,343)(165,296,312)(169,344,260)(170,331,272)(176,249,348)
(178,382,213)(179,318,276)(180,228,365)(182,362,229)(183,383,207)
(184,325,264)(185,305,283)(187,372,214)(188,298,287)(190,363,220)
(191,279,303)(192,350,231)(193,309,271)(199,290,284)(202,274,297)
(211,308,254)(215,322,236)(216,310,247)(217,232,324)(221,238,314)
(222,269,282)(230,281,262)(233,241,299)(240,244,289)]],
[2,56181504,0,"2",[[383,1]],3,"L2,383 on projective points.2",
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[(1,234,6,167,239,312,119,374,191,270,163,177,273,147,240,70,295,206,283,
335,66,153,383,43,382,32,318,176,31,34,54,213,221,35,302,123,362,
322,280,277,152,82,216,333,256,310,142,288,344,261,125,120,202,168,328,
45,341,300,96,16,380,14,27,316,78,264,368,33,214,321,272,251,252,
326,131,279,36,128,192,19,253,296,196,37,381,364,373,275,100,235,170,
228,175,55,327,160,227,201,241,294,199,211,140,76,122,200,20,355,287,
229,343,204,304,40,205,230,336,111,72,357,255,363,197,360,305,51,24,
93,159,247,135,237,347,26,47,311,18,236,107,219,377,323,92,244,242,
60,291,56,126,375,346,165,7,370,267,317,198,246,332,178,109,46,136,
162,324,268,84,48,116,376,65,13,104,224,284,79,173,99,182,103,297,
299,298,95,308,314,190,271,29,258,154)(2,231,127,356,114,195,71,77,
290,87,86,88,282,203,286,212,306,101,161,281,372,320,9,269,337,301,
117,61,223,249,339,276,207,53,139,187,68,118,15,378,220,39,10,259,
329,94,325,143,141,293,62,8,166,278,149,367,74,338,359,38,148,250,
138,226,292,361,334,80,25,188,22,130,28,313,274,49,155,180,345,81,
181,42,156,98,30,365,185,263,309,245,174,186,91,144,184,158,225,58,
330,210,157,215,150,285,110,12,21,4,348,189,89,132,366,193,257,349,
106,254,59,133,134,113,64,171,352,17,121,307,69,358,371,5,369,289,
85,44,340,57,217,183,265,260,124,41,97,243,75,129,52,169,303,233,
108,105,63,23,262,83,350,164,172,331,351,354,209,67,353,3,342,384,
232,319,50,102,179,90,315,145,238,112,208,222,115,194,11,266,73,146,
218,379,151),(1,340,144,333,52,353,289,47,56,131,25,209,180,256,75,
115,204,282,177,63,114,253,187,291,295,39,83,140,249,11,124,183,379,
16,87,13,206,382,230,188,319,119,207,20,185,383,264,149,26,55,311,
327,218,364,142,160,224,41,76,345,352,344,72,102,22,376,314,137,322,
143,164,155,120,182,122,99,254,170,58,21,194,360,215,94,274,34,240,
312,3,308,213,154,61,301,111,336,62,112,85,59,162,350,337,23,217,
381,335,299,284,260,28,250,303,346,378,320,234,134,146,6,29,241,363,
98,150,278,370,300)(2,211,141,233,361,31,148,270,100,123,365,377,277,
191,133,165,208,261,101,251,227,212,176,130,294,106,174,161,349,70,44,
17,67,175,18,210,68,357,298,203,126,199,271,95,237,35,296,151,317,
108,71,341,257,30,7,329,9,356,347,368,189,374,197,135,107,27,57,
167,159,166,53,88,287,351,369,147,293,184,200,74,103,362,247,128,326,
109,304,10,192,323,281,129,305,116,42,113,132,328,5,118,262,371,46,
90,216,220,324,258,15,66,334,229,307,14,54,255,331,302,104,380,73,
82,222,158,77,178,367,171)(4,110,138,117,332,245,286,168,205,372,297,
8,91,96,259,375,292,157,32,384,156,238,190,40,24,193,181,330,318,
105,89,321,273,355,127,97,354,219,136,252,33,38,121,214,139,306,343,
225,266,179,12,373,19,125,173,348,186,276,309,201,69,366,80,195,242,
244,339,223,272,280,36,81,78,45,152,50,86,243,236,226,265,169,65,
358,37,198,196,283,232,263,290,221,248,279,228,315,313,92,153,64,342,
246,285,275,268,43,79,359,84,51,48,93,231,239,288,172,267,269,316,
49,145,60,310,202,235,325,163,338)]],
[3,Factorial(384)/2,1,"2",[[383,1]],382,"A_n",["A",384,1],384],
[4,Factorial(384),0,"2",[[383,1]],384,"S_n",["A",384,1],384]];
PRIMGRP[385]:=
[[1,Factorial(385)/2,1,"2",[[384,1]],383,"A_n",["A",385,1],385],
[2,Factorial(385),0,"2",[[384,1]],385,"S_n",["A",385,1],385]];
PRIMGRP[386]:=
[[1,Factorial(386)/2,1,"2",[[385,1]],384,"A_n",["A",386,1],386],
[2,Factorial(386),0,"2",[[385,1]],386,"S_n",["A",386,1],386]];
PRIMGRP[387]:=
[[1,Factorial(387)/2,1,"2",[[386,1]],385,"A_n",["A",387,1],387],
[2,Factorial(387),0,"2",[[386,1]],387,"S_n",["A",387,1],387]];
PRIMGRP[388]:=
[[1,Factorial(388)/2,1,"2",[[387,1]],386,"A_n",["A",388,1],388],
[2,Factorial(388),0,"2",[[387,1]],388,"S_n",["A",388,1],388]];
PRIMGRP[389]:=
[[1,Factorial(389)/2,1,"2",[[388,1]],387,"A_n",["A",389,1],389],
[2,Factorial(389),0,"2",[[388,1]],389,"S_n",["A",389,1],389]];
PRIMGRP[390]:=
[[1,29431740,1,"2",[[389,1]],2,"L2,389 on projective points.1",
["L",[2,389],1],
[(3,389,387,385,383,381,379,377,375,373,371,369,367,365,363,361,359,357,355,
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)(4,390,388,386,384,
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),
(1,2,197)(3,196,198)(4,314,79)(5,113,279)(6,43,348)(7,209,181)
(8,142,247)(9,81,307)(10,273,114)(11,334,52)(12,286,99)
(13,291,93)(14,162,221)(15,30,352)(16,311,70)(17,362,18)
(19,130,248)(20,305,72)(21,265,111)(22,54,321)(23,330,44)
(24,159,214)(25,284,88)(26,215,156)(27,41,329)(28,98,271)
(29,91,277)(31,154,212)(32,377,376)(33,211,153)(34,231,132)
(35,256,106)(36,160,201)(37,176,184)(38,290,69)(39,151,207)
(40,255,102)(42,364,379)(45,267,85)(46,351,388)(47,217,133)
(48,144,205)(49,289,59)(50,229,118)(51,251,95)(53,86,258)
(55,74,268)(56,216,125)(57,174,166)(58,208,131)(60,383,342)
(61,92,244)(62,171,164)(63,134,200)(64,371,350)(65,353,367)
(66,170,161)(67,124,206)(68,222,107)(71,236,90)(73,340,372)
(75,155,167)(76,169,152)(77,116,204)(78,199,120)(80,390,315)
(82,219,96)(83,378,324)(84,168,145)(87,313,385)(89,374,322)
(94,101,202)(97,191,109)(100,148,149)(103,381,301)(104,356,325)
(105,345,335)(108,382,295)(110,369,306)(112,128,157)(115,281,389)
(117,303,365)(119,141,137)(121,384,280)(122,140,135)(123,296,366)
(126,320,339)(127,349,309)(129,373,283)(136,308,341)(138,359,288)
(139,354,292)(143,343,299)(146,264,375)(147,252,386)(150,302,333)
(158,323,304)(163,360,262)(165,344,276)(172,326,287)(173,232,380)
(175,312,298)(177,347,261)(178,338,269)(179,368,238)(180,235,370)
(182,240,363)(183,361,241)(185,387,213)(186,336,263)(187,243,355)
(188,270,327)(189,250,346)(190,278,317)(192,293,300)(193,234,358)
(194,260,331)(195,316,274)(203,297,285)(210,218,357)(220,337,228)
(223,332,230)(224,328,233)(225,318,242)(226,310,249)(227,239,319)
(237,266,282)(245,246,294)(253,275,257)(254,272,259)]],
[2,58863480,0,"2",[[389,1]],3,"L2,389 on projective points.2",
["L",[2,389],1],
[(1,29,83,314,184,134,245,224,334,166,348,33,69,219,151,307,371,139,71,
221,257,330,124,344,66,45,156,106,364,207,261,2,10,38,291,290,127,
287,143,389,16,48,304,49,19,182,360,61,46,218,308,267,138,204,259,
266,277,85,60,235,310,343,336,26,140,15,223,319,386,286,200,5,232,
353,278,302,315,295,297,198,91,111,279,52,188,149,135,173,372,116,210,
95,142,248,317,93,192,338,305,322,276,213,158,64,270,186,251,300,53,
215,225,191,43,339,247,99,65,75,237,378,39,104,20,226,132,77,14,
356,373,340,98,197,361,42,148,195,80,174,306,117,155,141,102,238,11,
179,199,92,381,383,363,376,12,325,58,285,90,4,292,359,67,275,150,
264,342,335,368,55,230,205,13,24,31,86,152,23,370,72,244,229,318,
108,271,241,374,242,274,289,147,3,163,388,387,252,280)(6,36,272,129,
8,165,27,240,326,202,180,385,321,324,250,137,379,296,203,122,341,34,
331,332,181,366,194,171,355,176,283,365,144,100,212,234,56,78,190,146,
313,7,114,323,119,96,312,109,346,347,256,337,168,87,382,299,153,40,
354,357,293,110,88,352,50,263,125,282,161,18,254,284,97,349,89,157,
265,214,154,175,233,160,44,81,183,17,351,281,268,320,170,288,118,333,
178,51,189,377,258,62,316,236,105,123,216,369,37,217,177,220,103,164,
169,311,222,41,82,206,59,47,63,35,94,380,21,350,384,162,131,30,
211,303,28,145,262,375,79,260,159,128,294,328,269,298,196,255,227,243,
231,84,208,249,68,367,121,126,187,70,113,73,253,309,74,167,185,54,
362,228,32,301,101,239,112,345,172,390,120,358,22,9,327,273,107,209,
246,130,57,115,136,76,25,133,201,329,193),
(1,42,204,213,145,214,346,35,344,73,278,61,321,211,129,29,185,324,195,
250,181,166,215,137,312,119,234,251,5,198,279,136,120,102,133,95,123,
357,361,297,50,162,368,281,97,288,269,149,94,305,239,99,247,224,328,
113,165,291,316,286,240,169,78,248,311,298,343,124,194,327,156,75,364,
59,160,386,303,33,258,7,168,121,322,183,57,272,294,289,217,98,70,
63,13,111,31,354,296,370,174,51,350,186,27,384,56,340,159,342,190,
233,377,388,188,52,282,276,82,339,189,243,362,249,10,164,172,39,223,
9,375,300,109,277,88,256,65,378,356,142,326,193,201,355,116,3,122,
176,26,283,89,83,313,177,365,376,132,175,23,206,25,309,369,338,179,
15,314,191,383,69,11,334,254,352,302,295,267,148,76,71,93,308,182,
43,244,197,358,107,332,62,367,205,306,389,290,209,38,171,241,22,67,
54,117,287,196,125,79,49,74,200,252,37,141,118,266,126,60,271,216,
96,77,268,84,385,203,315,68,4,8,242,270,232,263,245,229,86,167,
360,114,131,246,53,228,150,199,184,115,170,41,180,336,236,154,44,304,
87,292,21,330,19,151,220,152,161,323,2,192,147,91,106,202,333,363,
139,261,273,225,18,47,301,372,40,230,108,46,255,212,24,237,348,158,
55,6,101,66,30,374,58,72,222,16,130,90,187,253,260,80,100,380,
231,337,280,138,127,284,210,382,103,36,12,157,45,221,387,345,14,317,
219,146,48,351,20,366,144,320,208,353,329,262,371,155,81,238,227,85,
28,134,373,265,285,105,112,178,275,235,349,143,293,307,379,335,299,264,
359,310,207,17,128,341,153,110,319,257,135,325,381,64,318,347,140,92,
104,226,390,32,163,259,274,218,173)]],
[3,Factorial(390)/2,1,"2",[[389,1]],388,"A_n",["A",390,1],390],
[4,Factorial(390),0,"2",[[389,1]],390,"S_n",["A",390,1],390]];
PRIMGRP[391]:=
[[1,Factorial(391)/2,1,"2",[[390,1]],389,"A_n",["A",391,1],391],
[2,Factorial(391),0,"2",[[390,1]],391,"S_n",["A",391,1],391]];
PRIMGRP[392]:=
[[1,Factorial(392)/2,1,"2",[[391,1]],390,"A_n",["A",392,1],392],
[2,Factorial(392),0,"2",[[391,1]],392,"S_n",["A",392,1],392]];
PRIMGRP[393]:=
[[1,Factorial(393)/2,1,"2",[[392,1]],391,"A_n",["A",393,1],393],
[2,Factorial(393),0,"2",[[392,1]],393,"S_n",["A",393,1],393]];
PRIMGRP[394]:=
[[1,Factorial(394)/2,1,"2",[[393,1]],392,"A_n",["A",394,1],394],
[2,Factorial(394),0,"2",[[393,1]],394,"S_n",["A",394,1],394]];
PRIMGRP[395]:=
[[1,Factorial(395)/2,1,"2",[[394,1]],393,"A_n",["A",395,1],395],
[2,Factorial(395),0,"2",[[394,1]],395,"S_n",["A",395,1],395]];
PRIMGRP[396]:=
[[1,95040,1,"2",[[10,2],[15,1],[30,2],[60,3],[120,1]],1,
"m12#396.1",["Spor","M(12)",1],
[(1,2,4)(3,6,11)(5,9,16)(7,13,21)(8,14,23)(10,18,28)
(12,19,30)(15,25,39)(17,27,43)(20,32,51)(22,34,55)
(24,37,60)(26,41,65)(29,46,72)(31,49,77)(33,53,82)
(35,57,87)(36,58,89)(38,62,95)(40,63,97)(42,67,92)
(44,61,93)(45,70,106)(47,74,111)(48,75,112)(50,79,116)
(52,76,114)(54,73,94)(56,85,125)(59,91,134)(64,99,100)
(66,101,78)(68,103,148)(69,105,151)(71,108,137)(80,117,166)
(81,119,167)(83,121,170)(84,123,173)(86,127,178)(88,129,182)
(90,132,187)(96,138,194)(98,141,199)(102,146,135)(104,150,126)
(107,154,213)(109,157,217)(110,159,155)(113,162,224)(115,164,228)
(118,120,145)(122,172,238)(124,175,158)(128,180,249)(130,184,255)
(131,185,257)(133,189,216)(136,192,265)(139,196,268)(140,197,270)
(142,201,275)(143,198,272)(144,203,277)(147,183,253)(149,207,271)
(152,211,287)(153,212,288)(156,215,209)(160,220,193)(161,222,298)
(163,226,302)(165,230,300)(168,233,310)(169,235,313)(171,237,316)
(174,240,244)(176,243,320)(177,245,321)(179,247,324)(181,251,317)
(186,258,334)(188,260,336)(190,262,338)(191,264,339)(195,239,242)
(200,263,340)(202,276,278)(204,273,346)(205,279,352)(206,281,259)
(208,283,356)(210,285,267)(214,290,315)(218,292,361)(219,294,363)
(221,297,360)(223,299,367)(225,301,368)(227,304,359)(229,306,351)
(231,232,309)(234,312,358)(236,314,286)(241,319,333)(246,318,372)
(248,250,326)(252,327,374)(254,329,355)(256,331,291)(261,322,375)
(266,343,282)(269,335,380)(274,349,337)(280,354,341)(284,357,373)
(289,345,385)(293,362,323)(295,296,344)(303,348,387)(305,353,376)
(307,308,371)(311,350,388)(325,370,347)(328,369,392)(330,377,393)
(332,378,382)(342,383,394)(364,390,366)(365,391,384)(379,395,396)
(381,386,389),(1,3,7)(2,5,10)(4,8,15)(6,12,20)
(9,17,11)(13,22,35)(14,24,38)(16,26,42)(18,29,47)
(19,31,50)(21,33,54)(23,36,59)(25,40,64)(27,44,69)
(28,45,71)(30,48,76)(32,52,81)(34,56,86)(37,61,94)
(39,41,66)(43,68,104)(46,73,110)(49,78,115)(51,80,118)
(53,83,122)(55,84,124)(57,88,130)(58,90,133)(60,92,136)
(62,96,139)(63,98,142)(65,100,144)(67,102,147)(70,107,155)
(72,109,158)(74,106,153)(75,113,79)(77,105,152)(82,120,169)
(85,126,177)(87,128,181)(89,131,186)(91,135,191)(93,137,193)
(95,121,171)(97,140,198)(99,143,202)(101,145,204)(103,149,208)
(108,156,216)(111,160,221)(112,161,223)(114,163,227)(116,165,231)
(117,162,225)(119,168,234)(123,174,241)(125,176,244)(127,179,248)
(129,183,254)(132,188,213)(134,190,263)(138,195,267)(141,200,274)
(146,205,280)(148,206,185)(150,209,284)(151,210,286)(154,214,173)
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(260,316,362)(262,339,382)(264,341,380)(265,342,372)(268,344,383)
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(279,353,361)(281,355,377)(283,327,356)(285,298,366)(287,358,313)
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(304,369,390)(320,373,392)(329,334,379)(338,381,368)(343,384,375)
(349,389,391)(378,394,387)(393,396,395)]],
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(27,322,223,323,307,269,94,86)(29,98,160,84,362,169,236,251)
(30,249,207,106,144,388,208,34)(31,310,314,275,43,112,80,164)
(32,263,153,226,376,102,55,273)(36,264,225,332,159,392,287,267)
(37,337,147,374)(38,158,259,260,131,276,301,184)(39,154,352,45,68,346,
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(50,311,127,268,180,157,304,271)(53,325,227,165,370,148,104,229)
(58,187,145,305,161,242,177,218)(60,211,258,319,61,178,331,336)
(62,192,172,152,386,357,117,363)(63,166,115,373,194,387,266,368)
(65,395,358,360,366,81,76,390)(66,296,124,111,302,167,248,378)
(67,354,185,213,126,70,359,230)(69,209,90,389,255,100,201,270)
(77,196,93,122,345,237,252,369)(85,182,261,142,330,176,206,348)
(99,239,241,313,299,391,335,140)(119,216)(136,280,321,312,289,265,365,372)
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)(2,310,90,251,154,306,122,246,158,329,265,319)(3,157,161,208,322,32,
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(5,387,112,117,176,170,210,327,394,144,35,184)(6,127,339,216,292,288,
349,20,86,338,153,375)(7,230,376,42,325,183,359,352,308,106,125,380)
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313,389,104,350,84,291)(11,362,189,178,341,298,358,212,133,293,274,19)
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(21,225,257,169,70,205,164,364,207,370,331,39)(22,85,348,299,140,365,
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219,134,67,214,243,123)(28,377,138,72,61,381,343,240,29,93,273,226)
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305,384,256,101,332,192)(36,320,113,165,46,135,255,145,371,346,268,330)
(40,340,334,271,368,116)(43,202,75,149,315,357,241,203,235,142,258,172)
(50,120,115,130,355,266,162,301,285,209,393,187)(51,218,280,128,312,191,
261,195,395,323,245,99)(56,139,143,304,200,77,159,92,300,260,105,97)
(57,287,167,65,326,87,366,80,231,388,83,131)(71,267,233,89,286,237,
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(177,396,361,262,190,264)]],
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PRIMGRP[397]:=
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PRIMGRP[398]:=
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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)
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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,
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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,
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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),
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(8,154,243)(9,356,40)(10,189,206)(11,16,378)(12,242,151)
(13,366,26)(14,270,121)(15,299,91)(17,38,350)(18,208,179)
(19,140,246)(20,338,47)(21,198,186)(22,241,142)(23,215,167)
(24,386,391)(25,276,104)(27,39,339)(28,289,88)(29,98,278)
(30,275,100)(31,62,312)(32,268,105)(33,273,99)(34,117,254)
(35,321,49)(36,389,376)(37,301,67)(41,85,279)(42,183,180)
(43,191,171)(44,307,54)(45,165,195)(46,393,362)(50,137,218)
(52,364,385)(53,108,244)(55,395,351)(56,221,128)(58,65,282)
(59,106,240)(60,345,396)(61,97,247)(63,363,375)(64,382,355)
(66,170,169)(68,212,125)(69,77,259)(70,197,138)(71,258,76)
(72,107,226)(73,118,214)(74,153,178)(75,102,228)(78,152,175)
(79,92,234)(80,236,89)(81,367,353)(82,114,209)(83,192,130)
(84,122,199)(86,225,94)(87,136,182)(90,340,371)(93,200,112)
(95,358,348)(96,163,146)(101,365,335)(103,387,311)(109,185,111)
(110,164,131)(113,374,314)(115,133,157)(116,150,139)(119,141,145)
(120,337,344)(123,317,361)(124,304,373)(126,377,298)(127,372,302)
(129,369,303)(132,388,281)(134,370,297)(143,325,333)(144,331,326)
(148,285,368)(149,397,255)(155,305,341)(156,262,383)(158,294,349)
(159,248,394)(160,390,251)(161,380,260)(162,296,343)(166,322,313)
(168,310,323)(173,230,398)(174,300,327)(176,295,330)(177,316,308)
(181,346,274)(184,265,352)(187,379,235)(188,284,329)(190,334,277)
(193,288,320)(194,384,223)(196,213,392)(202,309,290)(203,280,318)
(204,381,216)(205,332,264)(207,237,357)(210,319,272)(211,359,231)
(217,293,291)(219,360,222)(220,266,315)(224,249,328)(227,250,324)
(232,336,233)(238,292,271)(239,306,256)(245,269,287)(252,286,263)
(257,261,283)]],
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111,14,150,63,89,158,293,303,395,117,9,254,103,391,113,205,215,350,
23,49,358,98,397,389,48,371,153,172,190,179,359,173,53,11,231,181,
141,244,300,331,333,384,249,187,76,349,274,372,85,114,298,57,326,160,
86,42,50,66,302,2,369,189,105,220,286,353,223,142,269,385,47,152,
39,61,250,3,129,251,396,351,83,81,262,216,265,16,22,130,5,79,
200,323,202,209,363,84,230,271,343,178,169,368,219,287,110,242,201,195,
148,272,207,20,263,10,135,390,106,30,270,171,8,41,127,166,162,125,
362,375,273,241,252,74,248,291,116,144,188,161,218,37,138,180,32,281,
93,393,204,297,387,214,99,194,12,72,386,365,226,225,310,193,284,67,
296,276,338,184,196,87,15,305,341,261,147,58,229,134,309,280,357,345,
332,317,4,52,131,382,240,380,325,35,44,186,88,352,21,253,18,43,
354,164,78,95,233,311,174,340,120,316,213,376,56,132,295,192,388,168,
334,197,275,17,34,344,154,69,94,255,91,156,24,322,68,77,183,128,
268,126,377,60,108,191,176,163,151,228,199,374,279,54,361,247,167,203,
97,25,312,324,170,232,212,45,224,315,198,283,282,143,122,40,100,314,
13,294,121,211,304,115,19,227,80,328,370,75,290,347,320,364,392,217,
260,38,256,267,235,133,146,383,346,342,381,71,104,337,238,82,6,118,
373,102,245,92,301,236,360,313,307,266,398,221,289,140,339,330,165,237,
278,28,145,299,306,185,308,33,107,378,90,96,243,292,246,31,29,157,
112,257,379,109,258,51,73,356,65,123,239,366,285,155,222,288,7,319,139
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325,321,15,202,78,207,274,170,212,65,338,58,368,326,25,43,305,199,
273,141,128,234,211,332,205,194,124,73,239,280,219,361,386,389,137,27,
91,336,281,47,359,278,125,139,365,250,335,149,327,96,64,254,214,267,
209,13,184,182,375,203,84,72,363,197,183,83,161,223,82,313,92,150,
167,362,367,48,179,133,44,360,3,38,67,351,381,304,284,123,257,181,
10,122,244,45,54,100,247,49,376,232,357,178,297,292,195,5,272,271,
140,200,228,330,391,158,18,262,302,227,253,142,75,76,196,220,299,107,
210,68,201,285,372,187,160,256,17,19,162,37,198,311,315,242,322,277,
186,22,283,353,316,109,7,98,55,62,70,290,95,355,77,53,145,392,192
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291,127,36,387,71,394,398,115,276,151,294,296,57,153,126,337,28,112,
245,103,206,14,93,117,237,238,171,60,86,11,51,295,155,318,379,85,
113,173,42,41,308,118,21,16,135,352,81,333,264,66,213,259,268,69,
191,303,132,56,190,29,9,328,358,246,275,310,349,269,180,134,265,342,
347,146,163,221,396,231,90,152,230,130,116,346,241,229,110,334,131,129,
300,104,46,99,59,249,217,382,164,374,63,344,174,188,35,350,266,32,
373,222,286,176,320,323,348,94,33,74,240,189,119,108,377,102,79,185,
172,40,114,8,270,288,383,341,255,371,248,101,143,39,106,235,111,298,
388,384,31,87,34,12,144,366,20,225,261,385,307,26,120,329,50,289,
370,147,138,97,4,156,369,154,314,224,364,397,165,80,331,390,105,61)]
],[3,Factorial(398)/2,1,"2",[[397,1]],396,"A_n",["A",398,1],398
],[4,Factorial(398),0,"2",[[397,1]],398,"S_n",["A",398,1],398]
];
PRIMGRP[399]:=
[[1,Factorial(399)/2,1,"2",[[398,1]],397,"A_n",["A",399,1],399],
[2,Factorial(399),0,"2",[[398,1]],399,"S_n",["A",399,1],399]];
PRIMGRP[400]:=
[[1,138297600,1,"2",[[56,1],[343,1]],1,"S4,7 on projective points.1"
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(18,53,46,39,32,25)(19,54,47,40,33,26)(20,55,48,41,34,27)
(21,56,49,42,35,28)(22,57,50,43,36,29)(59,64,63,62,61,60)
(65,100,93,86,79,72)(66,106,98,90,82,74)(67,101,99,91,83,75)
(68,102,94,92,84,76)(69,103,95,87,85,77)(70,104,96,88,80,78)
(71,105,97,89,81,73)(107,303,205)(108,309,210,111,306,207)
(109,304,211,112,307,208)(110,305,206,113,308,209)(114,345,240,135,324,219)
(115,351,245,139,327,221)(116,346,246,140,328,222)(117,347,241,141,329,223)
(118,348,242,136,330,224)(119,349,243,137,325,225)(120,350,244,138,326,220)
(121,310,247,142,331,226)(122,316,252,146,334,228)(123,311,253,147,335,229)
(124,312,248,148,336,230)(125,313,249,143,337,231)(126,314,250,144,332,232)
(127,315,251,145,333,227)(128,317,212,149,338,233)(129,323,217,153,341,235)
(130,318,218,154,342,236)(131,319,213,155,343,237)(132,320,214,150,344,238)
(133,321,215,151,339,239)(134,322,216,152,340,234)(156,352,254)
(157,358,259,160,355,256)(158,353,260,161,356,257)(159,354,255,162,357,258)
(163,394,289,184,373,268)(164,400,294,188,376,270)(165,395,295,189,377,271)
(166,396,290,190,378,272)(167,397,291,185,379,273)(168,398,292,186,374,274)
(169,399,293,187,375,269)(170,359,296,191,380,275)(171,365,301,195,383,277)
(172,360,302,196,384,278)(173,361,297,197,385,279)(174,362,298,192,386,280)
(175,363,299,193,381,281)(176,364,300,194,382,276)(177,366,261,198,387,282)
(178,372,266,202,390,284)(179,367,267,203,391,285)(180,368,262,204,392,286)
(181,369,263,199,393,287)(182,370,264,200,388,288)(183,371,265,201,389,283),
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118,3)(2,16,62)(4,23,63,72,165,228,324,218,283,191,311,341,296,
363,57,352,68,400,233,266,174)(5,37,59,93,315,176,331,264,396,177,
216,41,254,66,343,366,169,285,247,361,230)(6,44,60,79,215,397,345,
360,344,184,263,231,268,168,171,387,314,33,205,71,286)(7,30,64,86,
265,49,303,67,229,198,362,395,289,316,284,373,217,175,219,164,342)
(8,51,61,100,365,287,317,167,25,156,70,172,275,214,232,380,262,339,
240,313,398)(10,108,95,129,147,369,154,127,337,141,138,252,124,151,178,
144,132,31,111,13,258)(11,158,80,143,246,190,140,318,389,134,384,38,
110,103,350,123,280,271,153,26,209)(12,208,105,122,388,242,133,270,276,
148,189,320,152,349,52,109,85,386,139,46,160)(14,308,75,150,292,301,
126,223,24,113,87,193,131,204,239,137,375,325,146,43,356)
(15,358,92,136,195,45,112,77,222,155,235,374,145,297,291,130,327,203,
125,56,307)(17,107,69)(18,159,104)(19,206,97)(20,260,90)
(21,305,83)(22,357,76)(27,256,82,200,182,273,225,335,28,304,99,186,
377,47,211,89,250,346,294,367,391)(29,355,102,179,330,383,253,238,323,
332,192,245,370,32,157,96,300,34,259,74,279)(35,306,101,293,53,162,
88,379,382,376,202,42,309,91,322,224,221,278,199,290,244)
(36,354,84,272,40,207,81,329,269,390,299,348,351,237,54,210,73,393,
185,197,188)(39,161,78,336,321,48,257,106,236,251,50,353,94,243,298,
183,381,196,368,277,328)(55,255,98,372,334,249,181)(121,166,399)
(128,213,340)(135,267,288)(142,312,227)(149,364,173)(180,201,347)
(187,248,295)(194,302,234)(220,392,371)(274,333,378)(281,385,319)]],
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[(1,21,131,291,176,397,154,63,225,191,109,362,323,91,15,346,372,209,135,
237,78,277,118,177,274,311,143,18)(2,229,70,233,134,36,284,60,141,
94,19,180,155,305,156,363,120,167,251,50,113,301,325,350,148,380,390,290
)(3,322,347,351,267,74,34,64,85,44,359,8,358,219,181,239,337,370,
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344,144,103,292,190,117,189,26,260,139,375,178,379,11,56,235,218,112,
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(41,400,287,60)(42,397,157,108,349,58,333,76,365,118,75,345)
(44,281,324,264,308,303,94,268,356,185,187,256)(46,47,124,283,289,376,
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(56,88,285,183,269,335,174,299,135,138,119,322)(57,277,252,372,171,98,
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(64,79,130,95,176,309,298,152,344,151,186,379)(78,238,383,334,370,219,
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317,352,103,368,289,283,293,166,260,296,41,319,277,320,218,8,34,177,
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78,335,213,238,161,400,209,154,292,47,261,232,70,393,143,321,53,243,
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284,122,222,112,247,322,97,383,194,359,303,348,43,72,330,172,262,56,
46,131,228)]],
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56,40,268,61,391,153,309,325,350,206,174,243,58,140,277,361,396,33,
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(30,208,74,251,158,129,337,370,216,34,248,78,131,157,369,336)
(31,148,69,331,150,209,334,250,218,134,257,378,136,37,368,76)
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315,85,344,106,179,183,52,240,262,281,395,93,304,105,359,186,172,223)
(43,60,280,261,381,393,313,305,345,346,166,163)(45,360,266,161,383,53,
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170,319,48,184,321,160,71,38,93,246,167,305,56,197,323,142,74,35,
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97,243,162,314,55,189,330,159,68,24,81,260,171,318,53,186,327,145,
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(43,52,352,348,68,77,237,221,241,255,115,107,387,386,366,370,210,203)
(45,332,345,328,65,337,225,321,245,335,105,327,385,326,365,330,205,323)
(46,372,350,208,63,57,232,341,248,75,117,227,381,246,375,110,207,383)
(48,72,357,228,61,257,235,101,247,395,106,367,390,206,363,50,212,343)
(51,192,359,88,71,197,239,81,251,195,119,87,391,186,379,90,211,183,
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(8,365,307,192,82,51)(10,65,314,112,90,71,14,105,310,72,94,111)
(12,85,311)(17,125,304,352,96,271,18,205,313,232,83,31)
(20,165,320,172,100,171)(21,337,139,284,355,156,269,258,206,393,221,323,
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261,338,219,293,235,143,29,257,126,384,341,336,279,298,215,153,229,243,
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262,58,208,373,227,183)(23,37,137,124,344,356,276,278,218,213,233,223)
(24,357,136,264,358,216,273,238,203,33,237,123)(27,197,122,44,348,376,
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(30,77,134,104,350,76,274,118,210,73,234,103)(34,117,130,64,354,116,
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(40,177,140,164,360,176,280,178,220,173,240,163)(41,328,379,287,195,142,
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(50,68,374,107,190,62,54,108,370,67,194,102)(60,168,380,167,200,162)
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(146,389,241,326,399,281,335,159,289,255)(149,249,246,386,381,321,339,299,
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"A20 on 1-sets^2.3",["A",20,2],
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240,115,42,19,30,285,376,384,158,212,246,323,353,181,267,77,231,114,
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34,289,380,395,142,219,250,325,356,184,278,72,226,103,53)
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(24,256,37,250,27,244,36,257,30,247)(29,249)(32,253)(33,252)
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(92,213,152,333)(93,212,153,332)(221,240,238,231,225,234,239,235,228,226,
223)(224,236,237,230,227)(232,233)]],
[11,23392800,0,"4c",[[38,1],[361,1]],1,
"L2,19 on projective points^2.1",["L",[2,19],2],
[(1,17,377,366,86,87,27,32,232,221)(2,117,363,246,88,287,29,192,236,
121)(3,257,368,286,89,187,36,132,222,101)(4,177,373,206,95,347,25,
332,239,261)(5,337,379,266,84,167,33,212,235,341)(6,97,367,26,92,
227,21,12,237,361)(7,37,372,226,81)(8,297,369,186,96,127,22,112,
223,241)(9,197,376,126,82,107,23,252,228,281)(10,57,378,66,100,307,
31,152,234,381)(11,157,374,386,90,47,38,72,240,301)(13,217,375,346,
85,327,39,272,224,161)(14,397,370,46,98,67,40,312,231,141)
(15,357,365,326,99,267,24,172,233,201)(16,137,362,106,83,247,28,292,
229,181)(18,77,380,306,91,147,34,392,230,41)(19,277,364,166,93,207,
35,352,225,321)(20,317,371,146,94,387,30,52,238,61)(42,118,63,260,
308,291,149,194,396,130)(43,258,68,300,309,191,156,134,382,110)
(44,178,73,220,315,351,145,334,399,270)(45,338,79,280,304,171,153,214,
395,350)(48,298,69,200,316,131,142,114,383,250)(49,198,76,140,302,111,
143,254,388,290)(50,58,78,80,320,311,151,154,394,390)(51,158,74,400,
310)(53,218,75,360,305,331,159,274,384,170)(54,398,70,60,318,71,160,
314,391,150)(55,358,65,340,319,271,144,174,393,210)(56,138,62,120,303,
251,148,294,389,190)(59,278,64,180,313,211,155,354,385,330)
(102,103,243,248,288,289,189,196,136,122)(104,163,253,208,295,349,185,336,
139,262)(105,323,259,268,284,169,193,216,135,342)(108,283,249,188,296,129,
182,116,123,242)(109,183,256,128,282)(113,203,255,348,285,329,199,276,124,
162)(115,343,245,328,299,269,184,176,133,202)(119,263,244,168,293,209,195,
356,125,322)(164,173,213,215,355,345,325,339,279,264)(165,333,219,275,344)
(175,353,205,335,359,265,324,179,273,204),
(1,364,314,225,168,32,106,87,80)(2,363,316,237,171,35,118,89,79)
(3,376,317,231,175,38,109,99,62)(4,374,305,228,172,26,107,100,61)
(5,368,312,226,167,40,101,84,74)(6,367,320,221,164,34,105,88,72)
(7,380,301,224,174,25,108,92,66)(8,372,306,227,180,21,104,94,65)
(9,379,302,223,176,37,111,95,78)(10,370,310,230,170,30,110,90,70)
(11,375,318,229,179,22,103,96,77)(12,366,307,240,161,24,114,85,68)
(13,373,313,233,173,33,113,93,73)(14,365,308,232,166,27,120,81,64)
(15,378,309,239,162,23,116,97,71)(16,377,311,235,178,29,119,82,63)
(17,371,315,238,169,39,102,83,76)(18,369,319,222,163,36,117,91,75)
(19,362,303,236,177,31,115,98,69)(20,361,304,234,165,28,112,86,67)
(41,284,254,125,388,212,266,327,160)(42,283,256,137,391,215,278,329,159)
(43,296,257,131,395,218,269,339,142)(44,294,245,128,392,206,267,340,141)
(45,288,252,126,387,220,261,324,154)(46,287,260,121,384,214,265,328,152)
(47,300,241,124,394,205,268,332,146)(48,292,246,127,400,201,264,334,145)
(49,299,242,123,396,217,271,335,158)(50,290,250,130,390,210,270,330,150)
(51,295,258,129,399,202,263,336,157)(52,286,247,140,381,204,274,325,148)
(53,293,253,133,393,213,273,333,153)(54,285,248,132,386,207,280,321,144)
(55,298,249,139,382,203,276,337,151)(56,297,251,135,398,209,279,322,143)
(57,291,255,138,389,219,262,323,156)(58,289,259,122,383,216,277,331,155)
(59,282,243,136,397,211,275,338,149)(60,281,244,134,385,208,272,326,147)
(181,184,194,185,188,192,186,187,200)(182,183,196,197,191,195,198,189,199)
(341,344,354,345,348,352,346,347,360)(342,343,356,357,351,355,358,349,359)
]],
[12,46785600,0,"4c",[[38,1],[361,1]],1,"L2,19 on projective points^\
2.2",["L",[2,19],2],
[(1,29,68,381,349,8,21,69,388,341,9,28,61,389,348)(2,23,80,382,
343,20,22,63,400,342,3,40,62,383,360)(4,38,79,384,358,19,24,
78,399,344,18,39,64,398,359)(5,35,77,385,355,17,25,75,397,345,
15,37,65,395,357)(6,32,74,386,352,14,26,72,394,346,12,34,66,
392,354)(7,30,71,387,350,11,27,70,391,347,10,31,67,390,351)
(13,33,73,393,353)(16,36,76,396,356)(41,129,148,181,169,48,121,149,
188,161,49,128,141,189,168)(42,123,160,182,163,60,122,143,200,162,43,
140,142,183,180)(44,138,159,184,178,59,124,158,199,164,58,139,144,198,
179)(45,135,157,185,175,57,125,155,197,165,55,137,145,195,177)
(46,132,154,186,172,54,126,152,194,166,52,134,146,192,174)
(47,130,151,187,170,51,127,150,191,167,50,131,147,190,171)
(53,133,153,193,173)(56,136,156,196,176)(81,309,208,101,329,88,301,209,
108,321,89,308,201,109,328)(82,303,220,102,323,100,302,203,120,322,83,
320,202,103,340)(84,318,219,104,338,99,304,218,119,324,98,319,204,118,
339)(85,315,217,105,335,97,305,215,117,325,95,317,205,115,337)
(86,312,214,106,332,94,306,212,114,326,92,314,206,112,334)
(87,310,211,107,330,91,307,210,111,327,90,311,207,110,331)
(93,313,213,113,333)(96,316,216,116,336)(221,269,288,361,249,228,261,289,
368,241,229,268,281,369,248)(222,263,300,362,243,240,262,283,380,242,223,
280,282,363,260)(224,278,299,364,258,239,264,298,379,244,238,279,284,378,
259)(225,275,297,365,255,237,265,295,377,245,235,277,285,375,257)
(226,272,294,366,252,234,266,292,374,246,232,274,286,372,254)
(227,270,291,367,250,231,267,290,371,247,230,271,287,370,251)
(233,273,293,373,253)(236,276,296,376,256),
(1,161,169,69,65,45,55,275,266,6)(2,81,171,349,80,25,52,255,268,
106)(3,201,178,149,76,325,50,295,273,126)(4,301,167,389,79,225,57,
195,274,366)(5,41,175,269,66)(7,381,179,229,77,185,54,375,264,306)
(8,101,162,89,71,345,60,35,272,246)(9,61,165,49,75,265,46,15,
261,166)(10,281,173,129,63,205,58,155,276,326)(11,341,180,29,72,245,
48,115,262,86)(12,241,168,109,62,85,51,355,280,26)(13,121,163,209,
78,145,56,335,270,286)(14,361,164,309,67,385,59,235,277,186)
(16,321,170,289,73,125,43,215,278,146)(17,181,174,369,64,305,47,395,
279,226)(18,141,176,329,70,285,53,135,263,206)(19,221,177,189,74,365,
44,315,267,386)(20,21,172,249,68,105,42,95,271,346)(22,92,251,348,
120)(23,212,258,148,116,322,90,291,353,140)(24,312,247,388,119,222,97,
191,354,380)(27,392,259,228,117,182,94,371,344,320)(28,112,242,88,111,
342,100,31,352,260)(30,292,253,128,103,202,98,151,356,340)
(32,252,248,108,102,82,91,351,360,40)(33,132,243,208,118,142,96,331,
350,300)(34,372,244,308,107,382,99,231,357,200)(36,332,250,288,113,122,
83,211,358,160)(37,192,254,368,104,302,87,391,359,240)(38,152,256,328,
110,282,93,131,343,220)(39,232,257,188,114,362,84,311,347,400)
(123,203,218,158,156,336,330,290,293,133)(124,303,207,398,159,236,337,190,
294,373)(127,383,219,238,157,196,334,370,284,313)(130,283,213,138,143,216,
338,150,296,333)(134,363,204,318,147,396,339,230,297,193)(136,323,210,298,
153)(137,183,214,378,144,316,327,390,299,233)(139,223,217,198,154,376,324,
310,287,393)(184,314,367,384,319,227,397,199,234,377)(187,394,379,224,317)
(194,374,364,304,307,387,399,239,237,197),
(1,187,386,125,42,275,201,347,306,105,162,335,281,67,366,225,142,255,81,
27,6,185,382,135,41,267,206,345,302,115,161,327,286,65,362,235,141,
247,86,25,2,195,381,127,46,265,202,355,301,107,166,325,282,75,361,
227,146,245,82,35)(3,183,383,123,43,263,203,343,303,103,163,323,283,
63,363,223,143,243,83,23)(4,198,390,131,53,276,204,358,310,111,173,
336,284,78,370,231,153,256,84,38,10,191,393,136,44,278,210,351,313,
116,164,338,290,71,373,236,144,258,90,31,13,196,384,138,50,271,213,
356,304,118,170,331,293,76,364,238,150,251,93,36)(5,182,395,121,47,
266,205,342,315,101,167,326,285,62,375,221,147,246,85,22,15,181,387,
126,45,262,215,341,307,106,165,322,295,61,367,226,145,242,95,21,7,
186,385,122,55,261,207,346,305,102,175,321,287,66,365,222,155,241,87,26
)(8,194,397,139,60,272,208,354,317,119,180,332,288,74,377,239,160,252,
88,34,17,199,400,132,48,274,217,359,320,112,168,334,297,79,380,232,
148,254,97,39,20,192,388,134,57,279,220,352,308,114,177,339,300,72,
368,234,157,259,100,32)(9,189,389,129,49,269,209,349,309,109,169,329,
289,69,369,229,149,249,89,29)(11,193,396,124,58,270,211,353,316,104,
178,330,291,73,376,224,158,250,91,33,16,184,398,130,51,273,216,344,
318,110,171,333,296,64,378,230,151,253,96,24,18,190,391,133,56,264,
218,350,311,113,176,324,298,70,371,233,156,244,98,30)(12,188,394,137,
59,280,212,348,314,117,179,340,292,68,374,237,159,260,92,28,14,197,
399,140,52,268,214,357,319,120,172,328,294,77,379,240,152,248,94,37,
19,200,392,128,54,277,219,360,312,108,174,337,299,80,372,228,154,257,
99,40)]],
[13,46785600,0,"4c",[[38,1],[361,1]],1,"L2,19 on projective points^\
2.3",["L",[2,19],2],
[(1,202,388,190,347,243,299,78,374,306,275,152,136,169,51,340,85,101,204,
8,182,387,250,359,63,294,318,375,146,276,172,131,329,45,120,84)
(2,382,390,350,343,283,298,378,366,266,272,132,129,49,60,100,81,201,
208,188,187,247,259,79,74,314,315,155,156,176,171,331,325,105,104,4)
(3,282,398,370,346,263,292,138,369,46,280,92,121,209,48,200,87,241,
219,68,194,307,255,159,76,174,311,335,145,116,164,11,322,385,110,344)
(5,102,384,10,342,383,290,358,363,286,278,372,126,269,52,140,89,41,
220,88,181,207,248,199,67,254,319,75,154,316,175,151,336,165,111,324)
(6,262,392,130,349,43,300,98,361,206,268,192,127,249,59,80,94,301,
215,148,196,167,251,339,65,114,304,15,142,396,170,351,323,285,118,364)
(7,242,399,70,354,303,295,158,376,166,271,332,125,109,44,20,82,381,
210,348,183,287,258,379,66,274,312,135,149,56,180,91,321,205,108,184)
(9,42,400,90,341,203,288,198,367,246,279,72,134,309,55,160,96,161,
211,328,185,107,244,19,62,394,310,355,143,296,178,371,326,265,112,124)
(12,122,389,50,360,83,281,218,368,186,267,252,139,69,54,320,95,141,
216,168,191,327,245,119,64,14,302,395,150,356,163,291,338,365,106,264)
(13,22,393,30,353,23,293,38,373,26,273,32,133,29,53,40,93,21,
213,28,193,27,253,39,73,34,313,35,153,36,173,31,333,25,113,24)
(16,162,391,330,345,103,284,18,362,386,270,352,123,289,58,380,86,261,
212,128,189,47,260,99,61,214,308,195,147,256,179,71,334,305,115,144)
(17,222,397,230,357,223,297,238,377,226,277,232,137,229,57,240,97,221,
217,228,197,227,257,239,77,234,317,235,157,236,177,231,337,225,117,224)
(37,233),(1,312,60,77,104,248,121,352,220,97,224,268,281,392,40,337,
164,368)(2,319,45,70,107,255,122,359,205,90,227,275,282,399,25,330,
167,375)(3,314,53,66,109,258,123,354,213,86,229,278,283,394,33,326,
169,378)(4,308,41,72,120,257,124,348,201,92,240,277,284,388,21,332,
180,377)(5,310,47,75,102,259,125,350,207,95,222,279,285,390,27,335,
162,379)(6,309,58,63,114,253,126,349,218,83,234,273,286,389,38,323,
174,373)(7,315,42,79,105,250,127,355,202,99,225,270,287,395,22,339,
165,370)(8,301,52,80,117,244,128,341,212,100,237,264,288,381,32,340,
177,364)(9,318,43,74,113,246,129,358,203,94,233,266,289,398,23,334,
173,366)(10,307,55,62,119,245,130,347,215,82,239,265,290,387,35,322,
179,365)(11,311,51,71,111,251,131,351,211,91,231,271,291,391,31,331,
171,371)(12,320,57,64,108,241,132,360,217,84,228,261,292,400,37,324,
168,361)(13,306,49,78,103,254,133,346,209,98,223,274,293,386,29,338,
163,374)(14,313,46,69,118,243,134,353,206,89,238,263,294,393,26,329,
178,363)(15,302,59,65,110,247,135,342,219,85,230,267,295,382,39,325,
170,367)(16,316,56,76,116,256,136,356,216,96,236,276,296,396,36,336,
176,376)(17,304,48,61,112,260,137,344,208,81,232,280,297,384,28,321,
172,380)(18,303,54,73,106,249,138,343,214,93,226,269,298,383,34,333,
166,369)(19,305,50,67,115,242,139,345,210,87,235,262,299,385,30,327,
175,362)(20,317,44,68,101,252,140,357,204,88,221,272,300,397,24,328,
161,372)(141,152,160,157,144,148)(142,159,145,150,147,155)(143,154,153,146,
149,158)(181,192,200,197,184,188)(182,199,185,190,187,195)(183,194,193,186,
189,198)]],
[14,93571200,0,"4c",[[38,1],[361,1]],1,"L2,19 on projective points^\
2.4",["L",[2,19],2],
[(1,25,302,356,295,220,174,148,63,271,92,389,110,338,373,187,259,6,225,
301,36,282,360,175,208,74,151,83,269,112,398,370,327,253,186,239)
(2,345,315,216,294,160,163,268,72,391,90,329,113,198,379,7,245,306,
236,281,40,162,348,75,211,94,149,103,278,372,387,250,326,233,181,39)
(3,265,312,396,290,340,173,188,79,11,85,309,116,298,380,167,248,66,
231,81,29,102,358,375,207,254,146,223,261,32,382,350,335,213,194,159)
(4,45,304,56,284,60,164,48,64,51,84,49,104,58,364,47,244,46,
224,41,24,42,344,55,204,54,144,43,264,52,384,50,324,53,184,59)
(5,305,316,296,300,180,168,68,71,91,89,109,118,378,367,247,246,226,
221,21,22,342,355,215,214,154,143,263,272,392,390,330,333,193,199,19)
(8,65,311,96,289,120,178,368,67,251,86,229,101,38,362,347,255,206,
234,141,23,262,352,395,210,334,153,183,279,12,385,310,336,293,200,179)
(9,105,318,376,287,260,166,228,61,31,82,349,115,218,374,147,243,266,
232,381,30,322,353,195,219,14,145,303,276,292,400,170,328,73,191,99)
(10,325,313,196,299,20,165,308,76,291,100,169,108,78,371,87,249,106,
238,361,27,242,346,235,201,34,142,343,275,212,394,150,323,273,192,399)
(13,185,319,16,285,320,176,288,80,171,88,69,111,98,369,107,258,366,
227,241,26,222,341,35,202,354,155,203,274,152,383,270,332,393,190,339)
(15,205,314,156,283,280,172,388,70,331,93,189,119,18,365,307,256,286,
240,161,28,62,351,95,209,114,158,363,267,252,386,230,321,33,182,359)
(17,125,317,136,297,140,177,128,77,131,97,129,117,138,377,127,257,126,
237,121,37,122,357,135,217,134,157,123,277,132,397,130,337,133,197,139)
(57,124),(1,353,119,271,186,140,178,375,74,316,81,53,239,211,286,400,
258,155,14,356,101,273,199,131,166,380,78,315,94,56,221,213,299,391,
246,160,18,355,114,276,181,133,179,371,66,320,98,55,234,216,281,393,
259,151,6,360,118,275,194,136,161,373,79,311,86,60,238,215,294,396,
241,153,19,351,106,280,198,135,174,376,61,313,99,51,226,220,298,395,
254,156)(2,347,109,268,185,123,177,372,64,310,82,47,229,208,285,383,
257,152,4,350,102,267,189,128,165,363,77,312,84,50,222,207,289,388,
245,143,17,352,104,270,182,127,169,368,65,303,97,52,224,210,282,387,
249,148,5,343,117,272,184,130,162,367,69,308,85,43,237,212,284,390,
242,147,9,348,105,263,197,132,164,370,62,307,89,48,225,203,297,392,
244,150)(3,357,112,264,190,122,167,369,68,305,83,57,232,204,290,382,
247,149,8,345,103,277,192,124,170,362,67,309,88,45,223,217,292,384,
250,142,7,349,108,265,183,137,172,364,70,302,87,49,228,205,283,397,
252,144,10,342,107,269,188,125,163,377,72,304,90,42,227,209,288,385,
243,157,12,344,110,262,187,129,168,365,63,317,92,44,230,202,287,389,
248,145)(11,346,120,278,195,134,176,361,73,319,91,46,240,218,295,394,
256,141,13,359,111,266,200,138,175,374,76,301,93,59,231,206,300,398,
255,154,16,341,113,279,191,126,180,378,75,314,96,41,233,219,291,386,
260,158,15,354,116,261,193,139,171,366,80,318,95,54,236,201,293,399,
251,146,20,358,115,274,196,121,173,379,71,306,100,58,235,214,296,381,
253,159)(21,33,39,31,26,40,38,35,34,36)(22,27,29,28,25,23,
37,32,24,30)(321,333,339,331,326,340,338,335,334,336)(322,327,329,328,
325,323,337,332,324,330)]],
[15,Factorial(400)/2,1,"2",[[399,1]],398,"A_n",["A",400,1],400],
[16,Factorial(400),0,"2",[[399,1]],400,"S_n",["A",400,1],400]];
PRIMGRP[401]:=
[[1,Factorial(401)/2,1,"2",[[400,1]],399,"A_n",["A",401,1],401],
[2,Factorial(401),0,"2",[[400,1]],401,"S_n",["A",401,1],401]];
PRIMGRP[402]:=
[[1,32240400,1,"2",[[401,1]],2,"L2,401 on projective points.1",
["L",[2,401],1],
[(3,401,399,397,395,393,391,389,387,385,383,381,379,377,375,373,371,369,367,
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
)(4,402,400,398,396,394,392,390,388,386,384,382,380,378,376,374,372,370,
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),(1,2,203)(3,177,229)(4,151,254)(5,129,275)(6,89,314)
(7,249,153)(8,268,133)(9,323,77)(10,319,80)(11,371,27)
(12,93,304)(13,61,335)(14,159,236)(15,282,112)(16,32,361)
(17,198,194)(18,306,85)(19,216,174)(20,158,231)(21,86,302)
(22,241,146)(23,340,46)(24,36,349)(25,167,217)(26,246,137)
(28,156,225)(29,202,178)(30,141,238)(31,40,338)(33,332,44)
(34,291,84)(35,395,379)(37,135,237)(38,311,60)(39,227,143)
(41,262,106)(42,292,75)(43,88,278)(45,374,390)(47,295,67)
(48,76,285)(49,117,243)(50,126,233)(51,176,182)(52,99,258)
(53,286,70)(54,142,213)(55,155,199)(56,284,69)(57,370,382)
(58,145,206)(59,188,162)(62,197,150)(63,101,245)(64,130,215)
(65,125,219)(66,383,360)(68,366,375)(71,345,393)(72,123,214)
(73,226,110)(74,373,362)(78,96,235)(79,222,108)(81,201,127)
(82,107,220)(83,397,329)(87,396,326)(90,221,98)(91,154,164)
(92,317,400)(94,183,132)(95,368,346)(97,196,116)(100,388,321)
(102,313,394)(103,140,166)(104,320,385)(105,109,195)(111,359,339)
(113,149,147)(114,364,331)(115,372,322)(118,172,119)(120,353,336)
(121,330,358)(122,350,337)(124,391,294)(128,318,363)(131,277,401)
(134,136,139)(138,398,273)(144,365,300)(148,307,354)(152,255,402)
(157,399,253)(160,380,269)(161,305,343)(163,289,357)(165,384,260)
(168,265,376)(169,271,369)(170,247,392)(171,310,328)(173,280,356)
(175,248,386)(179,367,263)(180,333,296)(181,250,378)(184,327,298)
(185,316,308)(186,299,324)(187,281,341)(189,239,381)(190,387,232)
(191,276,342)(192,283,334)(193,264,352)(200,261,348)(204,377,228)
(205,325,279)(207,251,351)(208,389,212)(209,344,256)(210,309,290)
(211,297,301)(218,347,244)(223,312,274)(224,230,355)(234,288,287)
(240,266,303)(242,252,315)(257,293,259)(267,270,272)]],
[2,64480800,0,"2",[[401,1]],3,"L2,401 on projective points.2",
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[(1,192,253,154,355,378,370,266,111,51,9,268,136,29,103,159,263,297,330,
196,109,248,119,227,392,101,252,160,345,50,177,55,140,199,352,354,42,
59,293,135,155,385,142,183,254,216,394,286,325,375,329,261,121,333,161,
170,225,231,146,112,107,37,191,304,336,134,165,208,153,174,344,158,376,
97,214,292,156,202,379,312)(2,230,163,340,386,250,328,45,166,384,198,
368,389,334,377,8,206,238,351,105,35,30,396,311,317,372,381,209,21,
281,213,167,217,256,148,326,288,359,400,157,387,7,249,83,100,188,190,
343,402,87,365,92,197,382,290,41,150,315,23,294,33,346,212,245,279,
383,39,113,6,274,133,91,31,276,172,164,187,388,289,350)
(3,145,306,144,296,364,207,282,273,88,78,285,14,303,22,219,180,243,
131,211,13,339,302,295,222,337,47,117,116,310,68,69,181,62,324,65,
40,85,367,200,98,235,185,204,228,147,49,255,173,114,96,38,229,76,
10,262,265,283,110,233,319,20,152,189,348,84,176,75,34,275,15,182,
61,17,143,195,56,184,137,341)(5,358,86,347,399,125,81,360,127,267,
108,67,366,58,194,353,390,122,223,309,32,259,277,280,132,66,313,104,
46,28,369,287,93,395,314,338,357,307,44,342,175,57,102,77,218,80,
361,73,74,232,26,25,95,205,320,247,240,203,129,331,11,299,362,323,
120,239,128,257,64,54,269,260,335,178,246,398,236,397,139,201)
(12,94,90,258,18,151,371,106,220,363,60,43,242,270,321,19,291,316,
210,374,63,70,169,27,237,327,244,271,298,215,305,115,373,72,79,168,
332,226,251,123,221,272,300,99,82,179,322,36,171,391,124,284,52,48,
130,356,278,224,193,241,141,89,308,380,149,16,24,71,118,126,393,162,
234,53,401,301,349,318,264,186),
(1,353,386,375,57,380,75,86,139,56,313,201,152,126,112,199,366,322,279,
343,173,300,138,97,68,94,79,55,269,169,331,177,39,168,16,115,157,
259,30,124,193,117,222,272,267,123,226,50,390,26,114,76,166,156,333,
210,363,388,242,108,63,171,334,357,392,352,84)(2,33,165,125,160,183,
346,54,9,275,129,154,307,184,361,351,41,3,91,127,67,291,394,250,
245,295,400,324,393,87,258,360,402,101,349,78,340,186,348,248,62,38,
23,49,20,379,217,344,174,238,195,151,318,5,391,365,316,204,61,378,
31,42,137,60,142,131,164)(4,159,282,64,25,268,311,237,264,153,17,
288,384,233,359,256,34,214,172,220,287,35,224,15,27,72,350,277,51,
59,372,216,44,325,135,18,89,104,306,207,383,105,298,109,330,381,263,
69,116,312,266,194,377,236,252,376,119,232,271,150,354,188,244,227,225,
337,149)(6,278,362,103,328,65,40,47,234,231,98,32,342,179,270,355,
304,212,196,197,327,81,341,202,387,228,7,243,395,106,255,299,308,200,
132,74,148,22,336,120,178,309,389,356,96,260,144,80,370,24,371,335,
185,215,221,314,29,374,276,170,46,399,294,198,396,10,191)
(8,219,12,134,310,211,13,28,99,382,192,73,301,145,58,66,240,167,
45,90,102,293,82,230,297,345,303,83,261,158,284,133,229,100,364,253,
280,206,249,92,53,235,358,113,368,180,292,290,273,329,163,367,246,285,
398,141,265,281,140,323,251,205,401,48,254,136,187)(11,122,274,110,289,
130,315,176,36,190,320,321,305,213,162,247,338,175,85,19,286,283,70,
77,52,189,14,155,239,111,326,107,121,319,223,118,71,347,241,143,88,
203,296,302,332,182,146,93,147,37,373,257,21,161,128,208,339,397,181,
95,369,43,385,317,209,218,262)]],
[3,Factorial(402)/2,1,"2",[[401,1]],400,"A_n",["A",402,1],402],
[4,Factorial(402),0,"2",[[401,1]],402,"S_n",["A",402,1],402]];
PRIMGRP[403]:=
[[1,Factorial(403)/2,1,"2",[[402,1]],401,"A_n",["A",403,1],403],
[2,Factorial(403),0,"2",[[402,1]],403,"S_n",["A",403,1],403]];
PRIMGRP[404]:=
[[1,Factorial(404)/2,1,"2",[[403,1]],402,"A_n",["A",404,1],404],
[2,Factorial(404),0,"2",[[403,1]],404,"S_n",["A",404,1],404]];
PRIMGRP[405]:=
[[1,Factorial(405)/2,1,"2",[[404,1]],403,"A_n",["A",405,1],405],
[2,Factorial(405),0,"2",[[404,1]],405,"S_n",["A",405,1],405]];
PRIMGRP[406]:=
[[1,12180,1,"2",[[15,13],[30,7]],1,"L2,29#406.1",["L",[2,29],1]
,
[(1,14,13,12,11,10,9,8,7,6,5,4,3,2)(15,39,63,98,134,
102,137,180,147,105,25,36,60,95)(16,40,64,43,67,108,148,194,200,
106,140,182,142,183)(17,28,65,99,135,175,178,154,195,107,141,87,122,
165)(18,29,53,89,126,82,118,162,42,66,114,153,143,184)
(19,30,54,90,127,157,176,189,201,79,116,168,51,74)(20,31,55,91,
128,169,21,32,56,92,129,170,144,185)(22,33,57,93,130,171,159,198,
190,100,81,117,145,41)(23,34,58,27,38,62,97,133,174,101,136,179,
104,139)(24,35,59,94,131,172,86,121,164,46,69,110,146,186)
(26,37,61,96,132,173,177,199,160,103,138,181,83,119)(44,49,72,111,
150,192,202,161,156,191,188,84,77,125)(45,68,109,149,85,120,163)
(47,70,52,75,113,152,193,155,196,158,197,88,123,80)(48,71,78,115,
167,50,73,112,151,187,203,76,124,166)(204,250,277,268,293,286,232,242,
219,275,280,262,231,253)(205,251,285,237,294,224,233,306,220,266,305,209,
246,283)(206,252,228,256,216,291,234,270,221,288,304,240,264,273)
(207,244,238,296,225,303,235,259,222,302,210,247,265,297)(208,245,282,287,
295,243,236,271,223,299,226,254,214,290)(211,248,218,298,292,261,239,308,
212,249,284,260,263,307)(213,278,276,229,257,217,289,241,267,274,279,301,
230,258)(215,281,272,269,300,227,255)(309,346,390,397,321,340,348,335,391,
373,380,384,351,326)(310,323,330,337,324,406,369,396,392,372,315,338,332,
318)(311,377,356,362,385,404,381,344,341,371,347,379,339,395)
(312,314,322,387,349,357,313,353,366,317,358,316,388,401)(319,398,343,350,
389,320,405,359,363,354,394,325,378,336)(327,365,400,393,376,370,375,333,
367,361,329,331,342,403)(328,334,399,368,386,360,383,352,345,382,355,364,
402,374),(1,173,204)(2,39,205)(3,172,206)(4,62,207)(5,171,208)
(6,170,209)(7,169,210)(8,157,16)(9,82,141)(11,175,143)
(12,108,127)(13,102,211)(14,174,212)(15,342,213)(17,168,197)
(18,158,89)(19,134,214)(20,277,140)(21,307,202)(22,399,215)
(23,400,216)(24,262,107)(25,270,123)(26,324,217)(27,302,192)
(28,196,51)(29,41,218)(30,104,219)(31,322,220)(32,370,221)
(33,336,222)(34,359,223)(35,375,224)(36,401,225)(37,305,200)
(38,275,135)(40,80,118)(42,164,226)(43,74,150)(44,132,227)
(45,323,228)(46,282,154)(47,136,229)(48,264,111)(49,128,230)
(50,253,90)(52,198,231)(53,91,232)(54,109,233)(55,321,234)
(56,402,235)(57,403,236)(58,345,237)(59,348,238)(60,281,148)
(61,239,65)(63,271,126)(64,156,116)(66,103,240)(67,153,152)
(68,245,77)(69,360,241)(70,125,75)(71,372,242)(72,142,114)
(73,338,243)(76,329,244)(78,383,246)(79,199,247)(81,251,87)
(83,297,184)(84,166,248)(85,404,249)(86,319,250)(88,97,252)
(92,311,254)(93,261,106)(94,310,255)(95,309,256)(96,304,195)
(98,312,257)(99,149,258)(100,362,259)(101,295,182)(105,386,260)
(110,393,263)(112,388,265)(113,151,266)(115,331,267)(117,306,201)
(119,361,268)(120,296,183)(121,301,191)(122,124,269)(129,381,272)
(130,350,273)(131,283,155)(133,355,274)(137,285,161)(138,356,276)
(139,300,189)(144,346,278)(145,369,279)(146,303,193)(147,341,280)
(159,289,176)(160,379,284)(162,194,188)(163,328,286)(165,185,287)
(167,364,288)(177,380,290)(178,190,291)(179,358,292)(180,389,293)
(181,394,294)(186,390,298)(187,371,299)(203,340,308)(313,367,327)
(314,378,330)(315,368,325)(316,318,320)(317,387,376)(326,347,396)
(332,333,339)(334,391,351)(335,392,377)(337,395,365)(343,353,385)
(344,357,398)(349,384,382)(352,373,366)(354,397,363)(374,406,405)]],
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["L",[2,29],1],
[(1,59,359,227,97)(2,115,253,355,132)(3,397,237,214,326)(4,128,400,153,
37)(5,262,272,38,405)(6,64,328,175,121)(7,114,282,63,151)
(8,275,29,12,391)(9,244,174,230,92)(10,34,107,381,277)
(11,119,137,350,194)(13,138,276,283,204)(14,398,347,342,235)
(15,50,373,67,306)(16,73,187,403,252)(17,136,164,152,146)
(18,291,61,60,78)(19,209,309,48,71)(20,241,173,258,31)
(21,267,133,303,318)(22,218,259,149,317)(23,310,250,70,316)
(24,314,53,331,315)(25,401,200,43,263)(26,337,268,266,257)
(27,169,129,104,229)(28,55,148,302,371)(30,245,224,168,396)
(32,141,382,158,390)(33,340,233,134,65)(35,249,281,307,86)
(36,160,240,399,166)(39,308,100,270,363)(40,88,202,324,207)
(41,111,93,389,198)(42,242,377,394,213)(44,172,406,101,300)
(45,109,380,81,127)(46,356,186,62,313)(47,386,322,197,94)
(49,179,215,232,372)(51,339,162,358,56)(52,140,279,393,404)
(54,205,231,89,165)(57,216,296,264,130)(58,188,325,139,210)
(66,72,278,108,304)(68,238,155,311,225)(69,191,365,261,211)
(74,201,75,312,120)(76,106,321,271,82)(77,199,206,156,190)
(79,171,349,102,285)(80,196,90,91,295)(83,161,126,402,319)
(84,193,280,345,289)(85,178,385,348,346)(87,163,297,239,159)
(95,284,329,370,154)(96,354,145,336,228)(98,181,323,375,150)
(99,122,327,305,226)(103,360,182,170,392)(105,251,361,157,203)
(110,212,298,142,378)(112,180,254,383,338)(113,290,223,388,335)
(116,376,167,364,236)(117,248,147,125,288)(118,293,124,369,177)
(123,247,333,185,357)(131,379,135,143,344)(144,384,395,341,299)
(176,330,334,219,332)(183,366,387,287,246)(184,274,294,301,368)
(189,195,243,208,362)(192,255,292,269,343)(217,320,352,234,367)
(220,351,353,374,286)(222,273,256,265,260),
(1,298,96,308,289,281,23,354,111,97,255,217,239,83,284,315,98,74,266,
223,335,141,182,333,314,51,226,294,348,36)(2,259,363,356,241,326,209,
85,242,235,42,234,299,252,374,303,250,149,285,176,257,197,150,225,338,
7,185,293,32,330)(3,271,46,169,248,99,108,24,4,319,203,77,318,
146,403,366,263,31,94,254,332,245,219,224,334,180,118,220,204,287)
(5,103,380,392,312,121,75,371,172,87,13,79,177,310,216,345,365,181,
339,95,247,211,307,207,39,47,132,43,184,256)(6,102,170,295,388,90,
120,115,109,390,165,208,92,105,323,37,280,343,114,22,311,240,86,304,
123,117,364,188,231,26)(8,68,106,322,128,60,278,124,136,151,279,63,
55,107,361,163,337,302,58,327,336,126,362,262,158,368,125,67,38,238)
(9,168,89,30,167,129,78,321,386,391,324,93,119,316,11,40,222,261,
101,57,215,100,179,212,296,393,369,17,61,190)(10,82,277,387,50,152,
15,344,71,195,232,399,406,317,201,133,331,300,221,260,53,186,360,218,
273,269,194,139,384,65)(12,66,174,160,35,274,155,355,373,359,381,171,
282,159,193,192,116,153,404,276,110,199,104,402,396,122,156,27,389,401)
(14,272,346,161,305,367,148,342,140,237,320,127,227,372,253,48,196,162,
69,191,154,80,395,349,350,59,328,385,73,275)(16,29,352,178,52,214,
236,347,357,18,383,376,258,84,142,228,166,210,189,292,145,41,249,351,
244,112,291,375,398,230)(19,144,306,213,301,233,56,340,62,88,265,70,
200,353,229,198,378,206,173,138,270,44,130,267,135,329,379,297,377,34)
(20,290,183,246,113,286,268,341,251,370,243,21,143,157,264,28,49,175,
81,137,405,202,147,33,313,325,358,288,309,382)(25,400,187,76,64,134,
205,394,54,131,45,164,397,72,283)]],
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[(26,27,28)(53,54,55)(79,80,81)(104,105,106)(128,129,130)(151,152,153)
(173,174,175)(194,195,196)(214,215,216)(233,234,235)(251,252,253)
(268,269,270)(284,285,286)(299,300,301)(313,314,315)(326,327,328)
(338,339,340)(349,350,351)(359,360,361)(368,369,370)(376,377,378)
(383,384,385)(389,390,391)(394,395,396)(398,399,400)(401,402,403)
(404,406,405),(1,29,56,82,107,131,154,176,197,217,236,254,271,287,302,
316,329,341,352,362,371,379,386,392,397,401,404,406,28)(2,30,57,83,
108,132,155,177,198,218,237,255,272,288,303,317,330,342,353,363,372,380,
387,393,398,402,405,27,55)(3,31,58,84,109,133,156,178,199,219,238,
256,273,289,304,318,331,343,354,364,373,381,388,394,399,403,26,54,81)
(4,32,59,85,110,134,157,179,200,220,239,257,274,290,305,319,332,344,
355,365,374,382,389,395,400,25,53,80,106)(5,33,60,86,111,135,158,
180,201,221,240,258,275,291,306,320,333,345,356,366,375,383,390,396,24,
52,79,105,130)(6,34,61,87,112,136,159,181,202,222,241,259,276,292,
307,321,334,346,357,367,376,384,391,23,51,78,104,129,153)
(7,35,62,88,113,137,160,182,203,223,242,260,277,293,308,322,335,347,
358,368,377,385,22,50,77,103,128,152,175)(8,36,63,89,114,138,161,
183,204,224,243,261,278,294,309,323,336,348,359,369,378,21,49,76,102,
127,151,174,196)(9,37,64,90,115,139,162,184,205,225,244,262,279,295,
310,324,337,349,360,370,20,48,75,101,126,150,173,195,216)
(10,38,65,91,116,140,163,185,206,226,245,263,280,296,311,325,338,350,
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186,207,227,246,264,281,297,312,326,339,351,18,46,73,99,124,148,171,
193,214,234,253)(12,40,67,93,118,142,165,187,208,228,247,265,282,298,
313,327,340,17,45,72,98,123,147,170,192,213,233,252,270)
(13,41,68,94,119,143,166,188,209,229,248,266,283,299,314,328,16,44,
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189,210,230,249,267,284,300,315,15,43,70,96,121,145,168,190,211,231,
250,268,285,301)]],
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[(1,46,32,49,47,29,55)(2,370,5,364,145,75,378)(3,365,141,210,343,
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133,345,98,76,340,8,342,83,386,332,61,351)(4,166,152,264,375,74,
400,7,244,107,169,377,64,403,21,366,132,247,122,59,406,11,367,146,
387,188,63,130,6,369,136,388,371,77,196,10,121,131,390,262,78,385,
24,187,135,124,167,80,270,25,363,149,190,245,57,175,27,261,150,379,
374,60,253)(9,306,140,355,293,79,235,14,319,143,295,376,62,315,15,
352,138,389,227,67,328,18,292,151,229,307,68,361,13,368,134,309,320,
71,301,26,226,139,322,353,66,405)(12,277,137,280,278,65,286)
(19,144,147,372,73,81,28)(20,72,153,22,362,58,391)(30,50,43,35,
44)(31,33,54,38,52,48,51,34,37)(36,41,42,45,40,53)
(82,170,339,199,348,99,392,184,198,119,84,395,258,213,344,102,191,241,
110,164,105,265,337,209,347,85,248,118,155,350,89,393,333,212,185,88,
125,163,215,259,103,380,336,176,242)(86,346,94,211,329)(87,310,316,206,
290,104,230,303,203,341,91,394,223,202,317,96,296,338,197,304,93,356,
289,214,224,92,323,330,201,349)(90,281,274,200,275)(95,101,335,204,205)
(108,174,269,267,382,381,192,178,112)(109,157,129,158,402,263,397,189,249)
(111,161,327,260,298,383,231,182,240,120,160,404,218,312,321,357,181,251)
(113,172,384,266,193,246,126,154,252)(114,159,285,254,283,279,282,180,237)
(115,173,234,256,325,354,297,194,217,116,162,360,255,401,228,311,183,243)
(117,165,300,268,232,308,324,186,238,128,156,314,257,358,294,398,177,239)
(123,171,195,236,127,168,399,179,250)(219,272,273,276,271,284)
(220,313,222,305,288,359)(221,302,318,291,299,233)(225,287,326),
(1,340,401,277,327,202,178,387,40,329,25,370,404,200,183,309,238,347)
(2,130,233,281,162,67,112,231,50,163,78,121,234,211,154,75,115,224,
23,175,79,114,222,310,157,77,31,223,393,166,80,110,177,386,160,70,
4,235,394,159,68,116,217,392,33,69,127,226,395,155,60,124,220,346,
6,81,128,219,323,161,63,126,36,335,172,72,129,197,191,169,66,119,
9,396,173,65,117,221,248,171,29,118,232,365,174,61,109,229,296,164)
(3,385,359,254,140,92,246,357,38,141,103,363,360,199,132,100,294,341,
11,153,104,279,318,256,135,102,48,330,267,144,105,209,186,264,138,95,
21,361,268,137,93,308,243,266,32,94,382,352,269,133,85,379,291,259,
5,106,383,276,257,139,88,381,45,258,150,97,384,206,179,147,91,344,
18,270,151,90,321,305,236,149,30,333,358,261,152,86,189,355,255,142)
(7,391,299,275,15,315,251,282,42,303,250,366,54,204,193,364,300,205)
(8,196,389,271,317,14,253,398,39,316,312,244,399,35,184,388,292,350)
(10,400,53,274,325,306,252,212,34,334,298,342,27,216,194,280,288,304)
(12,328,313,237,324,41,241,397,46,339,213,187,390,201,185,22,301,349)
(13,351,26,286,326,272,240,311,37,336,52,331,402,207,195,210,181,345)
(16,403,368,285,203,182,247,297,44)(17,28,405,284,273,302,239,249,51,
43,337,367,369,215,176,190,295,290)(19,406,214,180,322,287,242,24,55,
338,283,319,314,198,192,49,289,348)(20,378,376,278,320,307,245,374,47,
332,375,362,377,208,188,372,293,343)(56,123,225,265,131)(57,111,230,170,
59)(58,82,228,356,158)(62,125,156,76,108)(64,107,87,380,165)
(71,113,134,101,168)(73,122,227,373,167)(74,120,218,148,84)
(83,99,354,260,136)(89,146,96,263,143)(98,371,353,262,145)]],
[5,Factorial(406)/2,1,"2",[[405,1]],404,"A_n",["A",406,1],406],
[6,Factorial(406),0,"2",[[405,1]],406,"S_n",["A",406,1],406]];
PRIMGRP[407]:=
[[1,Factorial(407)/2,1,"2",[[406,1]],405,"A_n",["A",407,1],407],
[2,Factorial(407),0,"2",[[406,1]],407,"S_n",["A",407,1],407]];
PRIMGRP[408]:=
[[1,Factorial(408)/2,1,"2",[[407,1]],406,"A_n",["A",408,1],408],
[2,Factorial(408),0,"2",[[407,1]],408,"S_n",["A",408,1],408]];
PRIMGRP[409]:=
[[1,Factorial(409)/2,1,"2",[[408,1]],407,"A_n",["A",409,1],409],
[2,Factorial(409),0,"2",[[408,1]],409,"S_n",["A",409,1],409]];
PRIMGRP[410]:=
[[1,34208760,1,"2",[[409,1]],2,"L2,409 on projective points.1",
["L",[2,409],1],
[(3,409,407,405,403,401,399,397,395,393,391,389,387,385,383,381,379,377,375,
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)(4,410,408,406,404,402,400,398,396,394,392,390,388,
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),
(1,2,207)(3,125,289)(4,344,69)(5,340,72)(6,94,317)(7,265,145)
(8,352,57)(9,377,31)(10,235,172)(11,50,356)(12,71,334)
(13,82,322)(14,23,380)(15,106,296)(16,227,174)(17,113,287)
(18,290,109)(19,86,312)(20,191,206)(21,349,47)(22,169,226)
(24,95,298)(25,112,280)(26,213,178)(27,39,351)(28,261,128)
(29,114,274)(30,303,84)(32,151,234)(33,164,220)(34,391,400)
(35,133,249)(36,333,48)(37,405,383)(38,304,75)(40,61,316)
(41,176,200)(42,228,147)(43,285,89)(44,295,78)(45,88,284)
(46,155,216)(49,222,146)(51,212,154)(52,122,243)(53,131,233)
(54,205,158)(55,185,177)(56,244,117)(58,364,403)(59,215,143)
(60,87,270)(62,406,357)(63,375,387)(64,218,135)(65,393,367)
(66,195,156)(67,167,183)(68,103,246)(70,410,345)(73,162,182)
(74,409,342)(76,148,193)(77,99,241)(79,83,255)(80,343,402)
(81,378,366)(85,121,211)(90,123,204)(91,166,160)(92,332,401)
(93,100,224)(96,189,132)(97,320,408)(98,353,374)(101,141,175)
(102,328,395)(104,150,163)(105,115,197)(107,126,184)(108,157,152)
(110,376,339)(111,384,330)(116,319,390)(118,308,399)(119,370,336)
(120,161,136)(124,396,305)(127,301,397)(129,371,325)(130,326,369)
(134,302,389)(137,142,138)(140,300,385)(144,327,354)(149,407,269)
(153,386,286)(159,331,335)(165,281,379)(168,311,346)(170,358,297)
(171,292,362)(173,315,337)(179,404,242)(180,263,382)(181,283,361)
(186,372,267)(187,398,240)(188,245,392)(190,314,321)(192,365,268)
(194,250,381)(196,350,279)(198,259,368)(199,355,271)(201,388,236)
(202,363,260)(203,293,329)(208,223,394)(209,360,256)(210,291,324)
(214,238,373)(217,299,309)(219,348,258)(221,266,338)(225,318,282)
(229,359,237)(230,288,307)(231,247,347)(232,252,341)(239,273,313)
(248,323,254)(251,264,310)(253,294,278)(257,306,262)(272,277,276)]],
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["L",[2,409],1],
[(1,341,114,211,91,181,158,262,259,325,377,94,193,293,408,304,205,186,352,
236,383,177,301,77,141,196,385,151,271,338,246,322,26,174,161,311,355,
314,164,372,72,218,291,61,93,135,87,176,320,88,103,213,344,384,396,
223,400,402,283,104,198,248,136,363,368,298,366,276,239,346,187,13,280,
85,359,226,90,288,302,221,375,102,303,60,240,287,401,348,100,122,334,
179,57,257,65,378,39,309,172,79,43,15,99,33,120,305,24,27,376,
123,329,206,81,203,130,153,379,285,155,115,362,214,250,124,37,292,146,
35,113,335,233,361,388,208,23,354)(2,76,407,222,42,69,197,95,317,
395,284,138,393,306,180,216,68,315,275,145,51,277,300,227,349,224,101,
307,54,403,406,125,310,397,331,7,387,351,258,121,391,52,365,173,373,
251,96,308,330,82,29,143,190,370,127,328,55,209,128,142,340,204,71,
345,150,9,243,84,191,154,64,132,62,67,294,182,232,326,147,28,30,
207,34,46,86,217,327,342,110,254,343,295,337,369,139,212,358,58,266,
116,75,119,269,256,404,108,184,92,159,279,45,234,289,353,129,253,47,
194,78,244,225,126,22,137,237,336,53,105,171,168,272,249,339,219,316,89
)(3,175,8,41,134,245,169,228,286,381,350,282,106,48,133,20,318,107,
364,374,220,17,265,347,109,238,231,59,21,162,157,36,195,281,260,405,
98,267,97,230,73,290,38,319,380,6,274,189,74,278,4,386,160,313,
264,360,252,263,201,299,215,131,229,167,178,70,166,117,270,44,18,152,
356,241,156,16,50,111,392,140,357,200,333,163,332,25,170,149,235,394,
273,268,409,371,199,192,321,83,165,5,210,56,66,323,112,410,297,382,
324,148,80,49,144,202,261,185,296,389,14,255,19,367,10,247,32,242,
118,40,11,390,312,188,398,183,12,63),
(1,393,56,123,401,108,71,98,176,329,188,164,66,359,398,60,15,181,219,
388,279,182,207,342,370,264,403,6,25,323,396,144,240,106,223,50,41,
408,75,209,210,111,287,180,4,268,33,154,335,20,410,293,381,338,341,
386,138,112,194,90,62,390,340,115,187,13,295,67,69,324,100,355,357,
129,3,237,309,84,34,362,334,230,312,286,38,83,86,43,131,14,404,
89,270,391,156,12,244,137,313,214,215,349,16,383,374,201,318,184,280,
28,101,399,10,21,160,54,82,217,242,145,36,205,243,409,364,26,65,
358,260,236,95,248,326,353,316,23,301,368,31,2,46,261,55,161,113,
322,157,206,407,146,70,208,121,173,344,81,22,155,307,128,239,292,170,
147,122,259,291,400,94,321,166,30,212,394,258,103,330,24,133,165,302,
277,254,132,185,296,117,269,402,343,80,251,303,216,354,278,17,218,267,
102,311,263,369,163,378)(5,350,142,337,91,255,104,253,19,99,298,152,
193,85,339,231,272,126,325,405,171,320,169,333,87,282,74,11,379,227,
232,265,199,328,9,345,183,288,266,361,397,195,224,143,78,135,375,77,
73,262,317,382,376,285,189,68,53,204,196,299,315,118,39,175,363,178,
167,294,252,233,110,124,250,247,88,273,198,395,35,238,119,387,284,211,
44,392,221,275,319,377,59,297,245,373,234,76,352,168,360,150,148,384,
116,58,92,57,271,327,222,18,283,114,372,134,120,93,8,331,304,290,
52,310,141,406,202,97,153,367,332,366,308,40,276,274,64,256,72,348,
190,51,179,127,365,47,105,149,203,32,380,213,140,37,305,186,389,29,
226,151,336,177,174,300,314,191,172,130,257,246,61,249,385,306,109,125,
228,220,371,356,235,139,48,42,107,162,351,347,49,289,346,281,200,229,
27,63,158,136,241,79,7,96,225,159,192,197,45)]],
[3,Factorial(410)/2,1,"2",[[409,1]],408,"A_n",["A",410,1],410],
[4,Factorial(410),0,"2",[[409,1]],410,"S_n",["A",410,1],410]];
PRIMGRP[411]:=
[[1,Factorial(411)/2,1,"2",[[410,1]],409,"A_n",["A",411,1],411],
[2,Factorial(411),0,"2",[[410,1]],411,"S_n",["A",411,1],411]];
PRIMGRP[412]:=
[[1,Factorial(412)/2,1,"2",[[411,1]],410,"A_n",["A",412,1],412],
[2,Factorial(412),0,"2",[[411,1]],412,"S_n",["A",412,1],412]];
PRIMGRP[413]:=
[[1,Factorial(413)/2,1,"2",[[412,1]],411,"A_n",["A",413,1],413],
[2,Factorial(413),0,"2",[[412,1]],413,"S_n",["A",413,1],413]];
PRIMGRP[414]:=
[[1,Factorial(414)/2,1,"2",[[413,1]],412,"A_n",["A",414,1],414],
[2,Factorial(414),0,"2",[[413,1]],414,"S_n",["A",414,1],414]];
PRIMGRP[415]:=
[[1,Factorial(415)/2,1,"2",[[414,1]],413,"A_n",["A",415,1],415],
[2,Factorial(415),0,"2",[[414,1]],415,"S_n",["A",415,1],415]];
PRIMGRP[416]:=
[[1,62400,1,"2",[[15,1],[25,4],[75,2],[150,1]],1,"U3,4#416.1",
["2A",[2,4],1],
[(2,3,5,9,17)(4,7,13,24,43)(6,11,21,38,68)(8,15,28,51,
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(16,30,55,41,73)(18,32,59,104,119)(20,36,64,81,46)
(22,40,71,124,201)(25,45,80,138,192)(27,49,87,149,233)
(29,53,94,160,243)(31,57,100,169,255)(33,61,108,179,265)
(35,50,88,151,103)(37,66,116,191,275)(39,70,122,199,54)
(44,78,134,95,162)(48,85,146,229,129)(52,92,157,67,118)
(56,98,141,120,195)(58,102,105,174,182)(60,106,175,261,341)
(63,112,185,148,232)(65,114,187,259,173)(69,115,189,274,350)
(72,126,204,290,361)(74,128,207,295,363)(77,132,211,91,155)
(79,136,217,304,325)(82,140,223,186,272)(84,144,125,203,288)
(86,147,231,314,379)(89,153,220,101,170)(93,131,209,273,145)
(96,164,111,123,190)(97,165,250,330,248)(99,168,214,180,267)
(107,177,263,343,385)(109,181,213,299,133)(113,161,245,278,159)
(117,193,258,336,266)(121,197,206,282,276)(135,215,301,368,356)
(137,219,306,334,271)(139,221,307,371,391)(143,226,184,270,230)
(150,172,183,269,348)(152,208,246,327,188)(154,238,320,384,337)
(156,202,286,260,339)(163,227,171,257,335)(166,252,331,393,194)
(167,254,333,377,413)(176,262,342,256,242)(178,264,345,397,360)
(196,279,351,235,234)(198,280,352,281,312)(200,283,355,329,392)
(205,292,340,396,403)(210,251,218,305,370)(212,297,365,401,416)
(216,302,315,380,346)(222,308,228,313,378)(224,310,375,353,400)
(225,237,294,311,277)(236,318,289,359,268)(239,321,386,349,338)
(240,323,387,362,404)(241,324,388,399,415)(244,326,389,285,347)
(247,328,390,414,367)(249,316,372,409,344)(253,332,394,410,398)
(284,303,369,300,354)(287,358,383,406,291)(293,319,382,309,373)
(296,364,405,376,412)(298,322,357,402,381)(366,407,411,408,395),
(1,2,4,8,16,31,58,103,169,256,326,144,34)(3,6,12,19,35,63,
113,186,153,237,61,109,182)(5,10,20,37,67,119,194,270,264,327,318,
279,189)(7,14,27,50,89,85,136,218,203,289,360,378,267)
(9,18,33,53,95,163,248,204,291,254,226,142,80)(11,22,41,74,129,
126,205,293,362,146,230,122,17)(13,25,46,82,141,225,312,307,199,282,
66,117,23)(15,29,54,96,160,244,232,316,261,304,295,221,181)
(21,39,36,65,115,190,75,131,210,296,364,134,214)(24,44,79,137,220,
174,197,47,84,145,228,252,157)(26,48,86,148,112,71,125,43,77,133,
213,300,219)(28,52,93,159,242,223,233,317,381,132,212,298,177)
(30,56,99,104,173,260,340,394,375,283,351,320,385)(32,60,107,178,215,
262,302,55,97,166,253,128,208)(38,69,121,198,281,354,379,392,355,49,
64,42,76)(40,72,127,206,294,73,108,180,268,347,398,361,403)
(45,81,139,222,309,374,359,363,397,413,162,247,185)(51,91,156,240,313,
321,358,201,285,356,401,292,250)(57,101,171,258,337,98,167,170,100,124,
202,287,155)(59,105,88,152,236,319,383,405,390,412,339,388,118)
(62,111,184,271,349,399,416,402,306,106,176,211,130)(68,120,196,149,164,
249,329,272,193,277,274,348,288)(70,123,200,284,265,346,229,255,334,380,
245,314,352)(78,135,216,303,116,192,276,290,323,384,389,179,266)
(83,143,227,286,357,301,333,370,94,161,246,110,183)(87,150,234,231,315,
165,251,195,278,90,154,239,322)(92,158,241,308,372,350,269,299,367,305,
257,331,175)(102,172,259,338,395,387,187,138,151,235,168,209,191)
(114,188,273,336,342,332,238,275,280,353,343,365,406)(140,224,311,377,373,
411,324,386,404,382,407,415,335)(147,217,243,325,369,409,414,297,366,408,
396,328,391)(207,263,344,345,310,376,400,393,371,410,341,330,368)]],
[2,124800,0,"2",[[15,1],[50,2],[75,2],[150,1]],1,
"U3,4#416.2",["2A",[2,4],1],
[(1,43,262,261,112,53,335,218,409,267)(2,201,263,317,77,36,147,185,83,
171)(3,265,62,275,128,252,336,51,95,301)(4,58,173,139,149,402,316,
229,39,100)(5,46,230,16,224,79,88,93,81,414)(6,358,270,108,337,
386,67,164,159,174)(7,412,169,287,366,321,228,315,168,141)
(8,236,10,226,298,357,362,389,13,256)(9,130,393,249,214,397,339,319,
373,320)(11,410,221,84,259,372,194,290,241,60)(12,162,207,318,234,205,
371,30,212,165)(14,260,401,107,311,152,172,157,103,334)(15,176,136,209,
73,186,118,370,72,399)(17,90,405,248,150,69,351,216,331,19)
(18,29,208,341,330,375,193,101,279,305)(20,349,332,61,140,383,80,42,
278,359)(21,345,338,215,343,294,191,406,326,52)(22,300,161,146,283,381,
82,195,253,309)(23,415,416,219,380,78,132,238,202,49)(24,166,365,411,
340,28,180,155,117,281)(25,203,54,187,153,307,154,45,110,47)
(26,86,251,109,384,246,293,167,40,122)(27,235,284,129,97,282,352,291,
239,91)(31,274,272,135,131,233,344,182,392,404)(32,184,413,175,271,390,
35,355,181,322)(33,89,333,144,142,395,247,273,299,400)(34,232,367,163,
137,138,312,127,237,200)(37,211,179,280,368,96,48,160,303,105)
(38,313,244,394,133,106,346,324,254,64)(41,217,123,99,308,151,354,242,
382,197)(44,158,222,227,243,148,57,374,295,245)(50,347,178,199,188,196,
177,225,250,104)(55,183,98,189,391,75,102,94,190,268)(59,286,323,327,
258)(63,407,257,369,388,348,76,350,204,85)(65,304,292,310,71,314,306,
329,220,297)(66,120,356,302,376)(68,115,119,385,277,396,387,328,379,70)
(74,113,134,360,145,325,408,114,125,285)(87,170,353,121,266)
(92,192,213,126,364,210,377,223,264,255)(111,342,206,288,116,398,269,378,
156,124)(143,198,363,296,231,403,361,289,276,240),
(1,193,387,244,128,250,324,295,150,40,248,183,50,271,54)(2,59,63,359,
352,232,38,297,158,206,235,148,381,356,185)(3,400,198,280,39,33,196,
207,6,114,240,406,116,91,318)(4,190,70,366,31,269,110,53,74,290,
87,266,194,307,132)(5,310,10,56,165,292,109,363,273,301,168,47,281,
404,60)(7,283,221,130,83)(8,86,361,302,80,243,383,249,140,107,157,
142,58,76,153)(9,152,89,350,179,144,246,119,24,386,315,217,202,412,
391)(11,189,117,298,322,99,32,215,155,66,303,219,173,279,172)
(12,353,236,262,348,294,340,97,105,29,180,18,134,306,402)
(13,272,68,126,100,351,143,139,174,160,257,65,253,34,195)
(14,163,145,332,309,49,407,228,171,176,410,42,101,403,203)
(15,254,344,275,409,377,178,103,138,61,67,367,115,278,389)
(16,167,365,364,201,274,120,379,338,216,88,213,357,192,98)
(17,26,259,51,36,263,277,166,268,384,78,212,380,382,376)
(19,159,286,255,147,264,84,127,141,75,247,238,270,372,369)
(20,25,258,95,326,122,408,374,224,394,92,375,164,124,137)
(21,96,209,133,204,57,311,342,393,234,146,288,208,220,129)
(22,385,360,333,28,320,388,73,358,52,188,327,390,300,55)
(23,104,349,313,156,282,106,343,368,123,299,337,251,397,187)
(27,94,191,184,43,181,175,355,291,131,85,135,136,82,321)
(30,102,245,312,225,347,260,405,231,182,265,399,239,197,413)
(35,341,199,161,218,323,415,331,214,328,227,267,317,233,336)
(37,62,411,296,230,304,289,48,256,284,200,44,237,371,223)
(41,398,72,276,93,46,345,392,329,90,305,242,416,169,335)(45,113,316)
(64,205,362,111,79,330,325,252,334,396,210,77,293,222,211)
(69,395,346,401,378,177,287,229,354,154,319,121,339,149,108)(71,112,241)
(81,314,370,261,118,170,186,285,373,308,151,226,125,414,162)]],
[3,249600,0,"2",[[15,1],[100,1],[150,2]],1,"U3,4#416.3",
["2A",[2,4],1],
[(1,22,119,289,87,42,395,5,142,361,169,356)(2,162,35,277,7,182,337,
326,77,109,11,329)(3,293,372,298,44,80,268,210,124,68,184,185)
(4,276,123,159,385,59,114,378,362,193,12,83)(6,229,81,168,297,65,
140,64,330,118,194,340)(8,353,34,255,354,94,341,14,270,158,192,179)
(9,46,137,226,148,189,211,212,320,147,200,299)(10,146,190,388,333,355,
280,235,259,36,183,202)(13,311,288,154,50,191,133,318,335,218,241,86)
(15,224,331,222,132,195,292,188,177,405,287,366)(16,267,286,223,283,135,
285,165,347,219,110,125)(17,393,332,365,321,122,52,305,67,304,198,312)
(18,401,197,176,258,144,208,264,149,392,120,217)(19,93,225,79,279,196,
21,221,90,39,25,38)(20,310,24,296,51,117,163,220,316,380,249,98)
(23,398,178,325,416,215,415,389,323,99,274,271)(26,53,308,375,408,302,
127,278,315,414,266,233)(27,391,265,55,400,126)(28,334,203,345,143,63,
239,150,73,207,85,253)(29,130,153,413,57,69,336,209,104,107,216,379)
(30,387,214,406,95,231,129,78,377,251,167,394)(31,234,141,96,367,363,
49,43,108,263,327,260)(32,364,346,245,33,246)(37,368,103,300,204,139,
350,348,349,97,138,281)(40,275,383,262,155,386,240,404,70,409,41,248)
(45,358,136,301,201,402,205,351,102,156,227,382)(47,410,206,48,407,294,
101,88,376,343,61,303)(54,314,186,342)(56,309,390,306,100,381,160,164,
317,344,412,174)(58,284,272,171,230,112,339,371,397,60,261,131)
(62,252,319,254,273,322,75,256,172,352,173,106)(66,338,269,105,360,145,
359,175,403,237,307,116)(71,187,84,291,82,290,111,151,236,166,257,134)
(72,243,370,247,128,228,199,76,232,152,181,121)(74,411,238,328,250,374,
399,113,369,170,92,313)(89,161,282)(91,115,180,384,157,396,213,357,242,
295,373,244),(1,171,52,162,255,151,79,374,345,19,370,395,296)
(2,128,84,219,21,387,204,69,251,410,377,164,230)(3,197,75,67,280,
153,329,312,35,111,188,9,140)(4,271,317,14,23,226,243,238,136,257,
56,48,200)(5,99,208,114,283,379,31,95,414,101,181,276,150)
(6,343,321,262,132,303,332,129,47,143,369,375,371)(7,133,416,383,74,
102,18,259,290,103,269,214,118)(8,49,179,388,100,274,93,330,260,210,
106,29,415)(10,366,309,174,195,211,236,198,156,310,275,287,209)
(11,248,339,16,166,120,385,141,292,348,105,42,376)(12,396,221,122,237,
228,51,301,147,154,364,81,353)(13,54,338,334,36,363,17,394,130,167,
270,218,381)(15,333,356,134,206,91,267,405,83,104,357,286,192)
(20,354,144,161,173,64,185,180,183,112,288,299,316)(22,300,402,235,110,
30,319,145,61,407,135,115,284)(24,392,202,223,324,400,62,63,212,139,
113,201,247)(25,73,403,315,138,94,378,305,289,336,293,322,78)
(26,191,325,227,294,160,253,190,85,76,137,361,170)(27,389,368,43,46,
401,92,50,116,246,186,298,117)(28,391,176,216,222,124,55,291,232,182,
33,71,60)(32,125,72,196,244,205,165,350,272,282,98,157,88)
(34,337,349,355,266,413,250,220,38,277,408,240,70)(37,194,108,318,258,
239,360,123,358,168,233,66,263)(39,380,187,342,347,177,107,285,307,109,
90,323,306)(40,372,242,119,148,411,155,45,82,268,89,126,231)
(41,59,53,365,265,65,278,367,281,352,314,344,213)(44,384,146,159,121,
331,152,409,142,225,169,193,97)(57,234,254,302,399,359,189,297,229,178,
172,224,327)(58,217,163,406,175,80,273,362,158,199,382,241,313)
(68,149,373,390,351,304,335,215,86,131,340,386,127)(77,203,264,311,328,
279,346,261,320,404,256,87,96)(184,295,341,249,397,326,412,245,308,207,
398,252,393)]],
[4,503193600,0,"2",[[100,1],[315,1]],1,"G2,4#416.1",["G",4,1],
[(1,221,305,345,284,358,64,408,193,121,401,272,201,298,175)(2,182,217,141,
312,266,113,189,346,103,231,374,35,378,187)(3,42,255,99,303,196,340,
132,110,359,191,413,351,148,85)(4,213,68,9,334,277,198,94,336,28,
185,205,73,278,344)(5,134,366,149,119,186,162,390,306,299,341,253,171,
258,120)(6,324,222,13,288,227,387,122,229,330,215,184,106,269,83)
(7,48,402,154,271,365,142,354,369,320,285,219,249,76,102)
(8,174,117,37,356,281,338,323,286,15,379,177,181,405,238)
(10,326,261,332,409,156,166,29,150,155,45,114,183,61,251)
(11,245,301,263,87,319,287,410,292,234,46,144,179,146,339)
(12,270,315,337,394,415,47,84,212,159,397,297,165,204,54)
(14,207,71,412,327,169,200,262,206,18,105,317,138,23,178)
(16,237,127,260,109,264,161,233,302,380,226,133,139,376,392)
(17,279,362,267,367,202,371,78,100,274,31,60,381,398,360)
(19,164,214,239,382,140,331,80,40,21,79,225,291,235,309)
(20,416,38,243,265,307,220,273,389,26,329,407,62,157,216)
(22,137,385,116,289,89,95,248,308,373,147,194,72,209,335)
(24,275,118,396,403,290,244,395,195,44,25,88,250,352,203)
(27,252,230,163,49,257,295,218,96,197,355,240,143,400,55)
(30,52,372,300,282,115,293,188,316,311,51,131,82,321,343)
(32,74,393,170,167,208,151,126,314,65,310,176,276,246,158)
(33,363,63,350,347,333,135,370,328,81,256,93,112,241,411)
(34,128,304,294,56)(36,399,173,43,357,86,50,211,404,130,92,283,414,
375,190)(39,160,342,97,247,104,232,318,69,90,391,199,325,322,101)
(41,192,123,107,53,406,228,223,75,348,368,268,153,383,388)
(57,168,172,111,353,210,108,129,361,259,152,296,67,66,70)
(58,386,349,224,377,98,59,124,236,254,180,77,91,242,145)(125,280,313)
(136,384,364),(1,269,260,297,164,365,89,246,93,99,221,196,200,190)
(2,384,262,201,205,14,401,228,296,53,48,202,220,407)(3,90,292,125,
85,162,369,258,377,305,79,357,235,252)(4,279,80,36,318,123,167,402,
266,334,186,10,137,95)(5,324,35,367,29,46,375,388,253,225,319,265,
383,170)(6,184,133,22,275,309,244,320,65,270,366,140,289,74)
(7,405,380,254,84,117,219,311,72,168,209,341,195,212)(8,393,67,285,
306,134,180,287,290,12,174,104,171,121)(9,197,353,351,18,97,329,337,
374,169,92,273,240,272)(11,356,348,303,283,19,51,242,82,114,350,115,
91,187)(13,236,326,291,336,94,55,267,60,307,207,358,132,234)
(15,76,230,250,386,111,247,17,39,333,50,293,113,299)(16,215,233,276,
268,101,349,103,325,152,321,191,328,413)(20,379,301,406,343,24,222,57,
288,71,245,56,64,206)(21,271,256,165,359,118,25,298,414,173,42,322,
347,216)(23,398,185,151,346,241,30,295,412,224,40,227,214,373)
(26,83,27,143,410,344,128,327,226,397,88,172,237,394)(28,135,146,148,
248,217,105,284,127,45,52,210,139,208)(31,399,198,302,66,147,362,392,
157,149,391,183,409,109)(32,389,41,158,408,385,316,335,86,255,178,312,
192,58)(33,232,138,257,261,161,163)(34,61,150,49,70,264,119,415,108,
281,110,211,277,304)(37,238,251,381,129,282,131,116,166,223,124,370,360,
313)(38,182,203,75,400,47,145,160,395,294,372,68,278,339)
(43,330,368,159,102,323,179,181,96,355,107,98,354,249)(44,136,199,243,
310,142,286)(54,274,154,314,213,338,193,59,120,300,363,204,396,364)
(62,177,361,153,352,156,188,239,100,176,317,73,87,378)(63,231,280,315,
144,77,81,106,78,155,112,403,331,382)(69,122,376,345,194,340,259)
(126,342,218,416,404,390,175)(130,371,141,229,189,411,308)(263,387)]],
[5,Factorial(416)/2,1,"2",[[415,1]],414,"A_n",["A",416,1],416],
[6,Factorial(416),0,"2",[[415,1]],416,"S_n",["A",416,1],416],

# this groups had been forgotten!
[7,251596800,1,"2",[[100,1],[315,1]],1,"G2,4#416",["G",4,1],
[(1,41,143,367,200,414,73,358,272,53,343,402,134)(2,394,184,252,28,
154,276,49,144,149,181,91,82)(3,400,236,168,132,260,100,147,219,
232,373,142,315)(4,158,171,279,304,162,308,52,241,33,352,39,125)
(5,66,246,393,10,47,292,229,317,354,345,151,370)(6,26,35,106,
351,104,170,203,364,88,7,37,337)(8,124,67,324,282,338,362,178,
101,397,180,222,348)(9,223,316,248,105,24,413,17,407,71,254,70,
363)(11,157,284,247,127,72,22,297,114,289,350,372,128)
(12,80,160,321,90,390,198,69,383,176,45,415,199)(13,280,322,391,
331,136,159,196,83,192,330,255,309)(14,126,375,288,161,235,215,216,
293,99,204,318,221)(15,366,117,58,32,342,103,353,240,62,202,238,
249)(16,81,410,201,36,140,77,190,283,305,21,119,60)
(18,237,335,382,89,93,153,115,374,179,121,291,385)(19,389,193,359,
214,412,332,233,268,138,258,76,25)(20,298,384,245,64,300,98,208,
137,398,295,275,50)(23,92,133,302,294,285,406,34,169,313,205,334,
123)(27,109,409,347,296,30,290,307,173,164,250,42,94)
(29,381,155,312,360,339,319,86,253,167,386,111,74)(31,165,269,314,
113,242,209,227,399,271,387,228,174)(38,85,356,243,61,408,112,257,
278,323,163,186,355)(40,231,54,206,110,368,346,185,361,263,239,189,
392)(43,51,395,135,336,287,212,56,281,376,87,207,388)
(44,146,211,46,75,166,311,299,277,188,264,194,225)(48,59,116,145,
129,220,150,156,349,333,224,301,102)(55,380,197,344,244,230,357,365,
131,63,274,403,303)(57,378,122,107,210,218,195,379,79,340,267,84,
261)(65,120,369,326,328,396,191,183,234,152,265,187,256)
(68,108,329,96,259,262,325,411,341,172,175,320,270)(78,139,148,405,
286,95,118,404,177,182,130,141,273)(97,416,327,251,226,377,401,266,
371,306,310,217,213),(1,285,315,9,129,407,197,152,206,322,33,253,111)
(2,93,310,5,320,261,81,403,413,61,46,296,307)(3,281,265,251,193,241,295,344,
286,49,162,240,243)(4,395,163,86,142,82,350,31,290,196,27,226,
355)(6,123,215,99,19,288,313,101,199,80,384,397,340)
(7,402,124,289,58,361,273,155,166,224,135,377,263)(8,76,379,149,
37,386,74,97,231,210,143,157,371)(10,133,98,272,113,78,299,176,
141,68,247,38,169)(11,287,50,171,208,349,353,393,150,398,45,266,
17)(12,18,359,268,103,205,259,87,382,346,16,21,374)
(13,368,174,236,66,222,115,323,267,14,39,297,77)(15,248,396,130,
181,217,92,312,389,100,376,85,238)(20,188,303,54,69,305,207,314,
190,227,233,309,184)(22,140,95,112,383,293,35,146,401,235,116,105,
127)(23,120,102,88,164,26,121,191,239,327,409,302,153)
(24,136,250,48,356,394,324,329,378,269,148,232,167)(25,339,404,144,
348,29,51,341,198,316,161,72,291)(28,410,159,34,338,392,319,71,
41,357,131,195,370)(30,154,366,221,192,400,202,262,375,278,64,201,
406)(32,258,362,294,390,373,372,411,363,203,160,280,213)
(36,414,345,79,186,381,237,256,292,298,399,331,91)(40,342,343,391,
306,94,90,388,276,114,47,325,270)(42,55,254,172,110,109,274,194,
249,318,147,354,337)(43,214,352,255,336,252,264,156,333,67,52,244,
220)(44,177,225,132,367,212,332,168,187,229,53,108,96)
(56,219,228,128,200,125,73,277,107,178,283,139,380)(57,63,334,75,
311,308,317,275,351,279,62,412,180)(59,151,385,360,218,118,211,416,
175,364,301,408,282)(60,204,83,65,189,145,335,387,173,365,122,223,
117)(70,158,170,326,84,234,330,138,369,284,126,328,134)
(89,347,300,304,245,216,358,104,260,209,137,165,183)(106,230,185,271,
246,257,179,119,405,242,321,182,415)]]
];
PRIMGRP[417]:=
[[1,Factorial(417)/2,1,"2",[[416,1]],415,"A_n",["A",417,1],417],
[2,Factorial(417),0,"2",[[416,1]],417,"S_n",["A",417,1],417]];
PRIMGRP[418]:=
[[1,Factorial(418)/2,1,"2",[[417,1]],416,"A_n",["A",418,1],418],
[2,Factorial(418),0,"2",[[417,1]],418,"S_n",["A",418,1],418]];
PRIMGRP[419]:=
[[1,Factorial(419)/2,1,"2",[[418,1]],417,"A_n",["A",419,1],419],
[2,Factorial(419),0,"2",[[418,1]],419,"S_n",["A",419,1],419]];
PRIMGRP[420]:=
[[1,36779820,1,"2",[[419,1]],2,"L2,419 on projective points.1",
["L",[2,419],1],
[(3,419,417,415,413,411,409,407,405,403,401,399,397,395,393,391,389,387,385,
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)(4,420,418,416,414,412,410,408,
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),(1,2,212)(3,211,213)(4,112,311)(5,358,64)
(6,12,409)(7,237,183)(8,243,176)(9,54,364)(10,98,319)
(11,20,396)(13,368,46)(14,140,273)(15,412,418)(16,159,252)
(17,341,69)(18,62,347)(19,184,224)(21,57,349)(22,255,150)
(23,365,39)(24,161,242)(25,78,324)(26,227,174)(27,290,110)
(28,404,413)(29,266,132)(30,43,354)(31,61,335)(32,218,177)
(33,99,295)(34,205,188)(35,283,109)(36,157,234)(37,45,345)
(38,93,296)(40,65,322)(41,275,111)(42,231,154)(44,261,122)
(47,209,171)(48,258,121)(49,162,216)(50,191,186)(51,245,131)
(52,304,71)(53,257,117)(55,126,246)(56,411,378)(58,282,87)
(59,401,385)(60,370,415)(63,115,249)(66,419,360)(67,221,139)
(68,82,277)(70,381,394)(72,84,271)(73,278,76)(74,133,220)
(75,367,403)(77,362,406)(79,379,387)(80,222,125)(81,148,198)
(83,407,355)(85,251,91)(86,235,106)(88,194,145)(89,363,393)
(90,138,199)(92,143,192)(94,116,217)(95,152,180)(96,223,108)
(97,135,195)(100,346,399)(101,170,156)(102,359,384)(103,210,114)
(104,168,155)(105,326,414)(107,124,196)(113,312,420)(118,144,165)
(119,123,185)(120,372,353)(127,164,136)(128,331,386)(129,325,391)
(130,137,160)(134,397,314)(141,389,315)(142,366,337)(146,351,348)
(147,342,356)(149,383,313)(151,284,410)(153,340,352)(158,395,292)
(163,380,302)(166,376,303)(167,371,307)(169,402,274)(172,265,408)
(173,339,333)(175,309,361)(178,298,369)(179,373,293)(181,416,248)
(182,263,400)(187,417,241)(189,338,318)(190,267,388)(193,382,270)
(197,398,250)(200,240,405)(201,328,316)(202,344,299)(203,357,285)
(204,291,350)(206,392,247)(207,308,330)(208,262,375)(214,321,310)
(215,377,253)(219,390,236)(225,286,334)(226,276,343)(228,300,317)
(229,289,327)(230,336,279)(232,281,332)(233,374,238)(239,301,305)
(244,272,329)(254,323,268)(256,320,269)(259,280,306)(260,297,288)
(264,287,294)]],
[2,73559640,0,"2",[[419,1]],3,"L2,419 on projective points.2",
["L",[2,419],1],
[(1,271,19,22,7,203,399,384,387,135,2,42,249,181,187,38,282,213,267,
410,146,352,262,154,419,106,388,52,324,340,253,5,255,20,241,216,286,
46,277,92,122,142,242,170,316,89,167,182,223,195,67,50,79,396,188,
209,57,331,243,276,118,47,413,80,207,176,406,43,31,234,315,175,391,
152,186,265,416,380,319,402,322,98,160,102,133,28,398,166,6,382,103,
125,245,298,185,184,138,78,237,159,60,296,332,131,94,61,72,395,272,
393,343,115,344,341,365,302,95,370,371,389,385,155,390,113,162,257,143,
392,202,3,76,58,290,256,37,105,86,233,394,227,338,32,376,196,289,
283,27,53,333,307,44,208,250,132,121,40,248,292,137,214,39,64,278,
205,212,85,174,206,297,310,358,93,270,168,70,397,180,329,415,309,148,
279,59,306,189,373,381,266,337,56,280,88,372,55,323,325,107,111,261,
177,215,417,377,171,45,420,335,49,355,259,305,112,178,119,412,287,228,
294,101,147,51,357,71,404,361,235,29,407,191,229,145,295,299,81,83,
351,34,318,126,350,69,140,25,33,217,100,347,127,258,97,409,77,226,
9,336,238,136,313,48,96,109,200,232,321,194,201,128,342,367,192,269,
114,158,366,285,274,156,198,362,99,73,353,379,123,117,210,30,374,68,
179,12,173,320,301,369,150,116,348,330,403,204,14,263,149,244,293,16,
251,21,17,35,36,311,104,41,65,62,291,63,13,134,11,334,345,312,
275,74,110,346,247,169,328,268,222,221,108,161,281,303,24,400,240,8,
378,273,304,246,308,84,4,87,26,408,141,220,254,15,231,91,172,375,
363,418,230,199,326,411,359,288,130,163,75,349,197,218,10,327,356,339,
211,183,224,239,317,90,236,164,264,284,314,129,360,120,190,165,386,151,
401,153,66,82,354,18,300,405,252,144,54,260,414,139,193,124,368,219,
225,157,364),(1,297,75,166,3,126,284,96,290,15,249,400,418,8,154,
218,80,392,277,210,164,300,257,193,140,150,219,114,185,146,188,127,266,
380,361,100,162,203,383,397,14,175,205,342,302,355,332,92,141,66,204,
374,158,291,402,101,260,359,184,411,276,283,405,119,118,32,172,398,9,
369,17,341,86,407,247,34,351,30,348,189,64,370,79,321,377,226,122,
60,133,50,299,335,130,112,331,16,223,97,207,381,263,280,28,386,275,
231,294,107,201,147,268,269,27,82,87,339,22,301,417,303,214,401,132,
379,85,52,159,139,43,240,183,42,128,346,58,304,270,365,25,134,384,
5,89,388,264,35,125,149,385,44,124,315,308,111,39,296,174,372,245,
414,220,13,396,360,24,413,357,404,325,340,26,191,51,19,78,222,375,
378,389,320,289,198,326,328,354,307,72,105,261,138,279,177,327,91,74,
363,47,367,194,142,155,416,251,371,157,358,59,93,318,376)
(2,237,295,102,136,255,38,242,362,197,40,53,419,246,148,250,121,104,
286,18,334,57,352,90,123,306,259,285,287,415,324,293,224,235,238,391,
117,176,144,4,169,273,288,209,256,200,171,253,217,182,393,199,368,241,
21,317,156,84,305,298,71,151,228,46,70,160,349,225,106,190,229,61,
170,248,343,309,137,267,67,153,12,373,152,56,36,143,110,234,63,212,
399,310,196,312,173,274,108,113,168,344,345,48,412,88,319,382,338,227,
167,333,350,232,406,98,390,179,282,83,65,278,314,145,62,135,73,387,
236,292,116,243,131,6,265,165,262,161,366,206,109,272,178,244,186,215,
23,163,77,76,208,330,337,202,11,254,353,94,211,322,37,239,409,129,
54,103,281,258,311,271,408,20,181,216,230,410,33,95,252,233,347,68,
7,49,10,81,394,45,55,420,356,313,31,403,336,221,115,395,41,187,
195,213,364,180,323,99,329,69,192,29,120,316)]],
[3,Factorial(420)/2,1,"2",[[419,1]],418,"A_n",["A",420,1],420],
[4,Factorial(420),0,"2",[[419,1]],420,"S_n",["A",420,1],420]];
PRIMGRP[421]:=
[[1,Factorial(421)/2,1,"2",[[420,1]],419,"A_n",["A",421,1],421],
[2,Factorial(421),0,"2",[[420,1]],421,"S_n",["A",421,1],421]];
PRIMGRP[422]:=
[[1,37309020,1,"2",[[421,1]],2,"L2,421 on projective points.1",
["L",[2,421],1],
[(3,421,419,417,415,413,411,409,407,405,403,401,399,397,395,393,391,389,387,
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)(4,422,420,418,416,414,412,
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),(1,2,213)(3,212,214)(4,229,196)(5,355,69)
(6,245,178)(7,347,75)(8,273,148)(9,292,128)(10,120,299)
(11,114,304)(12,24,393)(13,190,226)(14,54,361)(15,309,105)
(16,64,349)(17,136,276)(18,252,159)(19,195,215)(20,339,70)
(21,251,157)(22,241,166)(23,380,26)(25,155,249)(27,50,352)
(28,163,238)(29,138,262)(30,34,365)(31,222,176)(32,303,94)
(33,402,414)(35,322,72)(36,225,168)(37,118,274)(38,315,76)
(39,45,345)(40,294,95)(41,300,88)(42,96,291)(43,342,44)
(46,403,400)(47,183,199)(48,106,275)(49,327,53)(51,217,161)
(52,60,317)(55,56,318)(57,156,216)(58,191,180)(59,203,167)
(61,392,396)(62,112,255)(63,286,80)(65,372,412)(66,266,97)
(67,261,101)(68,232,129)(71,421,357)(73,186,170)(74,376,399)
(77,362,410)(78,162,189)(79,419,351)(81,381,387)(82,193,154)
(83,92,254)(84,383,382)(85,253,91)(86,198,145)(87,406,356)
(89,121,219)(90,206,133)(93,131,205)(98,224,107)(99,377,373)
(100,142,187)(102,119,208)(103,179,147)(104,391,354)(108,370,371)
(109,366,374)(110,182,137)(111,388,350)(113,124,192)(115,184,130)
(116,169,144)(117,411,321)(122,312,415)(123,394,332)(125,158,146)
(126,385,338)(127,306,416)(132,386,331)(134,417,298)(135,330,384)
(139,149,141)(140,363,346)(150,290,409)(151,320,378)(152,308,389)
(153,418,278)(160,360,329)(164,288,397)(165,359,325)(171,314,364)
(172,334,343)(173,341,335)(174,408,267)(175,405,269)(177,271,401)
(181,420,248)(185,404,260)(188,263,398)(194,358,297)(197,422,230)
(200,236,413)(201,390,258)(202,328,319)(204,395,250)(207,305,337)
(209,375,265)(210,270,369)(211,231,407)(218,307,324)(220,336,293)
(221,295,333)(223,367,259)(227,243,379)(228,340,281)(233,344,272)
(234,302,313)(235,368,246)(237,264,348)(239,284,326)(240,353,256)
(242,311,296)(244,316,289)(247,323,279)(257,310,282)(268,301,280)
(277,287,285)]],
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[(1,382,283,322,209,133,300,23,417,336,234,360,194,12,379,296,39,325,220,
8,138,323,231,53,59,157,239,254,333,203,377,29,392,415,305,397,6,
139,410,142,189,273,25,146,301,67,331,36,258,191,163,111,83,16,238,
363,207,393,128,249,421,85,132,284,135,268,297,389,279,302,245,317,71,
361,20,35,117,215,221,43,371,136,266,54,369,235,398,315,262,80,334,
40,358,277,251,394,141,65,372,411,312,2,183,137,91)(3,123,388,145,
374,173,140,332,204,407,160,48,46,380,148,225,293,367,307,373,153,290,
68,257,264,155,152,171,368,28,37,324,38,218,256,313,69,105,181,84,
47,81,356,64,15,420,378,419,24,269,44,175,339,130,120,243,97,414,
276,100,422,96,192,416,405,285,224,165,202,222,61,298,384,104,261,376,
58,14,286,350,86,74,357,185,309,27,87,291,270,265,242,211,149,232,
197,161,354,19,41,11,150,199,158,248,413)(4,403,187,247,385,89,337,
200,188,344,408,260,216,318,13,170,310,396,213,52,72,109,50,409,289,
278,82,178,272,174,418,280,177,31,154,144,355,99,230,5,250,275,316,
274,259,210,338,193,227,190,93,169,205,381,18,56,236,370,237,246,326,
103,122,119,10,17,206,404,121,321,387,327,401,49,126,314,228,226,114,
287,70,362,134,101,320,129,306,151,271,281,26,116,75,124,263,233,255,
340,113,77,42,125,63,32,9)(7,352,33,328,21,282,244,51,112,295,
57,179,400,22,127,45,288,182,102,78,345,131,391,186,166,319,98,168,
167,195,364,240,34,330,79,107,106,176,375,108,88,303,143,349,196,172,
92,406,229,147,252,294,95,217,399,162,223,30,412,253,366,241,342,267,
299,304,335,308,348,90,76,164,311,159,94,118,341,214,292,62,351,73,
66,365,347,329,208,201,343,212,402,60,353,156,180,115,383,110,198,184,
346,386,359,390,395),(1,395,50,402,226,366,106,393,421,241,201,250,231,
189,375,404,192,342,236,133,138,339,75,145,369,311,108,227,83,379,349,
308,109,359,222,220,128,343,361,76,332,348,378,71,374,411,356,265,25,
365,173,200,185,224,129,290,116,78,163,198,293,296,5,354,195,11,368,
140,397,151,419,176,371,196,19,28,156,299,303,417,118,67,297,362,84,
184,57,89,65,267,399,327,238,160,364,107,191,409,281,26,275,80,6,
325,268,211,110,36,261,90,255,127,345,9,172,376,298,209,137,269,51,
27,59,352,32,174,239,49,418,119,233,237,380,88,97,340,165,360,117,
385,139,396,168,105,341,182,111,240,243,338,373,38,420,246,407,312,351,
336,363,171,91,271,180,125,162,45,158,188,204,40,175,193,408,316,314,
177,7,228,187,157,33,309,8,225,167,391,41,197,398,403,300,194,344,
132,161,347,305,286,335,295,115,143,10,170,310,134,66,141,2,120,214,
154,215,279,79,42,39,392,155,289,304,208,207,102,334,389,410,313,384,
315,294,251,367,213,383,276,69,61,183,104,206,179,24,415,73,23,13,
64,72,248,87,113,100,258,212,86,68,34,422,253,307,284,414,85,412,
146,159,112,150,203,320,135,262,400,62,370,358,249,406,96,318,46,244,
131,190,302,388,230,277,60,21,17,301,245,164,94,394,317,272,273,101,
254,98,123,186,319,355,81,256,270,337,387,205,63,58,53,331,149,199,
266,280,35,181,217,350,413,18,282,15,263,264,219,142,22,372,291,235,
99,95,56,259,306,148,234,346,405,292,70,218,20,130,287,178,166,54,
136,274,401,216,333,386,4,377,390,124,31,122,252,229,283,114,82,48,
30,324,278,16,3,29,288,44,52,103,93,43,121,92,357,330,12,353,
55,47,260,153,323,169,285,242,221,152,223,126,147,202,14,329,328,232,
247,381,144,77,74,37,257,321,382,322,416)]],
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[4,Factorial(422),0,"2",[[421,1]],422,"S_n",["A",422,1],422]];
PRIMGRP[423]:=
[[1,Factorial(423)/2,1,"2",[[422,1]],421,"A_n",["A",423,1],423],
[2,Factorial(423),0,"2",[[422,1]],423,"S_n",["A",423,1],423]];
PRIMGRP[424]:=
[[1,Factorial(424)/2,1,"2",[[423,1]],422,"A_n",["A",424,1],424],
[2,Factorial(424),0,"2",[[423,1]],424,"S_n",["A",424,1],424]];
PRIMGRP[425]:=
[[1,3916800,0,"2",[[8,1],[32,1],[128,1],[256,1]],1,
"S4,4#425.1",["B",[2,4],1],
[(1,34,174,373,160,370,420,239)(2,129,114,338,242,324,346,384)
(3,30,348,109,188,201,298,329)(4,125,141,287,385,360,380,195)
(5,22,299,134,236,184,285,323)(6,289,43,99,83,186,404,153)
(7,152,363,136,302,366,128,388)(8,61,411,228,263,150,342,173)
(9,310,56,252,108,72,425,75)(10,117,379,122,249,223,162,352)
(11,176,403,42,119,422,35,331)(12,288,283,368,416,265,266,65)
(13,196,371,106,222,234,341,110)(14,205,32,246,64,90,405,118)
(15,29,391,163,349,317,104,407)(16,68,376,55,94,417,217,284)
(17,334,33,318,358,190,210,51)(18,269,281,260,272,178,308,192)
(19,67,197,303,378,305,149,316)(20,161,235,258,139,91,151,97)
(21,345,78,207,418,259,412,25)(23,180,326,268,76,365,47,262)
(24,350,330,423,395,156,225,290)(26,240,375,131,276,226,212,135)
(27,175,321,250,211,237,194,271)(28,386,336,214,200,87,202,116)
(31,101,402,59,220,144,86,364)(36,63,159,208,255,189,337,383)
(37,199,227,277,244,54,292,187)(38,295,96,312,273,168,406,177)
(39,158,286,164,257,335,256,229)(40,320,332,137,213,145,261,170)
(41,382,191,304,232,372,113,126)(44,274,353,238,319,84,181,347)
(45,315,398,198,362,400,157,88)(46,80,50,121,410,93,130,247)
(48,294,248,85,251,95,424,193)(49,275,387,307,155,183,344,204)
(52,98,120,415,148,81,356,206)(53,282,278,215,401,165,300,143)
(57,224,413,306,254,70,147,297)(58,270,333,392,279,296,374,89)
(60,421,169,154,291,381,140,127)(62,339,219,133,245,77,359,314)
(66,79,103,397,230,343,394,340)(69,115,409,100,105,301,216,124)
(71,185,92,253,243,146,361,172)(73,233,74,209,393,179,309,112)
(82,241,313,267,264,231,221,203)(102,396,182,351,369,311,167,123)
(107,218,142,132)(111,357,280,355,322,399,327,389)(138,367,293,408,171,419,
325,354)(328,414,377,390),
(1,336,170,257,111,415,316,136,377,304,335,295,182,81,91,203,98,298,315,
220)(2,396,135,122,328,263,383,379,293,343,226,19,314,342,71,284,79,
179,141,213)(3,375,282,139,165,308,187,324,132,58,108,286,17,200,358,
256,299,362,169,129)(4,84,192,337,171,339,344,43,280,23,145,290,193,
183,87,294,245,56,114,143)(5,350,376,168,47,266,74,399,107,207,69,
255,12,237,353,186,421,253,191,301)(6,49,29,161,389,185,273,425,309,
120,352,206,241,420,318,190,215,184,268,60)(7,248,68,400,401,156,33,
232,113,41,10,82,176,243,422,151,330,405,329,103)(8,197,326,423,59,
94,92,42,218,9,50,117,24,408,413,223,348,277,228,407)
(11,144,51,65,231,194,369,356,46,216)(13,130,52,21,240,354,398,418,
374,361,387,388,80,321,118,274,137,119,198,55)(14,61,152,67,355,199,
317,233,258,410,412,77,159,340,368,380,101,306,31,291)(15,16,53,70,
417,149,44,394,173,32)(18,155,167,72,196,28,373,310,157,297,313,162,
246,319,75,419,106,349,242,267)(20,230,247,54,288,251,259,174,210,89,
367,110,302,322,307,221,189,325,90,234)(22,208,63,124,386,100,202,131,
409,392,95,39,219,85,296,320,238,287,201,239)(25,281,86,244,402,212,
57,370,140,34)(26,148,133,73,269,123,333,270,195,88,250,229,99,138,
93,271,164,327,160,178)(27,121,381,37,262,205,146,334,272,104,397,225,
78,414,154,249,391,211,48,305)(30,158,175,338,393,384,292,303,404,252,
102,153,311,260,346,385,265,40,150,66)(35,424,97,163,166,188,83,363,
181,351,395,36,411,285,134,331,126,235,364,276)(38,96,390,236,366,345,
214,62,406,204,275,372,224,300,76,227,278,222,105,359)(45,279,371,125,
112,332,261,172,360,341)(64,289,147,347,416,128,382,254,109,357,127,312,
403,378,217,264,116,115,142,209)(177,283,180,323,365)]],
[2,Factorial(425)/2,1,"2",[[424,1]],423,"A_n",["A",425,1],425],
[3,Factorial(425),0,"2",[[424,1]],425,"S_n",["A",425,1],425]];
PRIMGRP[426]:=
[[1,Factorial(426)/2,1,"2",[[425,1]],424,"A_n",["A",426,1],426],
[2,Factorial(426),0,"2",[[425,1]],426,"S_n",["A",426,1],426]];
PRIMGRP[427]:=
[[1,Factorial(427)/2,1,"2",[[426,1]],425,"A_n",["A",427,1],427],
[2,Factorial(427),0,"2",[[426,1]],427,"S_n",["A",427,1],427]];
PRIMGRP[428]:=
[[1,Factorial(428)/2,1,"2",[[427,1]],426,"A_n",["A",428,1],428],
[2,Factorial(428),0,"2",[[427,1]],428,"S_n",["A",428,1],428]];
PRIMGRP[429]:=
[[1,Factorial(429)/2,1,"2",[[428,1]],427,"A_n",["A",429,1],429],
[2,Factorial(429),0,"2",[[428,1]],429,"S_n",["A",429,1],429]];
PRIMGRP[430]:=
[[1,Factorial(430)/2,1,"2",[[429,1]],428,"A_n",["A",430,1],430],
[2,Factorial(430),0,"2",[[429,1]],430,"S_n",["A",430,1],430]];
PRIMGRP[431]:=
[[1,Factorial(431)/2,1,"2",[[430,1]],429,"A_n",["A",431,1],431],
[2,Factorial(431),0,"2",[[430,1]],431,"S_n",["A",431,1],431]];
PRIMGRP[432]:=
[[1,40031280,1,"2",[[431,1]],2,"L2,431 on projective points.1",
["L",[2,431],1],
[(3,431,429,427,425,423,421,419,417,415,413,411,409,407,405,403,401,399,397,
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)
(4,432,430,428,426,424,422,420,418,416,414,412,410,408,406,404,402,400,
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),
(1,2,218)(3,428,8)(4,418,17)(5,174,260)(6,335,98)(7,307,125)
(9,266,164)(10,145,284)(11,234,194)(12,231,196)(13,306,120)
(14,400,25)(15,346,78)(16,286,137)(18,432,419)(19,103,317)
(20,76,343)(21,141,277)(22,323,94)(23,187,229)(24,377,38)
(26,189,224)(27,180,232)(28,374,37)(29,31,379)(30,356,53)
(32,162,245)(33,139,267)(34,298,107)(35,226,178)(36,422,411)
(39,165,235)(40,140,259)(41,84,314)(42,353,44)(43,115,281)
(45,102,292)(46,195,198)(47,337,55)(48,71,320)(49,111,279)
(50,124,265)(51,95,293)(52,315,72)(54,200,185)(56,193,190)
(57,405,407)(58,228,153)(59,412,398)(60,288,91)(61,255,123)
(62,408,399)(63,96,280)(64,112,263)(65,268,106)(66,104,269)
(67,209,163)(68,213,158)(69,81,289)(70,282,87)(73,217,149)
(74,135,230)(75,172,192)(77,92,270)(79,110,250)(80,406,383)
(82,160,197)(83,394,392)(85,175,179)(86,220,133)(88,118,233)
(89,128,222)(90,421,358)(93,360,416)(97,215,127)(99,389,381)
(100,114,225)(101,430,338)(105,151,183)(108,132,199)(109,184,146)
(113,414,342)(116,365,388)(117,134,188)(119,333,417)(121,384,364)
(122,352,395)(126,131,182)(129,429,311)(130,423,316)(136,161,142)
(138,402,329)(143,341,385)(144,334,391)(147,355,367)(148,376,345)
(150,420,299)(152,291,426)(154,366,349)(155,321,393)(156,340,373)
(157,325,387)(159,295,415)(166,344,359)(167,332,370)(168,371,330)
(169,297,403)(170,427,272)(171,312,386)(173,324,372)(176,262,431)
(177,296,396)(181,375,313)(186,326,357)(191,274,404)(201,271,397)
(202,425,242)(203,318,348)(204,256,409)(205,424,240)(206,301,362)
(207,249,413)(208,378,283)(210,401,258)(211,322,336)(212,247,410)
(214,308,347)(216,350,303)(219,363,287)(221,339,309)(223,368,278)
(227,369,273)(236,382,251)(237,304,328)(238,241,390)(239,276,354)
(243,380,246)(244,264,361)(248,302,319)(252,327,290)(253,285,331)
(254,305,310)(257,261,351)(275,300,294)]],
[2,80062560,0,"2",[[431,1]],3,"L2,431 on projective points.2",
["L",[2,431],1],
[(1,3,203,299,154,338,348,297,233,214,322,425,294,85,237,292,6,179,398,
358,18,390,24,165,364,23,198,161,423,378,291,356,183,33,285,177,159,
79,113,320,114,295,230,164,75,413,68,191,153,37,357,166,84,335,415,
39,54,219,34,325,367,173,365,176,270,20,314,118,139,302,148,222,190,
135,186,200,382,286,202,117,332,70,375,363,374,252,158,160,127,316,411,
263,145,408,403,201,98,128,185,28,218,290,57,234,405,399,196,52,133,
65,414,175,266,101,296,288,32,304,377,278,361,8,317,376,15,41,394,
77,152,141,289,388,421,11,149,371,110,212,156,21,429,43,309,419,199,
208,211,281,272,102,261,416,206,86,172,330,106,424,336,310,235,209,121,
9,215,373,29,339,129,284,13,273,264,334,337,346,126,236,72,116,94,
389,333,5,174,396,104,124,157,256,404,393,38,151,74,100,169,228,107,
184,267,168,241,83,257,249,14,279,370,131,50,412,63,349,146,140,311,
58,255,327,87,360,417,17,344,142,137,400,282,134,229,418,385,387,293,
171,182,170,45,213,428,343,259,163,345,359,410,355,323,397,243,406,427,
231,95,275,369,180,372,178,220,81,326,61,76,130,210,31,379,188,78,
392,354,47,132,40,381,315,250,431,225,432,36,386,368,260,82,362,189,
254,167,122,384,347,92,181,380,91,155,97,187,147,366,109,253,308,30,
251,120,223,331,312,248,197,207,391,246,342,112,2,239,274,319,193,240,
22,138,99,49,62,59,262,221,35,430,287,192,401,328,26,318,73,313,
321,55,298,19,46,64,195,341,90,216,125,71,150,238,300,103,422,194,
10,269,301,340,280,143,303,162,268,4,67,119,88,136,108,7,409,27,
426,48,111,277,383,242,402,265,205,244,276,105,351,123,12,245,307,395,
44,420,329,25,204,350,51,69,96,247,60,224,232,42,227,89,217,144,
353,258,115,80,324,283,56,53,66,16,407,93,305,352,226,271,306),
(1,151,15,145,431,69,101,68,133,141,74,427,21,58,335,242,12,321,322,
29,214,366,296,96,11,355,91)(2,402,138,52,397,197,127,279,34,171,
172,51,251,158,5,42,66,419,352,360,425,392,424,62,348,48,342)
(3,174,210,237,109,195,418,408,113,159,313,323,370,368,406,202,95,233,
204,249,310,383,338,320,394,385,211)(4,330,281,46,331,97,259,343,179,
45,337,112,231,28,332,55,284,241,116,371,205,53,38,278,13,413,153)
(6,102,26,90,374,213,217,401,387,222,120,230,93,43,245,191,111,94,
286,364,22,238,135,169,266,421,232)(7,409,136,235,329,167,132,9,61,
372,181,344,353,73,128,107,389,142,36,356,405,221,390,308,430,379,192)
(8,161,35,262,381,156,18,314,150,234,396,162,17,212,163,59,340,80,
50,215,25,10,288,122,377,252,209)(14,201,117,350,131,305,16,407,33,
290,177,270,64,79,130,328,160,199,157,273,354,423,265,208,186,175,196)
(19,124,300,412,65,147,189,264,287,247,378,269,295,71,410,299,375,218,
98,311,176,303,225,367,134,178,82)(20,400,263,373,271,106,92,276,280,
119,403,37,391,57,261,72,227,324,358,255,41,129,207,399,382,302,248)
(23,254,78,32,166,100,388,216,152,77,148,325,24,417,146,306,274,240,
184,243,236,426,144,293,404,339,267)(27,351,104,386,365,420,140,149,312,
121,432,54,361,326,164,258,357,84,56,301,114,63,185,103,272,88,137)
(30,86,47,188,362,143,376,292,49,297,318,307,285,228,70,139,220,336,
294,333,165,363,414,429,223,316,203)(31,415,239,40,226,154,89,200,349,
67,257,250,309,253,219,187,347,76,39,168,345,416,341,277,105,393,327)
(44,411,315,359,126,268,190,317,182,395,275,118,194,83,422,198,224,115,
246,206,229,304,346,428,81,193,369)(60,282,108,99,173,155,110,183,244,
289,260,398,291,87,125,123,170,180,334,380,85,75,298,384,256,283,319)]
],[3,Factorial(432)/2,1,"2",[[431,1]],430,"A_n",["A",432,1],432
],[4,Factorial(432),0,"2",[[431,1]],432,"S_n",["A",432,1],432]
];
PRIMGRP[433]:=
[[1,Factorial(433)/2,1,"2",[[432,1]],431,"A_n",["A",433,1],433],
[2,Factorial(433),0,"2",[[432,1]],433,"S_n",["A",433,1],433]];