/*
www-ATLAS of Group Representations.
(L3(2) x S4(4):2).2 represented as permutations on 524 points.
*/

G<x,y>:=PermutationGroup<524|\[
2,1,5,7,3,10,4,8,14,6,17,12,19,9,15,22,11,25,13,28,30,16,23,33,18,
36,37,20,29,21,31,43,24,34,35,26,27,49,51,53,54,56,32,52,60,61,63,65,38,50,
39,44,40,41,55,42,74,75,59,45,46,80,47,82,48,85,87,68,90,91,93,95,73,57,58,
99,101,102,79,62,106,64,109,110,66,113,67,104,116,69,70,120,71,123,72,126,128,130,76,100,
77,78,103,88,136,81,139,141,83,84,145,147,86,150,152,89,154,118,156,92,159,160,94,140,163,
96,166,97,168,98,170,149,173,174,175,105,177,179,107,124,108,142,143,184,111,187,112,148,132,114,
191,115,193,117,196,119,199,200,121,122,204,162,125,208,165,127,212,129,215,131,210,201,133,134,135,
176,137,223,138,225,181,216,228,144,231,186,146,235,237,238,151,240,153,243,195,155,246,198,157,158,
172,251,253,161,256,257,259,164,262,171,221,167,265,266,169,182,270,271,272,274,211,277,178,280,180,
248,283,183,286,287,185,289,290,292,188,294,189,190,298,192,295,300,194,303,304,197,307,226,310,311,
202,313,203,316,318,205,206,322,207,324,326,209,275,329,213,214,267,268,333,217,218,219,338,220,263,
276,222,278,279,224,345,335,227,323,285,229,230,351,232,233,354,234,355,236,241,357,297,239,361,242,
362,350,244,245,364,306,247,370,339,249,250,373,252,376,334,254,342,255,347,320,381,258,284,260,325,
261,382,386,264,388,331,391,269,315,282,393,395,273,309,379,397,317,399,344,281,366,319,401,402,302,
288,405,353,291,293,408,296,398,407,389,299,301,363,305,413,346,416,417,369,308,420,421,312,423,375,
314,377,378,340,427,321,327,409,431,426,328,433,330,360,422,332,436,336,438,337,396,341,358,343,400,
348,349,446,447,352,450,359,356,383,410,454,430,365,457,458,367,368,418,462,371,372,390,374,424,444,
385,380,470,471,412,384,432,387,439,435,392,445,394,434,440,441,442,453,425,437,403,404,473,449,406,
451,452,443,411,483,484,414,415,459,487,482,419,490,464,492,493,467,495,496,428,429,472,448,474,494,
491,477,501,479,502,481,461,455,456,485,486,460,488,506,463,476,465,466,475,468,469,497,498,499,500,
478,480,503,504,507,489,505,508,509,510,512,514,516,511,518,519,515,517,513,522,521,523,520,524]
,\[
3,4,6,8,9,11,12,13,15,16,1,18,2,20,21,23,24,26,27,29,5,31,32,34,35,
7,38,39,40,41,42,10,44,45,46,47,48,50,52,14,55,57,58,59,17,62,64,66,67,19,
68,69,70,71,72,73,22,76,77,78,79,25,81,83,84,86,88,89,28,92,94,30,96,97,98,
100,33,103,104,105,107,108,36,111,112,37,114,115,117,118,119,121,122,124,125,127,129,75,131,43,
132,133,134,135,137,138,140,142,143,144,146,148,149,151,49,153,51,155,157,158,53,161,162,54,164,
165,56,167,169,91,171,172,102,60,61,176,178,180,181,63,87,182,183,185,186,65,188,189,190,168,
141,192,194,195,197,198,130,201,202,203,205,206,207,209,210,211,213,214,74,216,217,218,128,219,220,
221,222,80,224,226,227,82,229,230,232,233,234,236,85,239,208,241,242,244,154,245,90,247,248,249,
250,252,254,255,93,258,260,261,95,263,166,264,173,267,268,269,99,101,273,275,276,278,279,281,282,
106,284,285,109,184,288,110,291,262,293,295,296,297,113,225,299,301,302,116,305,306,308,309,200,120,
312,314,315,317,319,320,321,123,323,325,327,328,126,330,331,235,150,332,334,335,336,337,339,340,341,
136,342,343,223,344,346,347,348,139,349,259,350,324,352,353,145,204,326,356,147,358,359,360,152,329,
363,364,365,366,367,368,369,156,371,243,372,374,375,159,377,378,160,379,292,380,382,383,384,385,163,
266,191,187,387,389,390,392,338,170,270,394,313,333,174,396,175,398,177,400,271,179,240,402,403,311,
404,406,407,303,253,399,409,410,411,412,388,370,193,310,414,415,196,418,307,419,199,287,422,424,272,
300,355,425,426,428,429,430,405,286,231,432,376,361,212,434,435,215,437,345,439,440,433,441,442,443,
444,445,228,448,449,451,452,453,357,237,238,455,456,354,459,460,461,246,463,464,465,466,467,251,468,
469,446,256,438,257,472,473,474,265,475,471,476,477,478,274,277,294,280,479,283,480,427,481,322,482,
289,290,408,416,298,485,486,454,304,458,488,489,362,491,421,494,483,316,318,484,470,497,498,499,493,
500,381,495,502,447,351,450,503,436,504,505,431,506,507,501,508,462,391,373,395,457,487,386,397,393,
509,401,423,413,496,417,492,420,510,490,513,515,511,517,512,520,514,521,522,516,518,519,524,523]
>;
print "Group G is (L3(2) x S4(4):2).2 < Sym(524)";