/*
www-ATLAS of Group Representations.
J2 represented as permutations on 525 points.
*/

G<x,y>:=PermutationGroup<525|\[
1,3,2,6,7,4,5,11,12,14,8,9,18,10,20,21,23,13,25,15,16,28,17,27,19,
30,24,22,33,26,36,37,29,38,39,31,32,34,35,44,45,47,49,40,41,53,42,55,43,57,
58,59,46,62,48,65,50,51,52,69,70,54,71,72,56,75,76,77,60,61,63,64,74,73,66,
67,68,86,87,89,90,92,93,95,96,78,79,99,80,81,102,82,83,105,84,85,107,108,88,110,
112,91,115,117,94,120,97,98,123,100,124,101,125,126,103,129,104,131,132,106,133,135,109,111,113,
114,141,142,116,145,118,119,121,150,122,152,153,155,157,159,127,128,162,163,130,164,165,167,169,134,
172,136,137,176,138,175,139,179,140,181,182,143,144,146,147,187,148,189,149,191,192,151,193,194,156,
154,198,200,158,203,160,161,207,209,211,213,166,216,168,195,170,171,173,174,190,196,224,177,227,178,
228,229,180,230,214,232,183,235,184,237,185,239,186,205,241,188,242,243,244,245,247,249,251,197,226,
225,199,201,202,204,257,206,259,260,208,263,210,266,212,269,215,217,218,219,220,273,221,275,222,277,
223,279,280,281,283,285,231,287,233,234,291,292,236,293,294,238,297,298,240,299,300,302,246,305,248,
308,250,310,252,253,254,315,255,317,256,319,258,306,320,321,261,262,264,265,296,295,267,268,270,271,
331,272,333,334,274,288,335,276,338,278,339,340,342,344,282,347,284,350,286,289,290,354,324,323,357,
359,361,362,364,366,301,369,303,304,307,337,336,309,311,312,378,313,380,314,382,383,316,384,367,318,
387,388,390,322,393,394,325,360,326,358,327,328,376,329,398,330,349,399,332,400,401,403,389,405,406,
363,408,341,411,343,402,345,346,348,386,385,351,352,373,353,420,413,355,356,423,425,410,365,368,370,
371,381,372,432,374,375,431,377,435,397,379,426,392,436,437,439,441,442,443,391,445,446,395,449,396,
412,450,451,452,454,407,404,457,459,409,414,415,461,416,463,417,418,419,467,421,422,448,447,424,427,
428,429,474,430,476,477,433,480,434,482,438,484,440,487,472,490,444,470,493,468,494,465,497,453,500,
455,456,503,479,458,481,460,505,462,506,498,464,509,510,466,496,512,469,471,513,491,473,486,514,475,
515,516,478,511,483,485,508,507,488,489,504,492,495,499,501,502,522,524,519,523,525,517,520,518,521]
,\[
2,4,5,1,8,9,10,3,13,15,16,17,6,19,7,22,24,20,26,25,27,11,29,12,18,
14,31,32,34,35,21,33,28,23,40,41,42,43,44,30,46,48,50,51,52,36,54,37,56,38,
39,60,61,63,64,66,67,68,57,45,62,53,47,73,74,49,59,78,79,80,76,81,55,82,83,
84,85,58,88,87,91,65,94,71,97,98,70,69,100,101,72,103,104,75,106,86,77,96,109,111,
113,114,116,118,119,112,121,122,110,99,89,95,90,127,128,92,130,93,120,105,134,136,137,138,139,
140,102,143,144,146,147,148,149,107,151,108,154,156,158,160,161,141,115,145,129,117,166,168,170,171,
173,174,175,123,177,124,178,125,180,126,142,183,184,185,186,131,188,132,190,133,172,150,135,195,196,
197,199,201,202,204,205,206,208,210,212,214,215,217,218,219,220,221,222,223,152,153,225,226,155,189,
157,203,179,159,231,233,234,162,236,163,238,164,240,165,216,187,167,200,169,246,248,250,245,227,176,
252,253,254,255,256,181,258,182,261,262,264,265,267,268,270,230,271,272,244,194,191,274,192,276,193,
278,198,224,282,284,241,286,288,289,290,207,263,235,209,295,296,211,269,239,213,301,303,304,306,307,
309,298,311,312,313,314,228,316,229,318,287,257,232,321,322,323,324,325,326,237,327,328,310,329,330,
242,332,243,305,273,247,336,337,249,277,251,341,343,345,346,348,349,351,352,353,259,260,355,356,358,
360,266,363,365,367,368,370,371,372,373,275,374,375,376,377,279,379,280,381,281,347,315,283,385,386,
285,389,391,392,291,292,395,293,359,294,396,397,297,338,299,387,300,369,331,302,402,390,404,308,364,
407,409,410,412,413,414,415,416,417,317,418,419,398,319,334,320,421,393,422,424,426,427,428,384,429,
430,333,431,335,433,434,339,380,340,411,378,342,408,344,438,440,399,350,366,444,354,447,448,357,449,
361,362,388,453,437,455,456,458,460,420,436,401,382,462,383,464,465,466,435,468,445,394,469,470,471,
472,473,400,475,403,478,479,405,481,406,483,485,486,488,489,491,492,446,423,425,495,496,498,499,501,
502,490,432,503,459,480,504,484,461,439,507,508,441,442,511,443,494,493,467,450,451,509,452,500,474,
454,517,457,510,518,519,463,520,521,482,477,522,523,506,505,513,476,515,514,487,497,525,516,524,512]
>;
print "Group G is J2 < Sym(525)";