/*
www-ATLAS of Group Representations.
A12 represented as permutations on 462 points.
*/

G<x,y>:=PermutationGroup<462|\[
1,3,5,7,2,10,9,12,4,15,17,19,21,23,6,16,26,28,8,30,32,34,36,38,40,
11,42,44,46,48,50,13,33,53,55,14,37,58,60,62,63,65,67,18,45,70,72,20,74,75,
77,79,22,81,83,85,87,24,89,91,93,25,95,97,27,98,100,102,104,29,106,73,47,109,31,
76,111,78,114,116,118,82,35,122,121,124,126,128,130,132,39,92,135,94,41,138,140,141,143,43,
101,145,103,147,99,108,107,71,49,110,51,151,153,52,156,155,158,54,161,163,56,166,168,170,172,
57,127,174,129,59,177,179,181,134,61,185,187,189,139,64,66,191,105,144,68,194,69,142,195,112,
150,198,200,202,80,204,206,208,210,119,160,213,215,217,218,84,167,221,223,86,224,225,173,88,229,
231,233,178,90,237,236,239,241,136,184,244,246,248,96,249,148,192,146,193,251,253,254,256,258,113,
201,259,260,115,205,263,265,117,266,268,270,272,274,276,120,216,277,278,280,281,123,282,283,285,125,
226,287,175,228,290,292,294,131,297,211,133,301,303,305,307,309,311,313,315,317,137,247,318,319,321,
149,252,323,324,326,152,327,328,154,330,332,308,157,333,334,336,298,159,269,235,271,342,344,162,345,
346,164,165,279,348,349,351,169,284,171,286,353,355,357,359,361,176,293,364,366,234,296,368,340,371,
180,302,374,376,182,378,380,382,183,310,385,257,386,388,186,389,390,188,190,320,393,395,196,197,325,
384,312,199,329,203,331,397,379,207,335,209,399,295,339,401,273,212,343,341,370,214,347,219,220,350,
222,352,227,354,405,316,406,408,230,410,412,414,416,232,417,338,337,267,365,275,419,421,362,238,423,
425,427,409,264,240,381,262,383,255,242,243,387,404,356,245,391,377,250,432,433,396,261,398,367,400,
299,402,403,314,288,289,407,438,306,439,375,291,413,373,415,436,369,418,300,420,437,441,411,394,304,
426,392,428,429,430,431,424,322,434,422,363,372,358,360,440,435,442,443,444,445,446,447,448,449,452,
451,457,453,454,455,456,450,458,459,462,460,461]
,\[
2,4,6,8,9,11,12,13,14,16,18,20,22,24,17,25,27,29,30,31,33,35,37,39,41,
42,43,45,47,49,51,34,52,54,56,38,57,59,61,1,64,66,68,46,69,71,73,74,7,76,
78,80,81,82,84,86,88,89,90,92,94,63,96,83,98,99,101,103,105,106,107,108,72,10,77,
110,112,113,115,117,119,120,121,123,124,125,127,129,131,133,93,134,136,137,138,139,118,142,140,102,
144,146,135,148,97,147,145,104,15,149,150,152,154,155,157,158,159,160,162,164,165,167,169,171,40,
128,173,175,176,177,178,180,182,183,184,186,188,114,190,55,191,192,189,174,193,132,143,3,196,197,
198,199,201,19,203,205,207,209,211,212,213,214,216,208,219,168,220,222,153,224,65,226,227,228,230,
232,234,235,236,238,239,240,242,243,244,245,247,141,79,250,5,111,233,179,252,181,255,257,249,202,
26,23,261,206,262,264,187,266,267,269,271,273,275,163,217,263,260,279,48,195,282,256,284,28,62,
286,288,289,290,291,293,295,296,298,299,300,302,304,306,308,310,312,314,316,87,248,70,67,320,322,
253,297,237,325,85,327,116,329,36,331,305,241,333,315,335,337,338,270,339,340,341,343,170,345,274,
347,330,280,58,21,350,254,200,352,44,194,354,356,358,360,362,294,363,365,283,367,368,369,370,372,
303,373,375,377,378,379,381,383,311,384,258,204,387,109,389,130,391,100,321,392,394,231,301,326,161,
122,156,319,396,332,374,371,313,246,398,399,400,223,277,276,278,344,221,218,272,215,402,32,251,403,
324,151,355,404,317,91,407,409,410,411,413,415,225,417,418,351,416,366,281,342,420,336,422,423,424,
426,428,265,386,382,429,309,430,166,328,388,53,50,60,126,431,287,432,359,434,435,419,95,436,348,
346,393,185,75,390,408,437,307,334,376,433,414,440,441,442,285,349,443,421,397,210,444,395,406,427,
445,353,446,447,259,448,357,292,449,450,172,268,380,425,451,452,453,454,455,456,318,323,457,401,458,
459,460,405,229,364,385,461,438,462,361,439,412]
>;
print "Group G is A12 < Sym(462)";