/*
www-ATLAS of Group Representations.
U3(8).(S3 x 3) represented as permutations on 513 points.
*/

G<x,y>:=PermutationGroup<513|\[
1,3,2,6,8,4,11,5,14,16,7,19,21,9,23,10,26,28,12,31,13,34,15,37,39,
17,42,18,45,47,20,49,51,22,54,56,24,59,25,62,64,27,67,69,29,72,30,75,32,78,
33,81,83,35,85,36,88,90,38,93,95,40,91,41,99,101,43,104,44,97,108,46,111,113,48,
84,116,50,80,79,52,121,53,76,55,126,128,57,131,58,63,135,60,138,61,107,70,143,65,146,
66,149,151,68,154,156,96,71,157,159,73,161,74,164,165,77,144,168,170,172,82,174,176,178,180,
86,183,87,186,188,89,191,193,195,92,198,199,94,140,139,175,204,98,117,207,100,210,212,102,214,
103,216,218,105,162,106,109,223,110,202,112,155,226,114,115,229,231,118,185,119,235,120,201,122,141,
123,240,124,242,125,245,247,127,250,169,129,253,130,249,256,132,259,133,262,134,265,267,136,137,271,
173,160,274,142,275,277,145,280,281,147,244,148,213,150,286,152,289,153,292,294,222,221,158,269,299,
163,302,300,166,305,167,308,310,311,171,285,314,239,238,177,317,179,261,211,181,321,182,323,189,184,
252,251,187,327,301,190,329,331,192,312,243,194,316,273,196,335,197,337,224,339,200,341,264,203,205,
344,206,347,349,208,209,338,353,355,236,215,357,358,217,359,361,219,363,220,366,367,369,370,225,228,
255,227,372,368,230,373,375,232,376,233,234,260,378,237,381,263,241,383,385,387,246,377,248,389,390,
343,254,392,257,395,258,398,399,400,266,402,268,282,270,340,272,391,326,276,346,345,278,410,279,413,
414,384,283,417,284,419,287,288,290,424,291,427,293,386,431,295,296,304,297,298,371,303,306,418,307,
309,322,313,426,433,315,439,318,352,319,364,320,432,324,325,342,328,443,444,330,446,397,332,333,334,
415,336,450,437,422,406,408,407,451,348,453,455,350,351,401,421,354,374,356,461,416,405,464,360,466,
379,362,452,463,456,365,388,380,472,474,473,404,476,382,478,448,460,393,394,482,396,465,441,487,403,
409,428,411,454,412,430,490,492,493,442,420,471,429,423,447,425,497,498,494,499,462,434,436,435,501,
438,502,440,504,484,481,445,505,480,491,508,449,510,507,457,485,458,459,469,512,511,467,468,470,509,
475,477,506,479,483,503,489,486,500,488,496,495,513]
,\[
2,4,5,7,9,10,12,13,15,17,18,20,21,22,24,25,27,29,30,32,33,35,36,38,40,
41,43,44,46,14,48,50,52,53,55,57,58,60,61,63,65,66,68,70,71,73,74,76,77,79,
80,82,84,69,86,87,89,91,92,94,34,96,97,98,100,102,103,105,106,107,109,110,112,114,115,
78,117,118,1,119,120,122,123,124,125,127,129,130,132,133,134,136,137,139,140,141,142,144,145,147,
148,150,152,153,155,72,51,149,158,160,113,162,163,31,166,167,138,169,171,23,173,175,177,179,181,
182,184,185,187,189,190,192,194,196,197,37,200,201,3,202,203,205,206,45,208,209,211,213,161,135,
215,217,219,220,221,222,146,216,224,225,108,188,199,227,228,230,232,233,47,234,236,39,237,49,238,
239,241,180,243,244,246,248,249,19,251,252,254,255,85,257,258,260,261,263,264,266,268,269,270,272,
273,159,274,95,276,278,279,93,282,111,183,283,284,285,287,288,290,291,293,295,6,296,297,298,300,
301,294,303,304,306,307,309,259,312,313,28,315,8,90,316,318,319,172,235,320,322,126,324,325,54,
176,326,292,328,11,88,330,332,151,81,333,168,128,311,334,59,336,338,116,340,165,229,342,343,210,
345,346,348,350,310,351,352,354,356,204,331,240,64,323,360,131,362,364,365,154,368,56,214,143,250,
371,156,341,99,265,374,207,299,377,121,83,375,379,380,335,262,382,384,386,355,388,256,104,361,26,
391,317,393,394,396,397,271,62,401,372,403,242,398,381,404,405,406,193,407,16,408,409,411,412,339,
415,416,390,418,277,420,421,422,423,425,426,428,429,430,432,157,101,226,302,370,369,433,434,435,164,
436,437,245,438,231,314,440,441,195,442,357,75,378,443,366,399,178,223,349,445,447,389,42,448,337,
449,198,347,275,191,174,444,321,452,450,454,456,344,367,457,353,458,459,460,462,463,281,465,395,466,
467,468,469,470,471,247,170,280,473,475,410,402,477,363,359,267,479,480,481,483,484,485,486,482,413,
212,488,453,472,358,489,491,427,494,327,493,414,495,496,419,476,431,424,446,500,289,308,305,439,387,
67,392,503,474,478,376,373,506,507,218,509,455,383,511,499,487,286,329,504,400,502,497,490,510,385,
451,513,492,501,464,417,508,253,512,505,461,186,498]
>;
print "Group G is U3(8).(S3 x 3) < Sym(513)";