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

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