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

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