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