/*
www-ATLAS of Group Representations.
U4(3):D8 represented as permutations on 540 points.
*/

G<x,y>:=PermutationGroup<540|\[
2,1,7,8,9,11,3,4,5,16,6,20,21,22,17,10,15,27,29,12,13,14,35,37,38,
40,18,44,19,47,48,50,52,54,23,58,24,25,61,26,63,64,55,28,69,70,30,31,75,32,
76,33,79,34,43,80,82,36,84,86,39,89,41,42,93,94,95,90,45,46,100,101,102,104,49,
51,108,110,53,56,114,57,115,59,117,60,119,120,62,68,124,126,65,66,67,125,130,132,134,71,
72,73,139,74,141,142,113,77,146,78,147,148,107,81,83,154,85,157,87,88,163,164,166,91,96,
92,145,171,160,97,175,98,178,99,168,180,155,179,103,185,105,106,188,189,127,109,111,112,197,199,
200,202,204,116,137,207,118,209,210,129,208,187,121,122,212,123,219,135,221,223,128,226,228,229,131,
196,216,133,138,136,236,237,239,240,140,242,162,143,144,248,250,251,253,255,257,176,149,260,150,151,
243,152,267,153,270,272,156,161,158,159,254,165,279,281,282,177,262,283,167,265,169,288,170,291,292,
172,296,173,174,300,247,245,268,301,277,181,182,305,183,184,308,186,201,297,232,312,231,190,317,191,
192,321,193,211,194,326,195,306,307,198,330,217,332,324,220,323,203,233,278,205,340,206,322,320,314,
342,235,269,213,345,214,215,218,348,318,349,299,222,353,336,224,225,358,359,361,227,244,365,287,230,
234,310,311,371,238,258,259,241,377,302,303,246,381,275,383,356,249,285,388,274,252,273,266,264,393,
256,395,396,397,261,347,263,344,400,402,290,392,355,404,271,407,276,390,333,280,412,331,284,286,416,
417,360,289,421,338,316,423,293,294,352,295,429,430,408,298,433,434,379,373,437,304,439,369,440,386,
441,309,444,368,420,313,448,315,449,451,375,453,319,456,343,457,337,325,459,327,328,329,462,426,334,
463,335,465,339,467,469,341,364,472,413,473,346,410,455,475,350,351,477,478,380,354,479,357,427,460,
399,424,442,362,363,485,480,366,367,487,454,370,489,372,374,376,428,493,378,495,497,486,382,384,491,
385,471,387,436,414,389,391,505,394,425,500,398,401,510,403,507,405,513,406,482,452,409,411,517,415,
509,418,419,422,432,503,470,520,518,431,447,435,525,438,526,450,504,443,528,445,531,446,533,516,461,
532,529,481,492,458,534,466,515,476,464,524,521,468,523,508,499,474,484,536,483,512,535,514,511,488,
490,538,494,502,540,496,501,498,506,522,519,539,527,537,530]
,\[
3,5,4,1,10,2,9,14,13,17,18,6,7,23,8,25,12,28,11,31,20,33,36,15,39,
16,42,45,38,19,49,21,53,22,56,24,48,60,62,55,26,65,27,67,30,29,72,74,51,66,
32,77,40,54,34,81,35,57,37,87,88,41,90,92,50,43,96,44,97,78,46,64,47,105,106,
101,109,52,82,112,83,61,58,68,59,118,71,121,122,104,63,103,110,94,128,116,131,69,70,135,
75,137,73,140,85,143,76,144,99,86,79,149,80,151,142,84,155,158,159,161,111,165,89,168,91,
170,93,172,95,174,176,157,98,164,178,100,182,102,156,125,186,153,107,190,108,192,126,195,198,113,
201,114,115,130,206,117,208,127,211,119,213,120,215,216,217,185,123,220,124,224,225,227,129,230,231,
133,132,233,134,235,136,238,138,139,241,163,141,244,246,249,145,252,146,147,258,148,260,150,262,234,
264,265,152,268,154,184,273,275,276,171,278,160,280,162,243,200,167,166,285,286,180,169,289,256,293,
294,173,297,299,271,175,177,181,179,302,303,304,183,279,237,309,310,187,267,188,313,189,315,191,318,
210,322,229,193,324,194,327,329,196,261,197,331,199,203,334,202,336,337,204,311,205,245,308,207,232,
236,209,212,344,214,282,347,342,218,219,222,221,351,354,223,346,283,320,360,226,330,364,228,367,368,
370,350,343,326,372,239,240,376,284,378,242,379,382,247,384,248,386,301,250,251,390,254,253,392,255,
375,383,257,259,349,398,396,263,401,266,272,403,269,270,405,274,408,277,409,410,281,356,413,415,287,
418,288,419,422,290,291,292,425,352,395,427,295,296,432,328,298,391,435,300,389,438,373,305,306,307,
341,442,339,445,312,407,314,433,450,316,452,317,454,319,321,323,458,436,325,362,400,460,333,332,463,
335,434,338,466,468,340,471,424,374,411,345,358,420,348,431,371,469,426,414,353,459,355,480,357,404,
359,482,361,484,472,363,366,365,486,393,369,488,490,473,475,476,492,377,456,496,380,381,437,387,385,
444,499,399,501,388,503,417,394,430,506,397,508,453,402,467,474,512,489,514,406,515,440,516,412,421,
416,429,487,507,510,423,521,428,513,522,523,524,448,470,441,439,517,465,443,529,446,532,447,449,451,
534,455,533,457,531,479,461,526,462,536,464,485,528,535,498,537,494,477,478,481,483,493,511,539,497,
505,491,518,530,495,509,525,500,502,504,520,527,519,538,540]
>;
print "Group G is U4(3):D8 < Sym(540)";