/*
www-ATLAS of Group Representations.
U6(2):2 represented as permutations on 672 points.
*/

G<x,y>:=PermutationGroup<672|\[
2,1,5,6,3,4,11,13,15,17,7,21,8,25,9,28,10,32,33,35,12,29,39,41,14,
45,47,16,22,51,53,18,19,59,20,52,63,65,23,48,24,72,73,75,26,79,27,40,83,85,
30,36,31,92,93,95,97,99,34,103,81,105,37,109,38,113,114,88,117,118,120,42,43,125,44,
129,130,132,46,136,61,138,49,142,50,146,147,68,150,151,153,54,55,158,56,162,57,165,58,169,
134,170,60,174,62,178,179,181,64,184,185,187,66,67,191,193,69,70,197,71,201,202,203,205,74,
208,209,140,76,77,177,78,219,101,220,80,223,82,225,128,227,84,231,232,234,86,87,239,241,89,
90,246,91,250,251,252,254,94,257,258,260,96,263,264,98,247,267,269,100,102,221,273,275,104,279,
280,131,106,107,286,108,290,291,110,111,295,112,299,300,301,115,304,116,307,229,309,119,216,313,315,
121,122,123,322,124,325,326,126,127,228,330,331,218,332,334,198,336,213,133,135,171,342,137,345,139,
347,141,210,195,351,143,144,310,145,358,359,360,362,148,366,149,369,370,371,373,152,166,375,376,154,
155,156,382,157,297,386,159,160,389,161,392,393,163,164,397,399,167,403,168,407,363,408,172,289,173,
413,414,415,175,176,380,418,419,421,423,180,426,349,274,182,183,320,354,402,186,432,255,434,188,189,
190,321,439,192,441,442,194,445,196,233,449,318,199,454,200,456,457,312,458,292,302,204,447,385,206,
207,448,388,465,211,212,214,404,215,470,217,473,341,475,477,338,222,482,483,224,486,226,490,288,471,
230,387,495,293,472,361,394,235,236,237,356,238,271,501,503,240,505,506,242,243,244,484,245,513,248,
249,514,515,516,281,517,253,395,489,324,256,352,328,259,525,526,261,262,357,383,529,265,531,266,532,
533,294,268,333,536,537,270,272,446,541,509,480,276,277,278,549,546,282,283,523,284,518,285,553,450,
287,556,500,558,504,540,296,560,298,502,563,492,519,303,550,305,306,570,508,308,409,323,327,311,425,
574,575,576,314,578,316,317,319,542,497,485,521,520,491,329,582,583,584,585,335,350,355,337,589,339,
528,340,591,544,412,593,343,344,372,461,346,599,573,384,348,464,437,545,577,353,603,460,604,564,428,
364,435,365,430,367,368,600,444,411,608,609,610,374,377,378,379,381,422,438,463,462,616,420,557,390,
391,619,476,396,611,398,400,401,586,613,405,406,607,628,431,410,459,587,479,493,417,602,588,416,440,
634,635,424,636,637,427,524,429,639,433,640,641,436,499,592,642,624,643,644,443,633,598,488,451,452,
453,494,455,612,650,652,466,467,468,469,534,543,548,474,625,478,565,481,630,656,651,658,572,487,507,
659,547,496,498,661,662,538,510,511,512,530,579,535,664,665,522,622,666,527,657,623,617,621,567,590,
655,654,539,668,594,667,669,571,551,552,554,555,646,559,561,562,566,568,569,663,638,671,672,660,580,
596,581,670,627,626,595,620,597,601,649,605,606,645,614,615,618,631,629,632,653,647,648]
,\[
3,4,1,2,7,9,12,5,16,6,19,22,23,8,26,29,30,10,34,11,37,14,40,13,43,
46,15,49,18,52,17,55,57,60,61,20,64,21,67,69,70,24,74,25,77,80,81,27,84,28,
87,89,90,31,94,32,98,33,101,36,104,35,107,110,111,38,115,39,42,119,41,122,123,126,127,
44,131,45,134,48,137,47,140,143,144,50,148,51,54,152,53,155,156,159,160,56,163,166,167,58,
72,59,172,175,176,62,180,63,162,66,186,65,189,138,192,68,194,195,198,199,71,171,204,73,207,
76,210,75,212,214,216,217,78,92,79,117,224,114,82,226,83,229,86,233,85,236,201,240,88,242,
244,247,248,91,221,253,93,256,96,259,95,262,213,97,265,100,268,99,206,271,102,274,103,277,106,
281,105,283,285,287,288,108,109,222,293,296,297,112,125,113,303,116,305,257,308,118,311,121,314,120,
317,318,320,169,323,124,302,276,327,329,128,164,129,333,130,133,325,132,338,340,135,136,343,139,191,
348,349,141,249,142,352,354,246,356,145,158,146,147,364,149,367,353,150,372,151,235,154,230,153,377,
379,381,383,384,157,361,184,387,390,179,161,394,376,395,398,165,401,404,405,168,407,170,410,208,412,
173,294,174,416,316,299,177,420,178,424,425,182,427,181,429,393,183,278,185,252,188,433,187,282,436,
437,190,440,409,344,193,443,446,447,196,450,197,452,280,455,200,382,417,202,396,203,459,355,205,461,
300,463,209,211,402,467,315,362,400,215,471,218,474,219,478,220,480,306,223,484,225,488,228,491,227,
493,243,231,324,232,432,234,497,360,500,237,335,238,502,239,479,385,241,507,509,511,456,489,245,496,
263,453,250,485,251,518,363,255,368,254,519,521,258,523,261,260,515,291,292,321,264,286,334,514,266,
445,267,534,270,275,269,304,539,272,542,273,538,543,545,547,319,279,451,435,550,524,284,531,527,554,
555,557,289,501,290,295,375,419,561,298,426,536,301,399,487,566,568,571,307,466,310,548,309,573,418,
312,378,313,411,579,374,476,580,498,322,337,326,581,328,564,330,494,331,332,583,587,336,512,457,540,
339,590,366,341,592,342,562,596,380,345,598,346,473,347,600,601,350,468,351,546,357,460,358,359,605,
606,599,431,365,588,544,371,369,470,370,607,373,611,486,613,560,569,503,563,386,558,388,617,389,499,
618,391,392,621,397,623,624,610,591,403,465,627,406,629,408,535,577,631,413,632,414,448,415,612,422,
421,423,529,622,462,638,428,522,430,449,578,434,490,438,439,589,441,585,442,552,646,444,647,597,526,
650,454,595,586,458,464,475,604,506,615,469,505,472,653,477,630,654,655,481,482,657,483,565,504,520,
492,495,619,510,525,559,508,633,537,663,608,513,639,516,517,556,551,593,666,528,634,530,645,667,532,
533,616,625,582,541,584,602,549,637,553,567,635,609,620,670,644,628,668,641,570,572,614,574,575,664,
576,659,636,594,649,671,648,669,626,603,662,660,652,658,672,661,642,643,651,640,656,665]
>;
print "Group G is U6(2):2 < Sym(672)";