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

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