/*
www-ATLAS of Group Representations.
U6(2):2 represented as permutations on 693 points.
*/

G<x,y>:=PermutationGroup<693|\[
1,3,2,6,8,4,12,5,16,17,19,7,13,23,25,9,10,31,11,35,36,30,14,41,15,
45,46,48,50,22,18,55,33,56,20,21,61,63,39,40,24,68,69,71,26,27,77,28,81,29,
84,86,87,88,32,34,57,94,96,98,37,102,38,64,106,107,109,42,43,115,44,119,120,122,124,
125,47,127,128,130,49,134,136,51,140,52,53,54,147,149,91,152,154,58,158,59,161,60,165,166,
168,62,172,173,175,65,66,180,67,184,185,181,186,188,70,171,192,193,72,73,121,74,201,75,76,
206,78,79,209,80,213,214,215,82,217,83,221,222,224,85,228,230,232,234,236,238,89,242,90,245,
246,92,249,93,251,227,252,95,255,257,97,261,163,262,99,100,267,101,271,170,116,103,104,276,105,
176,177,280,281,108,112,182,207,110,111,113,288,114,292,293,294,117,118,297,258,299,301,277,303,305,
123,309,310,290,312,126,183,208,129,319,320,307,131,132,133,326,135,330,331,333,137,138,337,139,340,
341,156,141,345,142,349,143,352,144,355,145,327,146,360,265,361,148,362,364,150,151,369,370,153,250,
155,157,372,375,159,379,160,195,359,260,162,164,263,385,240,381,167,338,387,389,169,390,391,274,393,
174,198,358,396,178,179,399,401,402,403,404,406,187,397,204,409,189,190,191,415,416,194,298,196,420,
197,423,199,425,200,429,212,308,202,203,435,205,439,440,315,427,442,444,210,211,447,449,450,451,453,
216,237,454,329,218,219,460,220,412,463,464,223,268,466,225,226,470,471,473,229,465,363,478,231,462,
483,233,353,354,235,459,488,278,259,239,241,243,347,244,421,493,468,494,247,248,498,253,484,430,254,
376,482,378,256,503,266,382,383,485,264,507,269,467,270,272,273,512,275,394,395,279,289,516,282,400,
283,284,285,286,524,287,407,517,291,410,411,334,530,532,295,296,438,536,538,300,365,534,302,542,304,
426,316,547,306,374,549,539,445,550,311,552,553,417,313,314,554,317,527,318,433,560,321,561,322,323,
324,544,325,328,568,461,569,571,356,332,456,350,335,336,346,339,388,367,576,342,343,578,344,582,583,
585,586,348,577,589,591,377,351,373,384,595,495,357,597,541,598,521,366,368,487,496,602,371,499,500,
501,592,380,603,604,605,386,608,557,580,611,392,575,614,533,398,408,518,618,520,492,522,622,405,623,
624,443,528,529,413,621,414,515,422,562,418,613,419,432,579,490,424,633,452,635,636,428,639,431,434,
627,436,437,441,638,642,509,594,590,446,448,535,645,570,565,647,574,455,457,564,458,588,649,567,513,
469,479,472,540,510,619,474,475,607,476,477,656,572,480,559,481,502,657,558,486,596,489,491,659,612,
601,497,504,505,506,637,584,508,609,610,511,600,537,514,651,663,664,519,581,667,531,523,525,526,668,
626,551,628,672,661,631,641,543,655,545,546,606,555,548,662,632,556,676,677,563,680,566,682,573,650,
615,652,653,681,634,587,593,683,599,671,630,640,616,617,685,666,620,625,669,670,660,629,687,674,688,
643,644,691,689,646,654,648,658,684,665,690,673,675,679,686,678,692,693]
,\[
2,1,4,7,3,10,13,14,5,18,6,21,9,24,8,27,29,32,33,11,37,12,39,42,43,
15,47,16,51,17,53,20,54,19,57,59,62,22,64,23,66,26,70,25,73,75,78,79,28,82,
85,30,34,31,89,91,93,35,97,36,100,38,103,105,40,108,41,111,113,116,117,44,121,45,76,
46,126,49,129,48,132,135,50,138,52,141,143,145,148,55,151,56,155,156,58,159,162,163,60,167,
61,170,77,63,65,176,178,181,182,67,171,68,187,69,190,72,164,71,194,196,198,199,74,202,204,
174,150,207,210,211,80,133,81,193,218,219,83,223,84,226,229,86,233,87,237,88,240,127,243,90,
247,248,92,184,95,157,94,253,256,96,259,99,118,98,263,265,268,269,101,112,102,272,274,104,277,
278,106,179,107,282,110,284,109,250,206,286,289,290,114,260,115,183,296,288,119,300,120,123,304,122,
307,203,124,311,125,314,315,128,317,131,321,130,323,325,271,134,328,137,332,136,327,335,338,339,139,
281,140,343,346,347,142,350,353,152,144,352,357,358,146,336,147,293,363,149,366,283,153,371,362,154,
342,372,374,158,377,380,224,160,191,161,285,383,326,165,266,166,386,169,388,168,276,273,172,392,173,
215,175,395,177,397,251,400,180,295,185,405,186,408,189,378,188,410,412,413,192,221,264,195,418,421,
422,197,424,426,427,200,249,201,431,433,436,437,205,382,441,208,443,209,394,446,448,212,301,213,214,
417,216,455,217,457,242,461,462,220,241,222,458,225,467,387,469,227,472,228,475,231,477,230,480,482,
232,485,235,234,484,236,239,384,238,476,270,430,403,491,244,468,245,246,495,447,486,341,252,500,497,
254,291,255,502,258,257,261,359,262,505,267,367,490,333,508,510,319,513,275,279,514,515,280,516,368,
519,521,365,523,525,526,287,298,528,396,292,440,531,294,534,464,297,537,299,303,302,452,541,543,544,
306,546,305,540,308,432,309,434,310,320,313,503,312,416,459,316,555,557,558,318,512,524,322,562,564,
565,324,552,456,454,329,570,330,331,423,334,379,572,483,337,574,504,340,499,389,404,579,580,344,584,
345,587,588,348,590,349,355,593,351,594,354,356,498,360,361,599,364,439,554,596,369,370,496,373,376,
375,470,393,381,602,385,460,561,390,610,391,613,438,529,615,616,398,399,619,401,568,402,582,501,407,
571,406,409,411,608,626,627,414,601,415,629,585,631,419,420,589,592,429,634,425,637,638,428,478,549,
435,567,640,535,556,442,445,450,444,643,644,632,449,583,646,451,453,639,603,465,605,573,463,575,466,
650,471,527,474,653,473,652,559,489,539,655,479,649,607,542,545,481,493,487,617,488,560,658,622,492,
494,657,569,591,578,506,507,660,509,661,547,511,551,623,517,595,518,665,666,520,522,600,614,597,530,
533,670,532,630,536,563,538,648,604,550,598,548,674,621,641,553,672,656,609,678,633,681,566,635,651,
576,577,676,581,586,668,606,647,671,664,612,611,684,669,618,620,686,624,625,659,628,667,636,680,642,
654,690,679,645,662,673,685,687,688,663,689,693,692,675,691,677,682,683]
>;
print "Group G is U6(2):2 < Sym(693)";