/*
www-ATLAS of Group Representations.
U6(2):S3 represented as permutations on 693 points.
*/

G<x,y>:=PermutationGroup<693|\[
1,4,5,2,3,10,12,14,16,6,20,7,15,8,13,9,29,30,32,11,36,22,38,40,25,
43,44,46,17,18,51,19,54,34,35,21,58,23,61,24,63,65,26,27,69,28,73,48,74,76,
31,79,53,33,55,83,85,37,59,88,39,91,41,64,42,94,96,68,45,101,102,104,47,49,108,
50,77,112,52,115,116,117,56,120,57,124,125,60,128,129,62,132,133,66,136,67,140,141,142,143,
70,71,103,72,151,152,154,75,157,158,160,78,163,165,80,81,82,171,138,84,174,175,177,86,87,
182,184,89,90,176,188,92,93,191,193,95,196,119,198,97,98,99,100,200,202,204,206,208,209,211,
105,106,216,107,220,221,109,110,226,111,161,230,113,233,114,237,238,239,240,242,118,245,187,121,122,
130,123,178,252,253,255,126,257,127,259,260,173,131,262,264,134,192,135,261,256,137,272,139,275,144,
271,145,281,146,205,147,287,148,149,292,150,296,297,298,294,153,302,303,304,155,156,222,310,311,225,
159,284,228,229,162,317,319,164,278,322,324,166,167,168,169,331,170,334,336,172,246,340,342,343,344,
345,179,180,349,181,195,183,353,185,186,194,189,359,190,362,364,366,367,369,270,201,197,372,374,199,
378,380,234,382,306,203,282,283,227,285,387,207,365,289,318,391,210,393,215,395,212,213,214,401,402,
315,217,218,219,407,280,409,411,413,223,224,417,419,314,301,422,231,290,232,329,426,235,428,236,431,
432,433,434,320,436,241,440,442,243,444,244,404,448,450,247,341,248,249,250,251,460,427,462,254,466,
467,468,258,471,472,356,449,358,263,476,478,265,482,266,288,267,268,368,269,486,453,273,490,274,425,
493,383,276,497,277,499,279,377,500,397,386,286,503,505,507,291,509,293,511,295,513,385,514,515,452,
299,300,403,337,521,522,305,523,307,410,308,526,309,517,512,528,312,469,313,524,533,316,536,537,375,
321,347,323,542,540,325,326,327,328,474,330,437,438,475,332,441,333,554,335,556,557,559,338,357,339,
451,400,371,454,455,506,484,564,546,346,568,348,570,571,572,350,351,352,418,470,354,355,495,435,439,
360,581,361,479,578,584,363,587,457,588,370,487,590,592,373,569,492,376,494,473,597,379,565,381,384,
601,558,388,602,389,456,390,563,392,510,394,415,396,398,399,580,414,595,519,610,405,406,408,420,614,
412,615,416,618,613,619,621,421,623,624,423,424,628,576,430,631,429,579,600,633,459,635,577,549,573,
551,582,598,443,638,445,446,502,447,627,643,645,508,458,498,566,585,461,491,463,464,465,550,629,653,
539,548,480,543,516,477,552,583,481,567,586,483,485,658,488,612,489,661,594,518,662,496,553,664,544,
501,504,647,666,626,648,607,668,665,520,670,591,530,525,527,672,656,529,531,667,532,654,534,535,650,
605,560,538,574,630,541,641,545,636,547,634,680,555,681,652,632,646,561,682,562,642,603,606,649,625,
677,640,575,622,655,617,676,589,689,690,593,596,663,599,609,604,620,608,692,611,674,616,685,671,675,
657,651,679,678,637,639,644,688,691,673,686,687,683,659,660,684,669,693]
,\[
2,3,1,6,8,11,4,15,5,18,21,22,7,24,26,27,9,31,10,34,13,37,12,41,14,
17,45,16,48,49,52,44,19,29,20,56,59,60,23,62,64,25,66,68,70,71,28,55,75,30,
78,33,32,81,35,84,36,87,39,38,89,40,92,42,58,95,43,98,99,47,103,46,51,106,109,
110,50,65,113,53,100,54,118,121,122,57,73,126,90,61,130,93,63,134,137,138,67,80,82,69,
144,146,148,149,72,153,74,156,77,159,76,116,164,79,167,143,169,108,83,173,86,176,85,179,181,
183,88,170,187,168,91,129,189,192,94,194,97,197,96,120,185,190,125,201,101,205,102,105,210,104,
139,214,217,218,107,172,222,224,227,228,111,112,231,234,235,114,131,115,241,117,243,119,140,237,247,
249,250,123,230,124,162,256,141,135,127,128,132,261,263,133,265,258,267,269,136,270,213,273,142,276,
278,279,145,282,284,285,147,288,290,293,294,150,151,299,152,301,155,238,154,306,308,289,157,286,158,
312,161,314,160,316,318,163,262,166,323,165,246,326,327,329,186,332,335,171,338,174,341,175,178,310,
177,188,182,180,195,351,291,184,354,281,357,358,199,360,363,191,216,193,350,271,196,370,373,198,376,
379,200,203,383,202,384,385,204,207,225,206,388,223,208,390,209,392,212,394,211,248,398,382,322,215,
368,403,404,280,219,408,220,412,221,414,415,418,226,421,229,254,292,424,395,232,233,300,429,309,236,
305,328,239,435,240,438,441,242,410,445,446,244,449,245,452,397,454,455,364,458,251,252,253,464,255,
463,257,469,355,259,260,461,474,475,477,264,480,483,484,266,342,448,268,485,487,272,488,491,423,274,
494,275,496,498,396,277,444,406,467,501,283,502,504,287,352,508,492,510,380,512,295,296,378,297,298,
407,518,302,520,303,304,433,334,524,307,515,430,527,346,367,311,530,532,503,313,315,534,317,320,319,
539,321,419,325,324,405,544,401,546,547,548,330,359,331,551,552,526,333,555,337,558,336,529,556,561,
339,387,340,366,456,343,344,440,345,566,347,371,348,369,349,574,473,575,470,353,577,507,356,427,550,
579,582,481,361,542,362,585,365,521,573,413,569,591,372,391,375,374,594,596,377,516,598,381,599,597,
386,562,499,603,604,389,513,497,606,393,607,587,472,450,411,399,400,434,402,543,563,537,612,613,409,
553,616,489,416,610,417,420,622,466,422,626,611,425,629,426,428,583,431,632,432,609,437,636,436,439,
565,443,442,628,517,451,592,640,641,447,644,453,457,646,459,648,460,570,462,650,618,651,465,625,642,
468,511,471,580,476,637,479,478,621,655,482,538,656,486,634,617,660,490,647,493,495,663,593,541,500,
665,509,506,667,505,627,654,514,519,615,522,525,523,586,620,659,528,673,674,531,549,533,638,600,535,
602,536,623,677,540,662,590,653,545,664,584,554,581,557,560,576,559,658,669,571,595,564,684,567,568,
685,572,633,578,671,687,588,639,589,643,605,678,676,679,601,675,668,661,608,691,614,686,693,670,619,
624,630,631,635,689,690,680,645,649,672,652,692,657,682,681,666,688,683]
>;
print "Group G is U6(2):S3 < Sym(693)";