/*
www-ATLAS of Group Representations.
6.S6 represented as permutations on 720 points.
*/

G<x,y>:=PermutationGroup<720|\[
1,6,5,12,3,2,20,19,17,15,26,4,30,28,10,32,9,38,8,7,45,43,41,36,25,
11,50,14,52,13,55,16,61,60,58,24,68,18,73,71,23,76,22,82,21,85,80,66,86,27,
89,29,92,93,31,57,56,35,103,34,33,110,108,106,101,48,115,37,119,120,40,125,39,128,123,
42,135,134,132,47,141,44,146,144,46,49,151,99,51,156,158,53,54,165,164,100,168,169,88,96,
65,176,59,181,179,64,184,63,190,62,193,188,174,195,67,198,197,118,69,70,205,204,75,208,72,
211,212,74,216,214,209,79,222,78,77,229,227,225,220,232,81,236,237,84,242,83,245,240,248,172,
87,253,254,255,173,90,260,91,262,263,265,251,163,95,94,273,274,97,98,280,278,150,155,113,284,
102,288,289,105,293,104,296,292,107,303,302,300,112,310,109,315,313,111,308,114,318,117,116,322,323,
324,326,328,122,121,333,207,124,131,335,126,127,213,130,339,129,343,344,334,139,348,133,353,351,138,
356,137,361,136,364,359,140,367,301,369,142,143,375,374,148,379,145,383,384,147,389,387,149,392,393,
162,270,152,153,154,401,402,382,259,157,350,159,160,410,161,412,366,390,332,252,414,417,166,167,422,
424,426,171,409,170,434,430,373,175,436,365,437,177,178,307,377,183,180,444,445,182,449,448,299,187,
234,186,185,454,453,452,290,194,459,189,463,407,192,468,191,471,466,196,476,474,478,199,200,201,337,
202,486,203,346,488,342,269,206,219,210,495,325,496,215,467,499,331,217,218,503,329,431,221,508,261,
224,399,223,512,433,226,517,516,231,521,228,362,524,230,286,267,233,532,235,533,534,536,283,239,238,
484,291,539,241,541,542,258,243,244,547,546,247,388,246,268,400,249,250,411,493,556,405,559,352,391,
256,257,489,565,397,568,312,570,279,264,394,266,481,271,579,577,272,567,419,583,585,275,589,276,591,
277,592,509,429,282,347,564,355,281,537,285,287,451,439,597,497,457,443,294,295,601,600,298,297,605,
438,306,305,304,606,550,442,588,309,610,563,611,311,580,554,317,340,314,617,618,316,614,621,320,625,
319,483,321,609,498,413,630,477,376,491,327,634,330,403,613,485,639,395,641,336,338,441,480,341,645,
527,646,345,642,648,578,555,349,428,651,562,354,599,654,657,358,357,659,572,661,360,526,626,363,598,
522,501,643,664,665,531,368,370,371,666,372,435,604,378,671,380,381,674,675,640,386,385,677,656,456,
637,676,553,465,507,396,682,679,398,683,660,511,461,432,404,647,418,406,619,408,681,519,632,688,689,
638,416,506,415,464,582,581,420,691,421,658,678,458,423,593,425,427,590,594,686,652,440,525,513,447,
446,668,603,538,450,455,670,697,479,460,462,701,490,472,684,704,469,470,569,707,473,700,712,624,475,
523,636,699,653,482,695,573,650,487,709,627,551,576,492,545,494,504,528,694,500,502,566,505,714,633,
510,596,629,514,696,549,515,586,518,561,520,663,662,529,530,535,667,602,715,607,540,706,690,543,544,
552,548,587,558,708,571,557,560,615,702,595,687,574,575,673,584,703,713,644,631,655,608,716,628,622,
612,685,692,616,717,672,620,680,635,720,711,623,693,649,669,698,705,718,719,710]
,\[
2,7,8,1,9,16,13,21,22,23,3,25,4,5,24,33,34,6,35,42,27,31,46,47,48,
10,11,15,12,54,14,57,39,62,63,64,17,70,18,19,65,77,78,20,79,49,51,53,26,87,
28,90,29,94,95,30,98,99,32,100,107,69,74,111,112,113,36,117,37,121,122,38,127,40,41,
131,83,136,137,138,43,143,44,45,139,149,152,50,154,157,52,160,162,97,166,55,56,104,170,171,
172,58,178,59,60,173,185,186,61,187,116,130,194,66,197,67,199,68,201,203,126,206,204,71,115,
72,213,212,73,75,218,211,76,219,226,142,147,230,231,80,234,81,238,239,82,244,84,85,249,86,
251,153,88,256,89,258,159,261,91,264,92,267,93,268,271,167,96,275,277,177,182,281,282,158,101,
286,102,290,291,103,295,105,106,299,191,304,305,306,108,312,109,110,307,196,120,114,319,320,200,118,
325,119,329,330,331,209,123,195,124,125,336,337,217,324,128,341,129,223,345,323,132,350,133,134,346,
357,358,135,356,233,247,365,140,368,141,371,302,243,376,377,144,381,145,385,386,146,148,390,250,150,
394,151,396,398,382,257,155,379,156,404,406,407,335,266,289,161,269,369,163,164,415,165,416,420,423,
168,427,428,169,429,285,298,174,301,175,300,176,439,441,294,442,374,179,180,446,447,181,183,435,438,
184,451,246,311,316,455,456,457,188,461,189,464,465,190,470,192,193,474,210,477,198,480,482,483,327,
484,202,487,208,334,490,205,491,207,494,349,340,214,497,215,500,216,466,383,354,505,220,430,221,509,
434,222,511,224,225,515,362,518,519,227,523,228,229,516,528,232,530,370,413,235,535,236,237,452,538,
380,499,240,403,241,400,242,543,544,303,548,549,245,387,539,248,552,554,395,252,557,253,560,254,255,
562,563,259,566,260,283,569,262,263,572,265,575,270,576,418,580,401,272,273,584,274,587,425,351,276,
590,432,593,592,594,278,279,280,426,284,445,292,287,596,288,574,443,293,437,599,450,602,603,296,297,
537,444,388,372,460,473,607,308,583,309,579,310,613,469,615,559,313,338,314,619,620,315,317,624,318,
626,479,375,321,628,322,506,468,631,326,588,635,636,328,492,618,332,333,571,541,643,644,339,540,501,
342,343,533,344,514,347,348,577,510,352,653,565,353,355,526,658,408,522,660,359,634,360,496,498,361,
363,364,529,366,666,367,605,667,668,454,412,373,661,551,378,672,476,650,654,384,655,670,453,677,389,
391,678,392,680,393,669,558,397,647,561,399,684,685,402,639,567,405,600,517,431,409,591,410,411,547,
665,690,414,612,582,417,419,682,586,433,421,633,422,692,424,687,585,570,651,436,598,448,440,694,696,
578,604,675,449,521,531,608,458,459,699,475,462,702,463,616,467,705,640,623,708,709,471,472,611,532,
713,478,629,481,671,632,485,486,625,638,707,488,489,546,493,688,495,525,524,686,649,502,664,503,504,
507,508,656,676,512,513,564,663,555,662,627,520,527,674,601,606,646,681,534,536,718,716,542,704,695,
545,550,679,553,659,556,698,712,581,657,568,573,706,652,689,719,720,589,595,597,645,693,609,691,610,
714,703,614,717,641,617,715,711,683,621,622,710,673,630,637,642,648,701,700,697]
>;
print "Group G is 6.S6 < Sym(720)";