/*
www-ATLAS of Group Representations.
6.A6 represented as permutations on 720 points.
*/

G<x,y>:=PermutationGroup<720|\[
2,8,13,10,1,24,12,5,31,28,37,18,29,45,42,3,44,23,4,58,34,38,7,30,6,
47,65,19,16,25,21,74,72,9,73,81,22,11,76,86,91,54,97,49,26,101,14,103,53,15,
94,98,17,50,68,78,82,70,20,104,80,89,115,119,55,117,120,27,106,59,125,56,61,39,130,
32,132,33,127,35,57,36,133,143,147,62,145,148,40,136,51,157,154,41,156,165,52,43,159,129,
60,172,69,46,173,48,161,166,164,134,177,180,179,181,66,186,63,185,67,64,187,194,191,197,79,
196,71,200,110,83,205,90,75,100,206,77,193,202,211,214,213,215,87,220,84,219,88,85,221,153,
225,162,152,107,231,109,99,236,92,238,93,150,232,95,108,96,239,192,195,242,247,105,102,251,248,
254,113,257,111,114,112,258,263,267,123,121,116,273,265,268,118,169,126,124,168,137,122,276,283,138,
284,128,280,287,135,131,282,291,288,294,141,297,139,142,140,298,303,307,151,149,144,313,305,308,146,
319,320,316,321,323,163,155,322,327,331,167,337,170,158,334,338,160,324,330,261,262,175,171,349,259,
176,351,255,174,250,356,182,178,253,357,246,245,189,364,183,348,190,184,365,370,375,379,198,377,380,
188,346,373,385,207,386,203,201,199,389,392,209,204,360,299,210,362,295,208,290,400,216,212,293,401,
407,408,223,410,217,396,224,218,411,416,421,425,228,423,426,222,394,419,227,226,233,229,243,230,443,
447,244,445,448,234,240,376,454,235,456,390,241,237,381,465,459,387,462,467,469,266,471,277,252,427,
249,475,422,478,479,260,256,480,485,292,487,289,489,269,264,493,490,417,499,278,414,500,270,496,274,
339,271,507,275,272,332,393,511,395,281,279,336,516,286,342,517,285,384,306,382,317,523,524,525,300,
296,526,531,534,533,535,302,301,541,309,304,545,542,368,551,318,371,552,310,548,314,350,311,559,315,
312,353,565,562,568,569,571,570,572,573,576,575,577,579,582,581,583,328,588,325,587,329,326,589,453,
593,460,452,341,540,343,486,508,333,450,538,335,488,599,344,600,340,512,347,536,345,532,519,592,354,
520,586,352,358,355,529,616,527,617,361,463,359,457,367,363,621,620,374,623,619,366,629,555,372,369,
630,505,550,509,504,626,383,468,502,628,378,458,606,609,639,391,388,640,476,473,574,578,398,397,402,
399,481,648,483,649,405,470,403,406,404,472,564,455,567,461,413,409,653,657,420,655,658,412,636,498,
418,415,635,557,503,560,556,624,429,554,627,424,671,539,430,673,537,428,433,431,434,432,437,522,435,
438,436,521,441,654,439,442,440,659,597,474,451,449,444,689,598,477,446,683,681,690,591,585,466,464,
625,622,684,682,693,514,694,692,513,688,669,637,670,638,697,484,482,698,492,495,494,601,491,561,602,
510,558,506,501,497,703,647,650,706,549,553,614,612,518,515,707,708,677,709,678,710,633,530,528,632,
687,685,546,584,543,672,547,544,580,701,675,704,699,713,714,700,705,702,613,611,566,661,563,715,656,
716,645,643,686,691,594,603,595,604,651,680,652,608,596,590,679,610,607,605,717,718,618,615,666,663,
662,667,634,660,668,631,642,641,646,644,719,720,665,664,676,674,696,695,712,711]
,\[
3,9,14,15,21,1,17,29,32,33,2,35,41,30,46,51,48,49,56,4,39,5,61,63,66,
6,7,54,26,8,71,22,75,79,77,10,84,87,11,12,92,93,13,95,31,70,34,55,69,107,
99,16,109,60,18,83,19,111,113,20,90,23,116,24,118,121,25,123,27,28,105,126,128,129,57,
134,62,137,102,138,139,141,36,144,37,146,149,38,151,40,153,52,158,162,160,42,168,169,43,44,
72,45,73,78,47,80,167,50,170,53,178,58,182,59,183,67,189,188,192,195,64,65,198,68,197,
175,194,176,203,97,74,166,98,207,76,165,171,174,212,81,216,82,217,88,223,222,226,227,85,86,
228,89,229,147,91,215,235,108,240,110,148,233,94,214,245,246,96,209,204,100,101,249,252,103,104,
106,255,114,259,261,262,112,264,115,266,271,274,124,269,117,277,279,119,280,281,120,282,122,125,180,
127,181,135,130,289,292,131,132,133,136,295,142,299,301,302,140,304,143,306,311,314,152,309,145,317,
243,230,150,163,154,325,328,155,156,332,333,157,335,341,339,159,343,161,164,208,210,345,347,350,172,
352,353,173,354,355,177,359,361,358,179,286,285,251,190,254,366,368,371,184,185,376,186,378,381,187,
383,374,191,196,199,193,201,387,390,200,202,393,395,397,205,380,398,206,379,399,211,403,405,402,213,
234,244,291,224,294,412,414,417,218,219,422,220,424,427,221,429,420,225,431,433,435,437,439,441,444,
231,446,449,232,451,453,241,457,460,458,236,464,466,237,238,463,239,468,242,470,247,472,248,473,253,
476,367,250,363,260,481,483,256,486,257,488,258,263,491,494,278,265,497,267,498,501,268,503,270,505,
275,509,508,409,413,272,273,512,276,465,467,515,283,338,518,284,337,521,287,522,288,293,290,300,527,
529,296,532,297,536,298,537,539,303,543,546,318,305,549,307,550,553,308,555,310,557,315,560,489,563,
566,312,313,490,316,541,319,542,320,574,321,578,322,580,323,584,324,585,329,591,590,594,595,326,327,
596,330,597,447,331,583,342,344,448,598,334,582,336,519,601,520,602,340,517,348,516,346,605,349,606,
607,351,609,611,613,615,356,618,357,499,362,500,360,430,428,622,364,624,625,365,627,372,631,632,633,
369,370,634,373,635,375,617,384,636,377,616,382,385,386,391,641,642,388,389,392,396,394,538,540,643,
645,647,400,650,401,551,406,552,651,652,404,524,407,523,408,434,432,654,410,656,659,411,661,418,663,
664,665,415,416,666,419,667,421,649,668,423,648,672,425,674,675,426,676,565,568,456,462,535,438,534,
459,454,436,681,442,683,679,680,440,685,443,686,662,660,452,687,445,691,576,577,450,461,455,612,614,
514,513,469,471,477,695,474,475,696,478,600,479,599,480,484,699,700,482,485,487,533,495,531,640,492,
493,639,496,701,704,504,620,619,502,510,506,507,511,626,628,603,604,690,525,689,526,530,711,712,528,
653,655,573,547,575,588,693,694,544,545,589,548,556,621,623,554,561,558,559,562,688,567,692,678,564,
677,569,570,571,572,715,579,716,581,592,673,586,587,644,646,671,593,713,714,610,608,657,658,637,638,
717,629,710,718,630,709,720,719,708,707,669,670,698,697,684,682,705,702,703,706]
>;
print "Group G is 6.A6 < Sym(720)";