/*
www-ATLAS of Group Representations.
6.A7 represented as permutations on 720 points.
*/

G<x,y>:=PermutationGroup<720|\[
2,5,10,7,1,9,16,23,19,13,31,28,3,30,21,4,45,49,6,26,42,56,24,8,38,
53,63,36,70,39,33,75,11,77,68,12,87,61,14,73,54,15,97,100,47,29,17,104,50,18,
115,112,20,94,120,57,22,125,128,132,25,92,66,140,137,27,139,85,152,46,155,107,93,159,79,
166,82,164,32,175,179,34,170,150,35,186,89,189,37,188,196,135,40,41,202,205,99,69,43,101,
44,212,213,108,72,219,105,48,217,123,228,114,233,52,116,51,240,232,199,121,55,247,227,250,126,
58,255,130,257,59,102,133,60,263,62,268,145,174,148,142,276,64,122,273,65,285,289,67,275,184,
294,98,297,299,156,71,304,224,162,308,307,74,264,172,317,167,76,324,193,183,315,78,330,222,177,
336,80,335,180,81,344,341,83,84,349,187,86,194,190,88,355,360,323,90,352,197,91,368,244,369,
239,204,151,95,206,96,377,380,245,382,385,131,215,306,103,390,225,158,221,394,106,138,397,218,109,
401,110,229,111,176,161,237,234,113,410,373,118,413,372,242,291,117,209,119,243,419,143,423,425,251,
124,173,430,332,256,127,258,129,147,388,157,437,266,313,447,134,445,271,438,453,136,455,283,392,292,
279,466,198,141,470,473,465,144,478,287,484,146,483,259,489,309,149,400,203,346,493,298,153,300,154,
500,208,501,261,449,391,231,310,241,160,418,495,163,446,328,512,318,165,396,515,326,464,169,325,168,
519,365,171,528,252,530,433,531,405,339,230,334,537,178,535,343,378,182,345,181,492,374,507,350,185,
545,366,488,547,358,552,477,191,551,362,559,192,558,565,524,195,569,278,371,293,200,201,409,541,314,
216,379,506,207,302,575,383,210,331,386,211,578,440,296,376,214,403,406,395,220,514,398,223,452,370,
402,226,274,417,337,577,589,399,236,411,235,593,415,303,238,407,481,509,420,246,329,599,424,248,426,
249,353,533,603,431,253,608,254,288,611,612,442,457,301,260,614,262,522,357,451,375,448,265,504,616,
267,408,460,469,463,602,269,290,498,270,316,628,272,521,476,467,277,340,621,472,503,280,474,281,637,
282,444,480,639,284,404,627,434,485,286,513,359,427,458,646,647,295,389,520,510,505,496,626,650,439,
414,633,631,305,497,342,543,597,311,312,568,461,643,319,516,320,632,661,321,527,322,598,625,327,619,
664,494,421,667,384,532,333,557,653,468,663,539,605,338,482,347,587,348,672,546,351,548,354,538,562,
487,554,675,356,475,678,428,563,560,361,435,642,363,680,566,364,685,584,570,367,677,502,491,412,576,
381,393,579,387,689,690,490,692,511,693,695,670,529,416,697,673,525,574,508,699,618,594,443,600,422,
634,624,604,429,549,523,590,609,432,688,561,613,436,615,441,617,450,666,592,571,454,580,657,456,606,
459,540,629,462,705,471,660,572,644,544,652,555,567,640,479,656,550,486,601,707,582,573,641,687,651,
499,706,668,630,586,648,696,583,553,517,662,518,669,665,526,596,588,534,536,542,701,635,698,710,659,
711,620,679,556,684,671,713,715,564,638,645,708,702,622,691,581,658,694,585,655,623,607,591,700,595,
681,610,719,720,654,636,686,649,674,709,712,676,714,682,716,683,703,704,717,718]
,\[
3,1,11,12,17,14,4,2,6,27,8,32,37,34,35,43,46,5,48,40,15,7,36,59,9,
20,64,65,10,67,74,22,80,25,78,86,88,13,90,83,84,95,98,16,103,51,106,105,110,104,
18,19,109,41,21,85,123,23,129,24,131,26,136,71,141,146,143,144,28,99,29,30,149,160,161,
31,163,55,173,176,33,178,62,171,185,127,60,91,192,191,38,39,195,200,203,42,207,102,208,209,
45,44,214,216,117,220,47,222,218,226,49,130,50,217,238,241,52,53,54,184,245,56,249,57,252,
254,58,96,87,260,259,261,264,61,116,269,270,63,272,120,153,280,157,278,284,286,66,288,126,282,
68,204,69,70,302,305,72,73,306,168,309,232,311,228,75,187,321,76,77,314,119,329,331,79,333,
181,338,337,324,139,81,82,340,348,248,124,351,134,353,356,198,361,89,363,359,177,345,92,93,370,
94,373,128,374,240,97,378,301,381,100,101,387,388,211,372,235,385,243,137,223,172,396,107,108,179,
230,201,289,403,111,112,212,406,407,113,114,369,414,115,416,352,308,118,242,418,121,421,122,186,156,
159,429,125,158,434,436,145,439,188,405,441,132,433,410,133,446,135,452,274,456,461,458,459,138,464,
199,140,295,468,471,142,197,477,479,481,290,487,486,395,147,148,488,150,371,151,152,347,496,497,390,
154,328,155,221,503,505,506,507,319,292,326,162,239,426,382,164,350,325,165,166,518,167,520,525,526,
169,170,470,502,529,332,174,485,175,533,330,346,538,540,495,519,180,275,542,293,182,183,277,246,544,
517,267,424,189,437,553,190,555,276,556,364,430,561,193,194,564,196,339,233,227,341,202,392,494,205,
206,401,376,237,273,384,258,577,210,412,413,312,580,213,578,343,215,219,583,316,399,504,386,224,225,
586,557,587,229,231,379,590,234,575,449,541,236,595,313,596,572,244,349,298,307,598,247,287,549,283,
527,250,251,432,605,606,253,610,467,255,550,256,257,511,448,443,566,262,263,344,593,515,558,265,266,
383,615,397,268,619,393,402,342,623,584,514,271,318,582,625,480,609,628,279,303,475,616,634,455,281,
442,638,445,438,358,492,285,419,512,534,490,644,516,440,291,294,641,648,296,297,629,649,299,300,653,
535,304,427,655,428,656,417,310,476,335,315,543,317,630,654,508,320,522,491,663,647,322,323,500,400,
631,327,666,640,528,545,420,643,334,447,336,478,367,626,612,465,537,671,659,673,599,546,639,354,355,
357,469,551,676,632,457,360,645,423,681,567,362,569,548,665,657,365,366,613,498,368,375,377,380,687,
531,688,652,617,581,389,391,627,394,398,686,588,404,667,591,408,409,614,411,585,701,415,601,608,521,
422,425,444,523,683,493,431,674,435,603,635,571,704,450,622,565,680,451,702,453,637,454,574,576,594,
524,460,552,483,462,463,466,472,703,473,474,682,602,568,536,482,484,658,559,489,579,670,607,570,597,
692,499,539,501,620,532,509,510,513,684,695,530,604,708,633,685,672,706,689,700,642,693,624,547,563,
660,554,661,592,690,621,560,562,677,662,573,679,618,713,646,668,699,696,705,711,589,715,664,710,600,
650,636,611,675,697,719,669,720,651,709,712,678,714,707,716,694,691,698,717,718]
>;
print "Group G is 6.A7 < Sym(720)";