/*
www-ATLAS of Group Representations.
2.S6(3).2 represented as permutations on 728 points.
*/

G<x,y>:=PermutationGroup<728|\[
4,8,12,1,19,23,27,2,33,37,41,3,48,52,36,59,63,24,5,72,76,62,6,18,88,
92,7,99,67,87,108,38,9,115,46,15,10,32,129,132,11,138,112,128,100,35,53,13,157,161,
148,14,47,171,174,178,152,170,16,166,70,22,17,195,199,203,29,98,211,61,77,20,202,143,90,
21,71,225,228,111,213,224,173,89,240,97,30,25,84,75,254,26,259,239,188,187,86,68,28,45,
274,267,125,282,286,271,210,31,265,295,80,43,137,304,34,310,314,307,319,321,325,169,153,331,103,
190,136,44,39,317,339,40,343,281,149,127,113,42,354,356,350,212,74,352,303,362,155,51,135,320,
369,57,123,376,147,162,49,342,386,337,50,156,392,394,398,60,172,406,122,58,54,167,83,55,299,
404,413,56,217,419,327,425,429,411,296,435,96,95,300,126,223,214,444,196,64,194,451,454,65,328,
447,73,66,463,242,402,279,466,246,107,69,142,81,192,448,480,179,434,486,418,483,226,191,82,78,
222,494,79,255,491,332,441,436,499,478,484,457,373,94,85,461,205,507,511,505,209,519,251,522,258,
248,405,266,91,229,529,536,250,93,456,294,430,543,545,109,253,102,550,508,553,106,275,313,101,272,
276,301,384,207,341,134,104,551,468,562,105,542,393,517,557,291,438,334,261,110,185,440,333,175,189,
277,335,145,114,585,309,118,364,306,116,474,591,273,117,498,595,130,338,119,150,120,601,367,598,121,
415,181,200,561,330,124,231,298,293,302,353,160,318,131,520,280,158,133,554,532,363,617,615,385,141,
621,144,336,139,624,140,590,583,458,614,489,146,346,308,609,401,323,600,151,481,632,408,238,426,375,
154,640,382,521,515,642,378,387,278,349,159,383,527,538,648,453,163,288,164,635,575,596,165,537,654,
366,206,528,176,252,168,620,372,660,603,184,414,177,412,326,420,534,220,180,416,659,668,613,665,182,
374,653,569,183,262,639,588,673,218,186,233,658,292,475,297,232,568,610,193,526,669,201,215,502,574,
197,559,391,198,524,260,237,359,684,479,241,464,204,462,625,208,652,284,566,594,556,518,696,311,439,
523,493,235,460,216,370,644,221,236,661,219,633,576,361,698,230,700,477,227,616,623,634,315,234,676,
589,449,695,547,245,674,243,269,587,604,244,560,548,671,380,572,289,472,247,340,379,249,476,455,707,
445,388,403,256,663,645,345,628,417,715,257,399,389,629,680,643,287,263,651,264,717,504,513,549,268,
283,619,270,344,690,471,290,558,452,512,329,285,649,622,699,469,672,442,428,577,686,516,710,450,396,
488,570,611,719,677,711,636,358,662,305,704,509,432,501,357,312,641,631,470,316,397,599,324,597,368,
322,657,410,510,650,683,626,637,365,443,578,627,423,360,348,495,347,706,552,407,351,564,496,355,465,
607,612,533,539,702,593,371,487,497,395,582,608,682,431,377,592,381,541,482,531,675,714,390,563,605,
544,467,427,400,691,726,602,437,421,409,485,584,530,679,424,701,716,422,446,718,514,567,433,506,646,
500,580,727,664,540,685,638,606,459,681,571,687,688,709,555,655,712,703,728,503,473,705,490,565,492,
666,630,693,586,697,618,525,725,689,573,581,692,724,647,535,667,546,670,579,722,723,720,721,713,708,
656,678,694]
,\[
443,558,574,189,481,198,354,308,452,277,148,278,25,150,631,665,630,248,156,664,532,239,602,43,11,
399,139,175,573,367,712,231,536,113,441,130,517,10,386,600,509,19,409,307,280,633,59,99,17,589,
101,120,539,513,242,375,302,7,317,421,165,385,237,611,170,289,645,109,72,122,495,626,692,338,392,
721,510,506,212,699,209,62,722,58,556,211,216,213,56,433,588,522,585,650,384,403,710,323,453,396,
596,606,621,318,473,293,610,459,41,468,147,546,570,193,455,63,479,13,358,196,411,202,700,687,451,
474,326,581,541,16,659,35,9,319,437,298,306,551,84,394,478,131,548,327,291,6,438,114,512,92,
184,108,220,153,686,343,26,619,349,117,270,32,138,635,668,223,205,330,563,27,288,251,40,112,299,
225,107,724,215,132,121,652,660,366,250,154,501,461,98,583,717,111,356,519,381,359,584,272,168,435,
125,503,263,309,315,716,61,15,547,256,445,540,320,402,463,140,678,634,57,340,670,390,188,586,651,
371,480,654,395,467,355,404,149,462,294,673,275,520,550,488,161,312,667,91,53,625,174,182,523,679,
727,666,73,152,357,30,310,682,416,55,496,485,677,332,8,434,476,134,185,728,377,116,494,31,146,
713,562,363,285,680,457,393,482,124,328,96,521,587,612,347,127,500,33,432,555,567,316,374,286,590,
240,264,273,187,23,391,266,227,105,475,643,449,89,579,260,466,698,20,613,439,535,408,210,412,230,
2,648,420,714,313,222,169,578,173,259,401,565,352,179,544,50,203,141,360,60,238,155,207,158,283,
454,718,705,65,39,118,534,605,14,601,69,715,133,199,505,181,4,414,78,624,145,333,572,331,364,
487,3,37,119,472,598,201,560,658,471,486,346,655,365,329,424,64,691,68,646,249,497,622,93,335,
431,255,528,491,1,703,642,151,674,425,322,97,701,29,81,723,160,49,561,511,615,345,429,341,383,
206,208,576,95,274,344,564,86,527,387,657,268,417,444,656,407,608,566,533,662,157,582,559,167,362,
22,311,593,641,458,685,262,683,70,618,339,178,166,406,369,524,465,80,292,21,644,529,241,200,696,
483,514,129,192,303,398,163,639,382,351,623,176,569,531,137,376,305,464,265,214,428,76,353,469,477,
629,545,254,325,575,504,71,690,87,675,552,636,337,460,79,400,82,300,446,126,702,52,115,389,296,
704,51,553,616,595,258,577,321,507,88,271,172,726,427,470,42,336,261,123,447,537,632,647,693,484,
224,373,28,436,164,627,617,226,423,183,243,159,681,5,110,177,725,708,342,676,508,279,324,106,297,
370,515,144,290,543,252,456,410,530,194,350,604,348,490,380,614,253,304,518,236,44,287,334,554,640,
637,418,448,295,233,442,498,267,197,671,526,684,103,697,142,594,314,499,38,426,135,235,162,580,415,
489,695,246,48,492,661,628,180,228,171,379,542,591,102,195,653,46,12,378,90,709,688,720,669,502,
232,24,281,397,413,217,597,603,422,190,245,67,609,269,47,388,620,244,516,276,405,372,663,18,689,
45,301,538,104,706,219,361,100,85,94,557,143,707,229,711,571,430,221,257,66,450,607,36,54,186,
128,599,234,83,638,34,284,549,77,368,719,592,568,136,694,419,440,525,282,672,218,75,649,493,74,
191,247,204]
>;
print "Group G is 2.S6(3).2 < Sym(728)";