/*
www-ATLAS of Group Representations.
S12 represented as permutations on 792 points.
*/

G<x,y>:=PermutationGroup<792|\[
1,4,6,2,10,3,14,8,17,5,11,22,13,7,15,28,9,18,33,20,36,12,23,41,25,
44,46,16,29,30,51,32,19,34,55,21,37,59,39,40,24,42,65,26,45,27,71,57,74,76,
31,80,82,84,35,56,48,90,38,93,95,97,99,64,43,66,67,68,107,70,47,72,73,49,75,
50,77,78,79,52,81,53,83,54,85,117,106,88,89,58,91,92,60,94,61,96,62,98,63,144,
146,147,135,104,139,87,69,108,132,157,111,160,113,150,164,166,86,169,171,120,174,176,178,180,182,
126,127,185,187,130,131,109,133,153,103,194,196,198,105,140,141,142,143,100,145,101,102,210,149,114,
151,152,134,154,155,156,110,158,159,112,221,223,225,115,165,116,167,168,118,170,119,172,173,121,175,
122,241,123,244,124,248,125,183,184,128,186,129,259,189,219,262,192,193,136,195,137,270,138,199,274,
201,277,216,204,280,282,215,285,209,148,211,212,251,291,207,203,217,218,190,220,161,222,162,302,163,
226,227,295,308,310,312,232,315,317,319,264,237,238,321,240,177,242,243,179,245,246,247,181,249,250,
213,252,338,254,341,334,344,346,188,260,261,191,263,236,265,266,324,268,269,197,358,272,360,200,275,
276,202,366,279,205,281,206,283,371,208,286,287,376,378,290,214,292,293,297,228,385,294,388,354,300,
301,224,394,304,397,306,307,229,309,230,311,231,313,314,233,316,234,318,235,320,239,415,323,267,325,
419,327,417,329,330,331,426,333,256,430,336,401,253,339,340,255,342,437,257,440,258,443,445,447,414,
364,352,353,299,452,454,357,271,359,273,461,462,363,351,365,278,468,469,470,472,284,372,373,478,480,
288,377,289,486,487,489,422,383,492,296,386,387,298,389,390,494,498,500,303,395,396,305,504,399,448,
337,402,508,404,464,511,407,513,455,410,411,412,474,350,322,416,328,418,326,420,421,382,423,424,524,
332,427,428,429,335,431,432,433,530,476,436,343,438,439,345,441,442,347,444,348,539,349,400,532,545,
451,355,453,356,409,521,457,458,459,490,361,362,552,405,465,554,467,367,368,369,471,370,473,413,475,
435,477,374,479,375,566,568,570,519,485,379,380,488,381,460,572,384,493,391,578,579,497,392,499,393,
501,502,503,398,587,506,589,403,509,593,406,512,408,514,601,516,517,518,484,520,456,522,523,425,525,
561,609,611,613,434,531,449,533,534,535,608,537,621,446,540,541,542,543,544,450,546,632,633,574,550,
551,463,553,466,555,556,639,558,559,560,526,562,563,564,565,481,567,482,569,483,571,491,650,549,575,
576,577,495,496,580,656,582,583,584,604,586,505,588,507,590,591,592,510,594,595,664,597,670,638,669,
515,602,603,585,605,606,674,536,527,610,528,612,529,614,615,616,677,618,619,620,538,622,667,624,681,
626,627,628,629,637,696,547,548,634,635,659,630,599,557,640,641,642,643,644,645,646,647,648,649,573,
651,652,706,654,655,581,657,671,636,665,661,662,663,596,660,666,623,668,600,598,658,717,701,607,675,
716,617,678,679,724,625,704,683,727,685,686,687,688,719,708,731,692,693,694,695,631,697,698,699,700,
673,702,703,682,705,653,707,690,709,710,711,737,713,741,715,676,672,718,689,747,721,722,723,680,726,
725,684,728,729,730,691,732,733,734,735,736,712,738,739,740,714,754,743,744,764,746,720,748,749,770,
751,752,753,742,755,756,757,758,759,760,773,762,763,745,765,766,777,768,769,750,780,772,761,774,783,
776,767,778,779,771,781,782,775,784,785,786,787,788,789,790,791,792]
,\[
2,5,1,8,11,12,3,16,4,19,21,23,6,25,7,29,30,9,34,10,37,38,40,13,43,
14,15,47,49,50,17,18,27,54,20,57,33,44,22,61,62,24,66,67,26,69,72,28,75,77,
78,31,32,85,86,35,89,36,92,39,96,98,41,42,102,104,105,45,108,46,110,112,48,114,83,
116,118,59,51,120,52,123,53,95,126,127,55,56,130,131,58,134,135,60,138,101,139,141,142,63,
64,148,65,150,151,68,153,155,70,158,71,161,73,163,74,167,76,170,79,173,80,81,179,82,84,
129,184,87,88,188,189,90,91,192,193,93,94,199,200,97,202,175,99,204,100,207,209,211,103,152,
197,106,174,107,214,109,216,218,111,220,222,113,226,227,115,230,231,117,233,177,235,119,147,238,121,
239,122,242,245,246,124,250,125,253,254,128,257,260,166,132,133,264,265,266,136,241,137,271,273,275,
140,278,143,279,144,145,284,146,203,160,288,149,154,292,156,294,157,296,159,298,299,224,251,162,303,
305,306,164,165,311,313,168,316,169,320,171,172,322,323,176,325,326,178,328,330,331,180,333,181,336,
182,183,339,340,185,186,345,187,348,263,190,350,191,237,352,353,194,195,196,357,359,198,361,362,363,
201,365,283,272,261,205,369,206,372,373,208,210,377,212,213,381,293,215,383,217,386,219,389,390,221,
223,307,395,225,398,399,228,400,229,403,367,405,407,232,409,411,412,234,415,417,236,419,420,240,422,
270,243,277,244,425,416,247,428,248,249,432,252,434,343,287,436,255,256,438,441,423,258,446,259,449,
262,445,274,267,268,269,455,456,458,459,433,463,464,276,466,437,280,281,471,282,474,476,477,285,286,
482,379,484,289,290,490,291,413,295,494,387,297,469,342,479,300,301,302,454,502,304,467,402,505,506,
308,309,509,310,510,312,408,314,478,315,515,493,317,318,517,319,518,321,488,520,324,522,327,329,431,
341,332,525,334,527,335,529,337,531,338,394,533,356,344,397,536,346,537,347,453,540,541,349,544,351,
354,498,355,549,442,500,358,368,526,360,486,427,553,465,364,555,366,556,557,495,559,560,370,404,371,
564,497,457,374,443,375,569,376,572,378,565,492,380,575,576,382,542,384,570,385,388,391,581,392,583,
393,552,396,585,584,588,401,426,592,594,595,406,598,410,602,414,462,604,418,489,421,534,424,607,550,
429,610,430,582,554,615,435,617,439,440,619,620,444,623,625,626,447,448,628,629,450,451,452,635,460,
461,468,547,637,638,578,640,470,642,580,472,473,475,567,480,644,481,561,646,647,483,649,485,487,521,
653,491,503,655,496,657,499,600,501,566,504,659,661,662,507,508,665,633,667,668,511,512,671,513,514,
613,603,516,605,519,523,675,524,677,679,641,528,682,530,684,532,686,535,622,688,689,538,562,539,691,
692,543,694,695,545,546,579,697,548,698,551,634,606,632,645,558,624,563,701,568,630,702,571,703,589,
573,574,707,577,709,669,683,586,712,587,713,597,590,591,643,593,650,715,596,705,716,599,601,631,720,
608,660,609,723,611,612,726,614,728,616,687,618,699,730,621,693,670,627,674,648,717,733,664,636,639,
734,680,735,651,652,724,708,654,666,656,658,740,714,663,742,743,744,672,673,748,676,678,751,732,681,
753,754,729,685,755,690,696,700,757,736,704,706,710,711,760,761,759,762,763,718,719,727,768,721,722,
752,725,771,741,772,731,739,737,738,750,775,765,776,777,745,746,747,769,749,764,778,781,756,758,784,
774,785,766,767,770,782,773,780,788,789,779,783,786,791,787,792,790]
>;
print "Group G is S12 < Sym(792)";