/*
www-ATLAS of Group Representations.
A9 represented as permutations on 840 points.
*/

G<x,y>:=PermutationGroup<840|\[
2,4,8,1,13,16,19,10,24,3,29,32,14,5,38,18,43,6,20,7,52,12,56,26,61,
9,65,68,31,72,11,22,64,55,82,85,73,39,15,93,95,28,45,101,17,105,108,36,111,114,
116,53,21,123,81,57,23,128,131,134,62,25,141,78,67,147,27,42,153,156,47,74,87,30,164,
50,168,33,172,174,34,83,35,181,48,186,37,191,189,196,198,199,94,40,97,207,41,212,215,145,
102,44,223,225,107,229,46,71,235,238,112,49,91,76,245,117,51,251,249,255,258,259,124,54,266,
268,233,129,58,275,133,208,59,135,60,285,288,290,293,295,143,292,63,299,218,77,149,301,66,305,
127,309,154,69,315,158,319,70,324,326,329,332,335,166,201,75,262,146,345,283,348,173,79,176,351,
80,355,244,357,359,182,84,242,365,178,188,371,86,195,375,192,88,298,296,89,197,90,113,200,92,
339,391,396,399,401,104,209,280,96,408,410,213,98,412,217,415,99,100,144,420,421,424,224,103,206,
430,431,211,231,437,106,253,151,442,236,109,448,239,110,121,453,364,455,185,247,458,115,461,254,463,
252,118,441,119,256,120,152,240,260,122,476,342,126,243,481,267,125,263,489,490,220,492,494,496,276,
130,501,140,504,132,429,432,343,322,286,136,137,287,269,291,138,297,294,139,278,382,142,381,219,270,
302,148,528,171,307,159,150,349,257,439,411,539,542,543,316,155,361,163,321,434,157,512,552,306,554,
328,556,160,330,161,226,334,565,162,318,568,323,516,165,574,314,167,170,577,346,169,272,304,388,514,
352,175,584,587,356,177,358,179,360,180,546,595,480,183,367,600,184,604,562,451,372,187,610,613,376,
190,619,617,624,626,193,194,629,204,631,585,470,308,386,636,395,640,643,555,202,397,203,589,384,647,
402,205,649,281,651,654,333,409,210,228,538,413,214,222,416,216,664,667,658,271,422,221,670,414,672,
325,418,419,404,331,433,509,227,549,681,683,438,230,536,689,232,443,234,655,532,350,603,449,237,697,
606,520,454,241,264,362,702,459,246,248,460,597,464,250,709,708,423,714,716,634,523,720,400,471,699,
477,261,715,680,591,482,265,727,632,354,398,273,327,289,300,733,347,735,487,737,497,274,340,740,726,
502,277,744,505,279,385,748,732,282,691,383,284,751,446,553,571,547,452,582,518,368,754,474,550,756,
551,757,530,558,303,752,694,759,313,760,310,495,311,540,312,768,534,341,770,772,317,557,513,320,755,
580,337,678,426,645,488,517,646,775,776,616,605,436,559,407,583,561,570,642,336,338,784,762,498,788,
695,578,344,782,526,596,713,779,586,389,353,485,790,486,608,363,684,592,719,456,783,701,579,795,601,
366,797,690,521,369,370,588,791,668,612,801,373,615,738,374,567,623,804,620,377,491,393,378,625,379,
627,380,525,511,527,506,661,787,387,508,637,390,468,808,641,392,686,622,749,394,529,473,793,650,403,
652,405,425,656,692,406,648,428,814,747,484,665,602,666,815,417,427,800,659,467,522,653,479,743,725,
820,440,515,594,673,682,435,563,593,817,569,541,810,677,447,729,444,575,445,789,794,698,450,723,503,
462,703,457,707,825,704,706,712,710,465,633,466,519,638,724,717,469,750,679,721,472,639,475,478,819,
734,728,483,510,835,834,635,621,500,736,493,537,802,838,741,499,507,812,700,533,763,786,742,809,773,
548,758,611,671,524,628,630,531,745,761,535,781,830,823,730,545,764,687,560,771,544,766,718,828,564,
769,705,840,566,685,573,598,581,785,572,660,711,693,576,607,590,731,657,799,796,599,663,816,696,609,
753,614,806,805,618,811,798,722,644,824,803,674,833,669,662,807,780,827,675,821,676,778,767,688,777,
839,829,836,818,746,826,739,837,792,765,774,813,832,831,822]
,\[
3,6,9,11,1,17,2,22,25,27,30,4,34,36,5,41,44,46,48,50,7,55,8,59,40,
63,66,10,70,73,75,76,12,80,13,86,14,89,91,15,96,16,99,54,103,106,18,110,19,115,
20,119,121,21,125,31,127,23,132,24,137,139,142,26,145,148,150,151,28,157,29,160,79,162,165,
167,32,170,33,175,177,113,172,35,184,187,189,37,194,38,182,39,202,204,205,208,210,42,216,43,
220,57,211,45,227,230,232,233,47,179,240,144,49,243,246,219,249,51,181,52,141,53,262,264,130,
56,270,271,273,58,277,279,281,67,283,60,289,61,171,62,197,242,298,64,107,65,300,155,303,306,
308,68,311,313,69,317,320,322,71,327,72,333,74,336,338,340,341,343,77,296,78,147,307,350,183,
353,90,81,82,83,362,363,84,366,85,369,193,373,374,87,378,326,88,178,383,384,386,387,389,391,
92,394,93,400,94,95,404,214,406,226,97,256,411,98,358,248,417,419,100,344,101,102,426,146,428,
104,432,105,435,237,439,421,302,108,445,447,109,416,450,452,111,112,456,114,418,253,460,116,462,117,
466,468,118,470,455,247,120,133,245,342,122,478,123,480,124,484,430,487,126,491,188,128,495,129,499,
500,345,131,287,506,508,134,511,135,163,515,136,236,517,143,518,138,291,519,520,140,304,522,305,524,
525,527,529,149,531,532,533,195,534,152,537,153,174,154,492,545,523,156,547,325,483,551,158,486,159,
555,557,558,166,561,161,563,566,477,567,569,164,269,572,575,347,576,423,168,554,337,169,218,173,581,
582,290,585,176,297,590,591,592,593,595,180,473,393,597,599,481,602,185,213,186,608,292,611,614,334,
617,190,622,191,192,548,241,310,630,196,261,633,198,463,199,639,200,201,644,646,294,625,203,315,403,
624,288,206,330,207,655,209,212,275,658,659,632,276,215,427,648,665,217,260,365,224,668,221,609,222,
673,223,485,225,675,676,678,679,228,472,229,685,686,688,231,588,690,398,234,669,235,238,489,596,637,
239,351,634,701,684,316,244,433,705,706,638,459,707,708,250,711,251,715,252,718,254,255,257,258,259,
587,606,650,263,550,494,420,265,674,266,267,729,268,727,731,425,734,272,368,738,346,740,274,357,601,
726,741,278,379,293,381,280,528,580,282,437,335,284,285,752,286,372,753,613,586,295,652,299,361,516,
301,693,722,589,556,318,510,749,397,309,763,765,604,766,560,312,356,769,314,457,771,507,319,323,321,
530,616,324,745,774,549,562,603,328,329,620,331,777,332,401,514,672,780,739,782,783,640,339,786,767,
579,552,410,348,349,544,382,352,399,683,395,396,354,355,641,792,464,407,359,756,360,793,364,742,797,
796,666,367,798,661,577,370,799,371,584,493,446,710,621,803,375,733,376,573,653,377,760,755,751,805,
804,754,380,539,660,791,385,761,775,388,571,627,390,770,626,784,392,498,443,541,694,810,402,635,725,
409,583,405,469,594,702,408,813,607,412,413,414,415,787,475,559,800,612,422,440,424,818,728,429,758,
768,431,680,822,434,788,497,441,436,513,735,438,703,825,578,442,821,444,521,448,449,695,724,451,453,
667,454,816,458,465,657,461,662,565,476,570,750,467,543,830,677,790,831,471,542,538,474,833,824,479,
482,600,663,820,488,829,490,781,795,776,772,811,643,496,698,664,501,502,807,503,504,505,656,509,512,
839,526,838,699,826,785,721,553,687,746,649,535,631,536,645,692,540,681,732,789,636,764,546,806,623,
819,835,564,801,618,568,713,840,832,696,743,574,716,642,837,736,651,779,598,610,605,697,615,817,748,
794,834,757,619,762,628,629,778,719,717,647,654,691,689,827,670,671,712,759,836,744,815,682,823,802,
700,704,709,714,812,809,720,814,723,808,730,737,747,828,773]
>;
print "Group G is A9 < Sym(840)";