/*
www-ATLAS of Group Representations.
M22 represented as permutations on 770 points.
*/

G<x,y>:=PermutationGroup<770|\[
1,4,6,2,9,3,12,14,5,17,19,7,22,8,25,27,10,30,11,33,35,13,38,40,15,
43,16,44,46,18,49,51,20,54,21,56,58,23,61,24,64,66,26,28,69,29,72,74,31,77,
32,80,82,34,85,36,73,37,90,92,39,95,97,41,65,42,101,103,45,106,108,47,57,48,100,
114,50,117,119,52,81,53,124,84,55,128,130,131,133,59,135,60,138,140,62,143,63,146,127,75,
67,149,68,152,154,70,157,71,159,161,162,164,165,76,168,170,78,172,79,175,177,178,180,83,139,
183,99,86,155,87,88,191,89,193,91,196,198,93,125,94,203,205,96,208,145,98,212,213,102,216,
218,104,169,105,129,224,107,173,109,229,110,111,234,112,113,239,241,115,153,116,245,118,158,249,120,
251,121,122,256,123,259,261,126,264,265,228,267,269,270,195,132,274,134,277,190,136,281,137,284,286,
287,289,141,292,142,295,297,144,300,301,303,147,148,308,310,150,240,151,315,317,318,320,223,156,225,
322,323,186,160,326,328,329,331,163,325,335,336,338,166,217,167,342,344,345,171,246,349,350,174,250,
176,354,305,282,276,179,359,360,181,363,182,262,366,184,185,370,187,373,188,189,271,377,273,192,380,
255,194,296,384,280,197,254,389,199,392,200,201,397,202,400,313,204,361,404,206,278,207,408,410,209,
210,413,211,416,253,418,420,214,321,215,422,424,291,426,219,429,220,221,434,222,309,226,227,439,235,
230,442,231,232,445,233,448,450,451,236,237,348,238,456,457,459,242,462,243,244,467,362,337,247,248,
472,473,428,252,368,476,477,479,257,258,293,347,260,449,483,263,471,355,487,266,490,482,268,374,493,
495,272,498,500,275,502,503,505,279,508,396,510,511,283,513,514,285,517,519,395,386,288,523,525,290,
432,431,527,294,529,530,532,298,533,299,536,443,302,538,455,304,419,306,417,307,545,311,547,312,548,
314,427,353,316,463,402,401,553,319,552,556,444,557,324,559,561,327,412,437,330,565,567,332,364,333,
334,563,575,558,415,339,340,578,341,580,582,343,430,560,585,466,346,509,587,589,367,351,352,478,475,
356,357,474,358,595,574,372,365,596,562,588,369,598,520,371,600,492,375,602,376,605,569,378,608,379,
610,381,382,612,383,614,616,385,468,387,388,621,390,391,625,627,393,630,394,489,521,632,398,634,399,
581,403,636,405,406,531,407,409,641,642,411,644,414,645,618,647,648,619,650,421,653,423,425,549,657,
658,435,433,659,592,436,438,454,440,464,441,485,452,594,446,664,447,667,497,669,671,672,674,481,453,
576,676,458,678,460,526,461,583,682,465,611,469,486,470,685,597,555,686,564,480,484,591,488,660,491,
643,494,691,623,496,613,662,499,695,501,586,504,606,506,696,507,699,540,543,701,512,703,604,673,515,
631,516,665,708,518,626,522,700,524,654,528,711,713,694,663,534,535,601,537,539,718,541,542,698,544,
721,652,546,635,661,722,550,551,554,599,655,607,640,566,628,726,568,727,570,728,571,572,624,573,681,
577,677,579,733,735,675,584,707,738,590,593,740,697,741,734,603,692,704,639,609,615,688,649,617,633,
620,744,622,693,705,745,683,629,746,720,637,742,638,749,751,719,736,646,716,710,651,656,754,724,730,
666,668,670,758,725,759,761,679,690,680,717,764,684,739,687,689,712,743,702,706,709,747,760,714,757,
715,766,767,723,768,765,750,729,731,748,732,762,770,737,756,752,753,755,769,763]
,\[
2,5,1,7,3,10,13,4,15,18,6,20,8,23,26,9,28,11,31,34,12,36,39,14,41,
16,27,45,17,47,50,19,52,21,55,57,22,59,24,62,65,25,43,67,29,70,73,30,75,32,
78,81,33,83,35,86,37,88,91,38,93,96,40,98,42,100,102,44,104,107,46,109,48,111,113,
49,115,118,51,120,53,122,125,54,126,129,56,132,58,134,60,136,139,61,141,63,144,147,64,148,
66,68,150,153,69,155,71,158,160,72,163,74,76,166,169,77,90,79,173,176,80,179,82,181,84,
184,85,185,87,187,189,89,192,171,194,197,92,199,94,201,204,95,206,209,97,210,99,101,214,217,
103,219,105,221,223,106,225,108,227,110,230,232,112,235,237,240,114,242,116,239,117,246,248,119,249,
121,252,254,123,257,260,124,262,127,266,128,268,130,271,131,272,133,275,278,135,279,137,282,285,138,
288,140,290,142,293,296,143,298,145,302,146,304,306,309,149,311,151,313,316,152,319,154,156,273,321,
157,324,159,261,327,161,330,162,332,334,164,337,165,339,167,340,343,168,170,346,348,172,174,351,175,
352,355,177,356,178,357,336,180,361,182,364,365,183,367,368,186,371,188,264,375,190,224,191,378,381,
193,382,195,385,196,386,388,198,390,200,393,395,202,398,401,203,402,403,205,405,207,406,409,208,411,
300,211,414,417,212,419,213,359,215,421,423,216,425,218,427,220,430,432,222,435,226,437,349,228,229,
440,231,292,380,233,446,449,234,236,452,258,238,454,244,458,241,460,243,463,465,468,245,247,469,470,
250,474,251,310,253,255,478,256,308,373,481,259,482,325,263,484,374,486,265,488,491,267,492,269,494,
270,496,499,274,501,276,504,277,506,280,509,281,283,322,408,284,515,518,286,520,287,521,524,289,422,
291,443,294,528,295,531,297,391,299,534,412,301,537,539,303,540,305,542,307,404,475,546,312,464,314,
490,550,315,551,552,317,457,318,547,555,320,512,323,558,560,326,562,328,329,564,566,331,568,333,570,
572,574,335,476,338,576,433,341,477,581,342,583,424,344,586,345,587,347,438,502,350,561,591,353,354,
455,592,358,593,360,362,363,519,597,366,369,590,595,370,599,372,480,601,376,603,606,377,439,379,609,
444,471,611,383,613,615,384,523,387,618,619,389,622,445,626,392,628,394,413,396,631,397,633,399,429,
400,598,544,637,629,407,639,533,630,410,632,483,610,415,646,416,649,418,420,651,526,654,655,426,428,
635,431,634,434,436,653,557,607,565,441,487,662,442,624,663,447,665,668,448,670,450,673,451,453,674,
675,456,503,459,679,461,589,681,462,683,466,650,467,684,472,473,579,687,479,489,636,485,553,549,582,
493,689,692,495,686,497,498,685,538,500,677,690,505,693,507,697,508,510,700,511,702,704,513,514,705,
516,699,530,517,535,522,709,617,527,525,710,712,529,644,532,714,672,536,640,716,541,719,575,543,588,
718,545,657,554,659,548,660,585,656,556,559,563,661,671,725,567,698,569,669,571,695,729,573,720,577,
722,578,731,734,580,584,736,723,600,739,614,594,596,612,602,742,604,605,608,724,696,667,616,726,620,
642,621,744,623,708,625,627,706,643,688,647,638,748,750,641,746,645,652,747,648,727,753,658,664,666,
707,755,756,701,676,760,678,761,680,735,763,682,758,694,713,765,749,691,751,703,717,711,764,743,715,
745,721,730,754,752,766,728,741,759,732,769,733,737,740,738,757,767,770,762,768]
>;
print "Group G is M22 < Sym(770)";