/*
www-ATLAS of Group Representations.
2.M22 represented as permutations on 660 points.
*/

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