/*
www-ATLAS of Group Representations.
M22 represented as permutations on 616 points.
*/

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