/*
www-ATLAS of Group Representations.
M22:2 represented as permutations on 616 points.
*/

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