/*
www-ATLAS of Group Representations.
M22 represented as permutations on 672 points.
*/

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