/*
www-ATLAS of Group Representations.
M22:2 represented as permutations on 672 points.
*/

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