/*
www-ATLAS of Group Representations.
3.M22 represented as permutations on 693 points.
*/

G<x,y>:=PermutationGroup<693|\[
1,3,2,6,8,4,11,5,13,15,7,18,9,21,10,23,25,12,28,30,14,33,16,36,17,
38,40,19,43,20,45,47,22,50,35,24,37,26,55,27,57,59,29,44,31,64,32,66,68,34,
51,52,72,74,39,76,41,79,42,81,61,62,85,46,87,48,67,49,91,93,95,53,98,54,100,
56,103,105,58,107,60,109,110,112,63,114,65,116,118,119,69,121,70,123,71,126,127,73,130,75,
132,133,77,135,78,137,80,140,82,83,143,84,145,86,148,88,150,89,90,153,92,155,94,158,159,
96,97,162,164,99,167,101,102,171,104,174,106,177,178,108,180,182,111,184,113,146,188,115,190,117,
193,169,120,196,122,199,201,124,125,203,205,128,208,129,210,212,131,172,152,216,134,168,220,136,175,
223,138,139,226,141,181,142,231,144,234,236,187,147,238,149,241,242,151,244,246,154,197,198,156,200,
157,251,160,254,161,257,259,163,209,165,262,166,264,266,215,170,268,270,272,173,221,274,176,277,225,
179,280,255,282,283,183,286,288,185,290,186,292,189,295,296,191,192,300,194,245,195,304,306,307,250,
202,311,313,204,228,315,206,318,207,260,320,211,323,213,326,214,328,217,298,218,331,219,334,222,336,
338,224,341,343,227,345,229,230,347,285,232,350,233,352,235,355,237,358,360,239,240,362,269,364,243,
301,367,369,247,372,248,249,375,376,377,252,379,253,314,256,316,384,258,387,261,390,391,263,393,394,
265,397,267,399,401,271,404,363,273,407,275,408,276,410,412,278,414,279,415,281,418,284,421,370,287,
424,289,353,354,291,429,431,293,359,294,361,297,333,299,436,438,302,416,303,349,442,305,373,445,308,
309,310,450,312,452,453,443,454,317,456,457,319,448,459,321,322,462,324,325,395,396,327,468,329,470,
330,471,403,332,428,474,335,337,477,339,479,340,480,342,344,368,485,346,487,489,348,491,492,351,494,
496,498,405,356,430,357,502,503,504,505,365,437,366,509,510,441,371,382,513,374,516,463,388,449,378,
518,380,381,383,455,385,386,526,389,460,515,392,447,531,532,521,525,398,536,400,402,540,542,406,544,
481,409,499,411,413,476,514,552,553,417,486,419,556,420,548,422,423,560,425,561,426,563,427,478,566,
567,432,433,434,435,569,571,572,439,440,575,577,444,482,461,446,581,451,583,557,466,522,527,586,467,
458,523,590,541,592,464,465,595,534,596,469,599,600,601,472,529,473,554,475,606,546,607,490,609,610,
611,483,484,543,613,488,520,558,578,493,495,562,497,618,565,500,501,620,506,622,507,508,623,574,511,
626,512,559,593,580,517,629,519,631,585,524,634,635,636,528,637,530,579,639,533,535,603,643,537,538,
539,646,597,648,619,545,547,650,549,550,551,612,555,653,644,655,617,564,605,568,657,570,573,624,660,
576,662,664,582,665,584,666,651,587,588,589,591,638,594,640,641,671,598,615,645,602,647,604,674,608,
633,677,614,654,616,656,621,669,661,625,659,627,663,628,630,632,683,668,658,670,642,680,678,649,685,
676,652,673,687,672,681,686,667,684,675,682,679,688,692,691,690,689,693]
,\[
2,4,5,7,9,10,1,12,14,16,17,19,20,3,22,24,26,27,29,31,32,34,35,6,37,
39,41,42,8,44,46,48,49,51,23,52,53,54,11,56,58,60,61,62,63,13,65,67,69,70,
15,71,73,45,75,77,78,18,80,82,83,84,38,86,88,89,21,90,92,94,96,97,25,99,101,
102,104,106,55,59,108,28,111,30,113,64,115,117,81,68,120,33,122,124,125,36,128,129,74,131,
79,76,134,40,136,138,139,66,141,142,43,144,146,147,149,116,47,151,152,91,154,156,157,50,123,
160,161,163,165,166,168,169,170,172,173,175,176,57,145,179,181,137,183,185,186,187,189,105,191,192,
194,155,195,197,198,200,95,190,202,204,206,207,72,209,211,213,214,215,162,217,218,219,221,222,148,
110,224,225,227,228,229,230,232,233,235,107,85,237,239,240,87,243,199,245,167,247,248,119,249,93,
250,252,253,255,256,258,132,260,261,210,98,263,265,153,100,267,269,271,103,262,273,275,276,177,278,
279,281,180,109,284,285,287,289,259,112,291,293,294,114,297,298,299,301,302,118,303,305,121,308,309,
310,312,314,286,126,316,317,127,234,319,321,322,324,325,130,327,329,326,133,330,332,333,135,335,337,
339,340,342,226,344,140,201,346,348,349,254,143,351,353,354,356,357,359,361,212,358,158,363,365,366,
150,368,370,371,373,374,307,193,282,320,378,159,380,381,382,383,385,386,388,389,164,379,392,295,395,
396,350,398,400,402,403,171,405,406,274,272,174,409,411,292,413,178,394,416,417,419,420,182,422,423,
425,426,184,427,428,430,277,375,188,264,432,433,434,435,437,362,407,439,440,441,443,444,196,446,447,
448,449,451,220,424,203,315,205,455,399,318,458,208,251,460,461,463,464,465,360,466,467,469,257,216,
459,421,472,473,336,338,475,476,334,478,223,391,481,482,483,484,486,418,488,490,270,231,266,493,495,
497,499,500,408,236,501,238,300,241,506,507,242,508,244,511,246,452,512,514,515,517,296,518,519,520,
521,442,522,523,504,524,525,456,527,528,479,529,530,450,533,268,534,535,537,538,539,541,543,498,545,
546,547,548,412,549,550,551,431,280,554,555,454,283,557,558,559,492,313,494,288,562,564,565,290,540,
415,457,471,560,568,570,436,573,574,377,576,304,578,579,580,414,306,582,510,393,311,584,585,387,587,
588,589,591,470,323,593,594,343,595,597,598,328,462,602,355,331,603,604,605,367,429,477,608,480,341,
516,505,445,612,345,614,615,347,571,384,616,617,474,352,563,619,489,621,618,364,572,491,624,625,590,
369,627,513,372,553,628,376,630,632,487,633,502,596,401,575,390,638,620,640,397,641,642,592,637,644,
645,503,647,404,649,496,586,410,599,651,611,646,652,654,567,631,606,569,566,656,552,658,659,438,661,
655,663,581,629,662,643,453,667,668,583,577,669,536,544,670,526,468,561,600,672,485,673,648,639,675,
676,613,678,679,626,531,674,653,680,657,509,635,636,666,681,682,607,684,609,532,685,686,542,687,650,
688,664,622,556,689,665,677,690,691,683,601,660,610,623,671,634,693,692]
>;
print "Group G is 3.M22 < Sym(693)";