/*
www-ATLAS of Group Representations.
M22 represented as permutations on 176 points.
*/

G<x,y>:=PermutationGroup<176|\[
1,4,6,2,9,3,12,14,5,17,19,7,22,8,25,27,10,30,11,33,35,13,23,39,15,
41,16,44,46,18,49,32,20,53,21,55,57,58,24,61,26,63,65,28,68,29,70,72,31,75,
76,60,34,80,36,71,37,38,86,52,40,90,42,93,43,95,97,45,79,47,56,48,101,92,50,
51,105,106,69,54,109,82,111,112,85,59,114,88,116,62,91,74,64,121,66,96,67,124,126,127,
73,129,130,104,77,78,113,135,81,137,83,84,107,87,141,89,120,134,143,117,94,144,145,98,147,
99,100,152,102,103,153,132,154,118,108,157,110,159,160,161,115,162,119,122,123,151,125,164,166,167,
146,128,131,133,155,171,136,172,138,139,140,142,168,148,165,149,150,163,169,175,156,158,173,174,170,
176]
,\[
2,5,1,7,3,10,13,4,15,18,6,20,8,23,26,9,28,11,31,34,12,36,38,14,40,
16,42,45,17,47,50,19,51,21,25,56,22,24,59,54,62,64,27,66,29,69,71,30,73,32,
77,33,78,35,81,37,72,84,87,39,88,41,91,43,68,96,44,76,46,98,48,100,102,49,103,
94,52,107,53,95,110,55,57,113,58,92,60,115,61,117,86,63,119,65,122,67,109,125,70,83,
128,74,121,75,131,133,79,80,136,82,112,139,85,140,89,142,130,90,144,93,104,108,97,146,99,
148,150,101,145,118,141,105,155,106,116,123,143,111,138,114,132,156,163,120,129,124,157,165,126,168,
127,166,169,170,134,135,160,137,171,162,154,147,158,173,149,153,174,151,152,172,159,161,164,176,167,
175]
>;
print "Group G is M22 < Sym(176)";