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

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