/*
www-ATLAS of Group Representations.
M23 represented as permutations on 253 points.
*/

G<x,y>:=PermutationGroup<253|\[
2,1,5,6,3,4,10,12,14,7,16,8,13,9,20,11,21,24,25,15,17,28,23,18,19,
33,34,22,37,39,31,41,26,27,44,36,29,48,30,40,32,52,54,35,57,58,60,38,63,64,
65,42,68,43,71,56,45,46,75,47,72,78,49,50,51,83,85,53,69,87,55,61,90,86,59,
93,94,62,96,98,81,100,66,103,67,74,70,107,109,73,111,113,76,77,116,79,97,80,120,82,
123,102,84,127,129,122,88,132,89,135,91,112,92,121,138,95,140,142,143,99,114,106,101,146,147,
149,104,144,105,154,156,108,158,159,110,162,164,115,166,117,168,118,119,128,171,124,125,148,126,176,
177,179,180,130,183,131,184,133,134,186,188,136,191,137,194,139,167,141,169,198,145,200,202,204,205,
150,151,208,152,153,203,182,155,157,214,160,216,161,218,220,163,222,209,165,224,196,207,170,199,172,
201,173,181,174,175,210,197,178,193,206,233,234,213,185,236,187,223,189,219,190,221,192,217,195,225,
241,227,229,228,230,242,232,211,212,245,215,237,238,248,243,226,231,240,244,235,251,252,239,253,250,
246,247,249]
,\[
3,4,1,7,8,9,11,13,15,14,2,17,18,19,21,22,23,5,26,27,6,29,30,31,32,
10,35,36,38,12,40,25,42,43,45,46,47,16,49,50,51,53,55,56,20,59,61,62,54,24,
66,67,69,70,68,72,73,74,28,76,77,79,80,81,82,84,86,34,33,39,88,89,60,91,92,
57,37,95,97,63,99,101,102,41,104,105,106,108,44,110,112,114,103,115,117,118,48,119,121,122,
124,125,126,128,52,130,131,133,134,116,94,58,136,137,132,139,141,138,98,140,64,144,145,65,148,
150,151,152,153,155,157,111,71,160,161,163,75,165,90,167,78,169,170,156,172,173,174,83,175,93,
178,85,181,182,87,100,185,158,146,187,189,190,192,193,96,195,196,180,197,199,179,201,203,147,206,
207,204,209,171,210,211,154,212,213,107,215,109,217,219,162,221,113,223,176,166,120,225,226,222,227,
123,228,159,216,229,230,231,218,127,232,129,235,184,186,237,238,205,208,135,220,239,143,240,191,142,
198,242,243,188,149,194,168,234,244,246,247,214,177,224,164,233,249,248,241,250,183,245,202,200,236,
251,252,253]
>;
print "Group G is M23 < Sym(253)";