/*
www-ATLAS of Group Representations.
12.M22 represented as 24 x 24 matrices over GF(121).
*/

F<w>:=GF(121);

x:=CambridgeMatrix(3,F,24,\[
0,85,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
47,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,85,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,47,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,85,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,85,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,47,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,47,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,85,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,85,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,85,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,47,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,85,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,47,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,85,0,0,0,
0,0,0,0,0,0,0,0,0,0,47,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,85,
3,43,8,59,81,35,17,68,112,74,82,111,34,22,68,48,63,55,44,92,71,38,117,37,
0,0,0,0,0,0,0,0,0,0,0,0,47,0,0,0,0,0,0,0,0,0,0,0,
107,108,62,83,15,107,94,39,57,46,68,83,21,112,103,80,36,87,64,27,23,11,88,54,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,47,0,0,0,0,0,0,0,0,0,
52,93,37,79,108,106,90,98,106,105,91,105,87,5,107,4,61,56,83,25,53,57,13,13,
57,7,89,24,42,82,81,75,108,74,97,50,44,103,22,80,101,76,29,112,42,17,114,106,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,47,0,0,0,0,0,0,0]);

y:=CambridgeMatrix(3,F,24,\[
101,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
63,86,37,0,31,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
42,60,27,80,50,12,118,36,33,77,120,104,120,88,46,36,2,74,50,30,40,67,7,7,
64,86,37,0,46,0,0,0,31,0,0,0,0,0,95,0,0,0,0,0,47,0,0,0,
15,35,37,44,92,76,88,13,48,52,36,85,61,58,80,71,22,39,23,76,106,12,103,113,
93,48,7,51,53,41,7,31,18,112,73,71,73,75,7,84,17,103,14,90,6,24,68,112,
115,33,44,58,115,117,97,18,102,119,100,106,108,1,116,117,29,20,16,107,69,22,50,83,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
24,56,120,39,35,67,51,36,109,83,80,10,115,24,35,45,42,84,99,15,104,109,120,66,
78,61,75,116,18,107,54,15,115,69,47,117,111,53,110,80,30,86,98,38,18,105,26,81]);

G<x,y>:=MatrixGroup<24,F|x,y>;
print "Group G is 12.M22 < GL(24,GF(121))";