/*
www-ATLAS of Group Representations.
3.M22 represented as 21 x 21 matrices over GF(121).
*/

F<w>:=GF(121);

x:=CambridgeMatrix(3,F,21,\[
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
78,54,120,12,118,0,14,0,4,0,0,7,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
64,68,100,32,89,99,43,22,44,118,12,77,120,14,0,120,1,0,12,0,0,
34,98,25,107,92,85,40,47,87,0,79,45,115,0,0,53,0,1,17,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
52,80,105,27,96,49,36,83,95,14,4,37,76,118,0,7,0,0,56,1,0,
82,50,39,93,31,37,101,95,27,70,22,105,63,62,0,99,0,0,69,0,1]);

y:=CambridgeMatrix(3,F,21,\[
100,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
39,47,117,0,32,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
61,103,11,54,30,93,100,71,83,6,57,6,98,116,29,58,119,64,41,67,84,
63,84,77,41,35,54,119,60,49,109,57,93,116,57,114,114,114,25,71,56,85,
64,95,104,96,78,0,90,0,36,0,0,1,0,0,42,0,0,0,0,0,0,
25,107,6,21,11,101,37,1,2,7,1,80,114,18,85,97,22,73,23,43,72,
114,19,84,90,72,117,51,41,76,6,59,6,46,23,6,44,57,33,115,59,106,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]);

G<x,y>:=MatrixGroup<21,F|x,y>;
print "Group G is 3.M22 < GL(21,GF(121))";