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

y:=CambridgeMatrix(3,F,21,\[
85,39,0,0,0,0,0,63,0,0,0,114,0,117,0,19,0,0,31,0,0,
83,47,1,0,0,0,0,84,0,0,0,87,0,23,0,53,0,0,73,0,0,
95,117,0,0,1,0,0,77,0,0,0,72,0,94,0,80,0,0,113,0,0,
0,0,0,0,0,1,0,41,0,0,0,0,0,119,0,62,0,0,99,0,0,
7,32,0,0,0,0,0,35,0,0,0,64,0,13,0,13,0,0,6,0,0,
0,0,0,0,0,0,0,54,1,0,0,96,0,50,0,75,0,0,51,0,0,
0,0,0,0,0,0,0,119,0,1,0,0,0,61,0,75,0,0,34,0,0,
0,0,0,0,0,0,0,60,0,0,1,0,0,117,0,21,0,0,65,0,0,
0,0,0,0,0,0,0,49,0,0,0,0,1,14,0,113,0,0,108,0,0,
0,0,0,0,0,0,0,109,0,0,0,90,0,29,1,34,0,0,73,0,0,
0,0,0,0,0,0,0,57,0,0,0,0,0,102,0,88,1,0,104,0,0,
0,0,0,0,0,0,0,93,0,0,0,0,0,104,0,3,0,1,67,0,0,
0,0,0,1,0,0,0,116,0,0,0,36,0,97,0,40,0,0,63,0,0,
0,0,0,0,0,0,0,57,0,0,0,0,0,115,0,105,0,0,114,1,0,
0,0,0,0,0,0,0,114,0,0,0,0,0,79,0,42,0,0,118,0,1,
0,0,0,0,0,0,0,114,0,0,0,0,0,109,0,36,0,0,47,0,0,
0,0,0,0,0,0,0,114,0,0,0,0,0,14,0,10,0,0,27,0,0,
0,0,0,0,0,0,0,25,0,0,0,1,0,46,0,108,0,0,41,0,0,
0,0,0,0,0,0,0,71,0,0,0,0,0,97,0,99,0,0,54,0,0,
0,0,0,0,0,0,0,56,0,0,0,0,0,103,0,109,0,0,14,0,0,
0,0,0,0,0,0,1,85,0,0,0,42,0,30,0,55,0,0,100,0,0]);

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