/*
www-ATLAS of Group Representations.
M22 represented as 20 x 20 matrices over GF(11).
*/

F:=GF(11);

x:=CambridgeMatrix(3,F,20,\[
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
8,3,6,5,8,0,3,0,7,0,0,4,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
8,3,6,5,0,8,0,3,4,2,7,7,0,9,0,4,1,0,0,0,
2,9,6,5,9,2,2,9,8,7,7,3,6,4,0,4,0,1,5,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
1,10,3,8,7,4,4,7,6,7,8,5,9,4,0,3,0,0,2,1]);

y:=CambridgeMatrix(3,F,20,\[
9,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
10,8,7,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
3,10,1,10,10,5,8,1,8,1,1,7,5,0,10,1,3,6,5,7,
9,3,8,0,10,6,9,10,8,8,8,9,8,4,5,1,4,2,0,7,
7,0,6,7,9,6,6,2,3,8,0,7,8,1,6,5,1,6,0,3,
4,5,9,4,10,0,9,0,7,0,0,1,0,0,2,0,0,0,0,0,
10,3,6,3,2,7,2,6,6,7,1,2,0,4,7,3,4,5,4,3,
2,5,6,0,2,5,4,3,5,2,6,7,6,4,7,2,9,6,1,6]);

G<x,y>:=MatrixGroup<20,F|x,y>;
print "Group G is M22 < GL(20,GF(11))";