/*
www-ATLAS of Group Representations.
M22:2 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,
0,0,10,1,0,3,0,8,4,6,1,7,0,5,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
8,3,1,10,9,7,2,4,0,6,0,0,0,5,1,0,0,0,0,0,
5,6,0,0,10,10,1,1,6,3,0,5,10,8,0,1,0,1,0,0,
2,9,8,3,1,4,10,7,2,3,0,9,10,8,0,0,1,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
1,10,3,8,10,3,1,8,4,3,0,7,0,8,0,0,0,0,1,0,
4,7,2,9,5,1,6,10,8,8,0,3,5,3,0,0,0,6,0,1]);

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

G<x,y>:=MatrixGroup<20,F|x,y>;
print "Group G is M22:2 < GL(20,GF(11))";