/*
www-ATLAS of Group Representations.
M12:2 represented as 16 x 16 matrices over GF(11).
*/

F:=GF(11);

x:=CambridgeMatrix(3,F,16,\[
0,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,10,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,10,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,10,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,10,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,10,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,10,0,0,0,0,0,0,
0,0,0,0,0,0,10,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,10,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,10,0,0,
4,4,8,8,2,2,0,2,0,2,1,1,0,1,0,0,
8,8,7,7,8,8,5,9,5,9,5,0,1,5,0,0,
0,0,0,0,0,0,0,0,0,0,10,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,10,0]);

y:=CambridgeMatrix(3,F,16,\[
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,
5,10,10,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
6,0,0,3,3,10,3,10,10,0,10,10,0,0,0,0,
1,0,0,7,7,6,7,6,0,10,6,0,10,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
2,5,8,2,3,4,4,4,0,8,8,1,2,5,0,10,
6,3,8,10,8,8,9,4,10,9,4,10,6,10,5,0]);

G<x,y>:=MatrixGroup<16,F|x,y>;
print "Group G is M12:2 < GL(16,GF(11))";