/*
www-ATLAS of Group Representations.
U6(2):S3 represented as 22 x 22 matrices over GF(11).
*/

F:=GF(11);

x:=CambridgeMatrix(3,F,22,\[
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,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
10,1,0,0,1,1,10,0,10,10,1,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,10,0,0,1,10,0,0,0,1,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,10,0,1,10,0,1,0,1,0,0,10,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,10,0,0,10,0,0,0,0,1,0,0,1,0,0,0,0,
10,1,0,0,2,1,9,0,10,10,0,0,1,0,1,0,10,0,1,0,0,0,
1,10,0,0,10,10,1,0,1,1,0,0,10,0,10,0,1,0,0,1,0,0,
0,0,0,0,0,10,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,
10,1,0,0,0,1,0,0,10,0,0,0,0,0,0,0,0,0,0,0,0,1]);

y:=CambridgeMatrix(3,F,22,\[
10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
1,1,10,0,1,0,0,10,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,1,0,0,1,1,0,0,10,1,0,0,1,10,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
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,
0,10,0,0,9,0,1,10,0,1,1,0,9,0,10,1,1,0,10,1,0,0,
1,0,0,1,0,10,0,0,0,1,0,0,0,0,0,10,0,0,0,1,0,0,
10,0,0,0,0,0,10,0,0,0,0,0,0,0,0,0,10,0,0,0,0,0,
10,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0]);

G<x,y>:=MatrixGroup<22,F|x,y>;
print "Group G is U6(2):S3 < GL(22,GF(11))";