/*
www-ATLAS of Group Representations.
M23 represented as 45 x 45 matrices over GF(11).
*/

F:=GF(11);

x:=CambridgeMatrix(3,F,45,\[
0,0,0,0,0,0,0,0,0,6,6,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,6,6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,2,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,5,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,5,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,5,3,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,2,0,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,5,8,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
6,6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
6,6,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
9,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,5,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,3,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,8,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,8,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,0,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,8,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,3,5,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,8,5,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,2,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,5,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,6,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,6,3,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,5,3,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,9,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,5,5,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,5,5,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,6,8,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,5,8,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,3,6,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,3,5,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,0,9,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,9,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,5,6,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,6,5]);

y:=CambridgeMatrix(3,F,45,\[
4,8,8,5,0,6,5,6,0,8,0,0,0,8,0,0,0,3,8,0,0,0,6,5,5,0,6,0,0,0,0,0,0,5,6,0,0,5,5,6,0,6,5,6,0,
0,0,0,7,9,7,7,7,9,0,8,0,8,0,0,0,3,0,0,8,0,9,4,4,7,9,7,7,0,0,7,0,0,7,7,2,9,4,7,4,2,7,7,7,9,
0,0,0,7,2,7,7,7,2,0,0,8,0,0,3,8,0,0,0,0,3,9,7,7,4,9,4,7,0,0,4,0,0,7,7,9,2,4,7,7,2,4,4,4,9,
3,7,3,6,6,0,0,5,5,3,0,0,0,8,0,0,0,0,0,0,0,6,5,0,0,5,5,0,3,0,0,0,3,5,0,6,6,5,0,0,5,6,5,0,5,
0,0,0,7,4,9,9,7,4,0,0,3,0,0,8,7,0,0,0,0,4,7,7,9,2,7,4,8,0,0,3,0,0,7,9,7,4,4,9,9,4,4,4,2,7,
0,0,0,4,7,9,9,4,7,0,3,0,8,0,0,7,0,0,0,0,7,7,7,2,9,7,4,0,0,3,0,3,0,7,2,7,4,4,2,9,7,7,7,2,4,
3,3,7,0,6,5,6,0,5,0,0,0,0,0,0,0,0,8,8,0,0,5,0,5,5,6,0,0,8,0,0,0,3,0,6,6,6,0,5,5,6,0,0,5,6,
0,0,0,9,4,4,4,9,4,0,7,0,4,0,0,3,0,0,0,0,3,4,2,7,4,4,9,0,0,3,0,3,0,2,7,4,7,9,7,4,4,2,2,7,7,
0,0,0,2,4,4,4,2,4,0,4,0,4,0,0,0,3,0,0,8,0,4,9,7,4,4,2,3,0,0,3,0,0,2,4,7,4,9,4,7,7,2,2,4,4,
5,6,0,5,0,6,2,7,7,9,4,4,6,0,5,9,7,7,5,5,0,0,0,8,4,7,9,2,4,4,0,6,5,3,0,0,4,2,7,3,5,6,7,7,2,
4,4,9,4,9,4,3,5,5,0,5,6,7,2,7,9,4,4,6,6,0,0,3,0,4,7,2,0,5,6,9,4,4,0,8,0,4,9,7,2,7,4,6,5,0,
7,7,9,7,9,7,2,7,7,9,7,7,7,9,7,0,6,5,9,9,0,8,0,0,5,5,0,2,7,7,2,4,4,0,0,3,5,0,5,9,4,7,7,7,9,
7,7,9,0,3,0,6,0,6,2,4,7,4,2,7,0,9,9,5,6,0,2,7,7,9,4,4,9,7,7,9,4,4,4,4,9,4,7,9,5,5,0,0,0,3,
4,4,9,8,0,0,4,2,7,0,5,5,7,2,4,0,5,5,7,7,9,9,7,7,3,5,5,9,4,4,0,6,5,6,5,0,4,7,9,4,7,2,0,8,0,
6,5,0,0,0,8,7,2,4,2,7,4,5,0,5,0,5,5,7,7,2,0,5,6,9,4,4,0,6,5,9,7,7,4,4,2,5,6,3,7,4,2,8,0,0,
4,9,4,3,6,5,4,4,2,7,9,7,0,6,5,5,5,0,2,4,4,0,5,6,7,4,2,0,6,6,2,4,4,7,2,4,0,3,0,2,4,7,0,3,0,
4,2,4,9,7,4,4,4,9,5,0,6,0,2,9,4,7,9,2,7,7,2,4,4,7,4,2,9,7,4,2,7,7,6,0,6,8,0,0,0,5,5,0,0,3,
6,0,5,9,7,4,6,5,0,7,2,7,0,6,5,7,4,9,0,5,6,9,4,4,6,5,8,9,4,7,0,5,6,4,2,7,0,0,8,2,7,4,3,0,0,
4,9,4,4,4,2,8,0,0,6,0,6,2,7,4,5,6,0,2,7,4,0,8,0,9,4,4,9,7,4,0,6,5,9,4,4,0,6,6,5,6,8,7,7,9,
5,0,6,4,4,9,0,3,0,5,0,5,2,4,7,4,4,2,0,5,5,0,0,3,2,4,4,0,6,6,9,4,4,8,6,6,9,4,7,7,4,9,5,6,0,
4,2,4,5,6,0,0,0,3,9,0,9,0,6,6,7,7,2,9,7,4,8,0,0,0,5,6,2,7,4,9,7,7,2,7,7,2,4,7,7,4,9,4,4,9,
6,5,0,7,7,2,6,5,0,2,4,4,6,0,5,9,7,4,6,5,0,7,2,7,3,0,0,2,7,4,0,6,6,9,7,7,0,8,0,4,9,7,6,8,6,
7,7,9,4,4,9,4,4,2,9,4,4,4,9,4,0,5,5,9,2,0,6,0,5,0,3,0,9,7,4,9,7,4,0,6,5,3,0,0,7,9,4,4,9,4,
7,7,2,5,5,3,4,4,9,0,5,6,7,9,7,9,4,7,5,6,0,7,9,7,0,0,8,0,6,6,9,4,7,2,7,7,0,0,8,6,0,6,4,9,4,
5,6,0,2,4,7,8,0,0,9,7,4,5,0,5,0,5,6,4,7,2,4,7,2,5,0,6,0,5,5,9,7,4,5,3,6,9,7,4,0,0,8,2,4,7,
4,4,9,9,4,7,0,3,0,0,6,6,4,2,7,0,6,5,7,4,2,6,5,3,7,2,7,2,4,7,0,5,5,7,2,4,0,6,6,8,0,0,9,4,7,
4,4,2,0,6,6,0,0,3,9,4,7,4,9,7,0,9,2,6,6,0,4,7,2,4,2,4,9,4,7,9,4,7,4,9,7,2,7,4,0,8,0,0,6,6,
9,7,7,0,5,6,0,6,6,7,4,2,4,7,9,4,9,4,7,2,7,10,2,9,7,9,4,3,0,0,0,0,0,0,6,6,6,5,0,4,2,4,9,2,10,
0,6,5,9,4,4,2,7,4,6,6,0,5,5,0,5,0,6,6,0,5,1,9,2,4,9,7,0,3,0,0,0,0,2,7,4,7,7,9,4,9,4,9,2,10,
9,4,4,9,7,7,9,7,4,7,4,9,7,4,9,4,2,4,4,2,4,0,0,0,5,0,5,0,0,8,0,10,1,2,4,7,7,7,2,5,0,6,0,0,0,
0,5,6,7,4,2,4,9,4,5,6,0,5,6,0,5,0,5,5,0,5,9,4,7,9,1,2,0,8,0,0,0,0,4,9,4,7,9,7,9,1,9,4,7,2,
2,4,4,6,6,0,6,0,5,4,4,2,4,4,9,4,9,7,4,2,7,9,7,4,2,10,9,3,0,0,0,0,0,6,0,5,5,0,6,9,1,9,4,7,9,
9,4,4,4,7,2,4,2,4,7,7,2,4,4,2,7,9,4,4,9,7,0,5,5,0,0,0,0,0,3,0,1,1,7,9,7,7,2,7,0,0,0,5,5,0,
2,7,7,9,10,2,7,4,2,5,5,0,6,6,0,6,0,6,6,0,6,7,9,4,9,7,4,0,0,0,0,0,8,2,9,10,9,4,4,9,7,7,9,4,4,
0,6,5,0,0,0,5,5,0,7,4,2,7,4,2,4,9,7,7,9,4,7,2,4,9,4,7,0,1,10,0,8,0,0,0,0,0,5,6,9,4,4,2,4,4,
9,7,7,9,10,2,7,4,9,7,4,9,4,7,2,7,9,4,7,2,4,5,0,5,0,6,6,0,0,0,3,0,0,9,2,1,9,7,7,0,5,6,0,6,5,
9,7,7,7,2,4,9,2,1,7,7,2,7,7,9,4,2,4,7,9,7,5,6,0,5,6,0,0,0,0,8,0,0,7,4,9,1,9,9,6,5,0,5,0,5,
0,6,5,6,0,6,0,0,0,7,7,9,4,4,9,7,2,7,7,2,7,7,7,9,4,4,2,0,1,1,0,3,0,5,5,0,0,0,0,4,4,9,7,9,4,
2,7,7,7,9,4,9,2,1,5,6,0,5,6,0,5,0,6,6,0,5,4,4,9,4,4,9,0,0,0,0,0,8,4,7,9,10,2,2,4,4,2,4,9,7,
4,2,4,0,8,0,0,6,5,9,0,2,0,6,5,4,4,2,9,4,7,6,6,0,0,3,0,9,7,7,2,4,7,4,4,2,7,2,4,4,9,7,2,7,4,
7,2,7,0,0,8,2,4,4,5,0,6,2,4,4,5,6,0,9,7,4,4,7,2,0,0,3,9,4,4,0,6,6,5,6,0,7,2,4,4,2,7,8,6,5,
6,0,5,3,0,0,9,4,4,6,0,5,2,7,7,4,4,9,0,5,5,4,7,9,8,0,0,0,5,6,9,4,7,7,7,2,5,3,6,5,0,5,9,4,7,
7,2,7,4,2,4,5,3,6,4,9,7,0,5,5,5,5,0,9,4,4,4,9,4,5,0,6,0,5,6,2,4,7,8,0,0,7,4,2,8,0,0,7,9,7,
7,9,7,4,9,4,4,9,7,6,0,6,0,9,9,4,7,2,9,7,7,4,9,4,7,2,7,9,4,4,2,7,4,0,0,3,5,5,0,0,8,0,5,0,6,
6,0,5,6,0,5,7,2,4,7,9,4,0,6,6,4,7,9,0,6,5,6,8,6,4,2,4,2,4,4,0,6,6,0,3,0,7,4,9,0,0,8,7,2,7]);

G<x,y>:=MatrixGroup<45,F|x,y>;
print "Group G is M23 < GL(45,GF(11))";