/*
www-ATLAS of Group Representations.
L2(23) represented as 13 x 13 matrices over GF(23).
*/

F:=GF(23);

x:=CambridgeMatrix(3,F,13,\[
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,
0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,
16,15,20,12,22,20,0,11,8,12,18,17,12,
5,1,5,19,4,16,10,14,19,9,7,8,9,
6,15,6,9,21,3,12,1,9,22,13,13,21]);

y:=CambridgeMatrix(3,F,13,\[
19,22,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,
4,7,4,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,
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,
17,19,12,1,8,14,14,5,0,13,4,1,10,
21,19,22,10,6,12,7,5,7,1,6,16,0]);

G<x,y>:=MatrixGroup<13,F|x,y>;
print "Group G is L2(23) < GL(13,GF(23))";