/*
www-ATLAS of Group Representations.
L2(23) represented as 19 x 19 matrices over GF(23).
*/

F:=GF(23);

x:=CambridgeMatrix(3,F,19,\[
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,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
16,16,10,21,10,3,8,14,9,3,13,18,12,0,8,12,2,20,13,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
20,20,10,20,19,21,5,2,8,15,16,19,18,0,12,16,11,13,16,
1,1,18,11,2,19,9,5,0,12,20,19,0,22,17,21,21,4,20]);

y:=CambridgeMatrix(3,F,19,\[
22,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
2,22,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
4,9,16,16,5,13,15,11,3,16,14,22,2,5,16,10,16,19,2,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
8,0,9,0,6,11,19,12,22,17,20,4,7,21,20,13,7,10,19,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
9,20,11,9,0,4,0,16,12,17,1,16,5,19,21,21,4,16,1]);

G<x,y>:=MatrixGroup<19,F|x,y>;
print "Group G is L2(23) < GL(19,GF(23))";