/*
www-ATLAS of Group Representations.
L2(19) represented as 7 x 7 matrices over GF(19).
*/

F:=GF(19);

x:=CambridgeMatrix(3,F,7,\[
0,1,0,0,0,0,0,
1,0,0,0,0,0,0,
0,0,0,1,0,0,0,
0,0,1,0,0,0,0,
0,0,0,0,0,1,0,
0,0,0,0,1,0,0,
7,7,17,17,7,7,18]);

y:=CambridgeMatrix(3,F,7,\[
10,17,0,0,0,0,0,
0,0,1,0,0,0,0,
15,14,9,0,0,0,0,
0,0,0,0,1,0,0,
0,0,0,0,0,0,1,
4,10,6,17,2,1,0,
0,0,0,1,0,0,0]);

G<x,y>:=MatrixGroup<7,F|x,y>;
print "Group G is L2(19) < GL(7,GF(19))";