/*
L5(2):2 as 30 x 30 matrices over Z[r2].
*/

F<r2>:=QuadraticField(2);

G<x,y>:=MatrixGroup<30,F|[
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,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,-1,-1,0,0,0,-1,0,0,0,0,-1,r2,0,0,0,0,0,0,0,-1,0,0,0,0,-1,0,0,r2,r2,
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,r2,0,0,0,r2,0,0,-1,-1,0,0,-1,0,0,0,0,0,r2,0,0,0,-1,0,-1,
1,r2,0,0,-1,0,0,0,0,0,0,r2,0,1,0,0,0,1,1,0,0,0,0,0,r2,0,r2,0,-1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
-r2,-1,0,0,0,0,0,0,1,1,-1,0,0,0,0,0,-r2,0,-r2,-r2,0,1,0,0,0,0,-1,0,0,0,
0,-1,-1,r2,0,0,0,0,0,0,0,0,0,0,0,r2,0,0,0,0,-1,-1,-1,0,0,0,-1,0,r2,0,
0,0,0,0,r2,0,-1,0,0,-1,-1,0,0,0,r2,0,0,0,0,0,0,0,0,-1,-1,0,-1,r2,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-1,0,0,0,1,0,0,0,0,0,-r2,0,-1,0,1,0,0,0,-1,0,0,0,0,-r2,-r2,0,-r2,1,0,0,
0,-r2,0,1,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,-1,0,-r2,0,-r2,0,0,0,-r2,0,1,0,
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,
1,0,0,1,0,-1,0,-r2,-r2,0,0,0,-1,0,0,0,0,0,0,1,0,-r2,-r2,0,0,0,0,-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,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
r2,0,0,r2,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,r2,-1,-1,-1,0,0,0,0,0,0,0]
,[
0,-1,-1,0,0,0,-1,0,0,0,0,-1,r2,0,0,0,0,0,0,0,-1,0,0,0,0,-1,0,0,r2,r2,
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,
1,0,0,1,0,-1,0,-r2,-r2,0,0,0,-1,0,0,0,0,0,0,1,0,-r2,-r2,0,0,0,0,-1,0,0,
0,-1,-1,r2,0,0,0,0,0,0,0,0,0,0,0,r2,0,0,0,0,-1,-1,-1,0,0,0,-1,0,r2,0,
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,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-1,-1,0,0,0,r2,0,0,0,0,-1,0,-1,0,0,-1,0,0,0,r2,r2,0,0,-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,
0,-r2,0,1,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,-1,0,-r2,0,-r2,0,0,0,-r2,0,1,0,
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,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
r2,0,0,r2,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,r2,-1,-1,-1,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-r2,-r2,0,-1,0,1,0,0,0,0,0,0,-r2,0,0,0,0,0,-1,1,1,-1,0,-r2,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,1,0,0,0,1,0,0,0,0,0,-r2,0,0,0,0,-r2,-r2,0,0,0,-1,0,-1,1,-1,0,0,-r2,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
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,
-1,-r2,-r2,0,0,0,0,0,0,0,0,-r2,1,-1,0,0,0,0,0,0,0,0,0,0,0,-r2,0,-1,1,1,
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,r2,r2,-1,0,-1,0,0,0,0,0,0,-1,0,0,-1,0,0,0,0,r2,0,0,0,0,0,0,0,-1,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,r2,0,-1,0,0,-1,-1,0,0,0,r2,0,0,0,0,0,0,0,0,-1,-1,0,-1,r2,0,0,
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,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
>;

c:=x;d:=y;