/* 
L3(8).2 as 18 x 18 matrices over the field of order 8.
*/
F2:=GF(2);
P<x>:=PolynomialRing(F2);
p:=x^3+x+1;
//Conway Polynomial
F<z>:=ext<F2|p>;

G<x,y>:=MatrixGroup<18,F|
[ 0, 0, 0, 0, 0, 0, 0, 0, z^4, 0, z^2, z^3, z^5, z^3, z^3, z^4, z, z^2, 0, 0, 0,
0, 0, 0, 0, 0, z^2, 0, z, 1, z^3, z^2, z, z, 1, z^6, 0, 0, 0, 0, 0, 0, 0, 0, 
z^3, 0, 1, 1, z^4, z, z^2, z, z^6, z^6, 0, 0, 0, 0, 0, 0, 0, 0, z^5, 0, z^3, 
z^4, z^4, z^2, z^6, z^3, z^4, z^5, 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0, z^2, z, z^2, 
z, z^4, 1, z^3, z^2, 0, 0, 0, 0, 0, 0, 0, 0, z^4, 0, z, z, z^3, 1, z^5, 1, z^2, 
z^2, 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0, z, z^2, z^6, z^4, z^6, z^5, z^4, z^5, 0, 0,
0, 0, 0, 0, 0, 0, z, 0, 1, z^6, z^4, z^3, z^4, z^2, z^3, z^2, z^4, z^6, z^2, 
z^3, z^5, z, 1, z^2, 0, z^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
z^2, 0, z^6, z^6, z^5, z^2, z^5, z^2, z^2, z^2, z^6, z^4, z, z^5, z^3, 1, z^2, 
1, 0, z^4, 0, 0, 0, 0, 0, 0, 0, 0, z^2, z, z, z, 1, 1, z^5, z^4, 0, z^4, 0, 0, 
0, 0, 0, 0, 0, 0, z^3, z^5, z, z^6, z, z^4, z^2, z^4, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, z^5, z^3, 1, z, z^6, z^3, z^4, z^2, 0, z^6, 0, 0, 0, 0, 0, 0, 0, 0, 1, z^2, 
z^5, z^2, z^4, 1, z^2, z^4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, z, 1, 1, z^4, z^3, 
z^3, 1, z^6, 0, z^6, 0, 0, 0, 0, 0, 0, 0, 0, z^2, 1, z^4, z^4, z^2, z^6, z^4, 
z^2, 0, z^6, 0, 0, 0, 0, 0, 0, 0, 0, z^5, z^4, z^4, 1, z^6, z^6, 1, z^6, 0, z^6,
0, 0, 0, 0, 0, 0, 0, 0 ],

[ 1, z, z^5, z^4, z^5, z^2, z, z^2, 0, z^6, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, z, 
z^4, z^4, z^5, z, z, 0, z^2, 0, 0, 0, 0, 0, 0, 0, 0, z^6, z^5, 0, z^3, z^2, 0, 
1, z^6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^2, z^3, 1, z^6, 1, z^4, z^6, 1, 0, z^4, 
0, 0, 0, 0, 0, 0, 0, 0, z^2, z^2, z^3, z^6, z^6, 1, z^6, z^6, 0, 1, 0, 0, 0, 0, 
0, 0, 0, 0, z, 1, 0, z^5, z^4, 0, z^5, z^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^2, 
z^3, 1, 1, z, z^5, z^2, z^3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, z^2, z^2, z^3, 1, 1, 
z, z^2, z^2, 0, z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^4, 0, 
z^5, z^6, z, z^2, z^3, z^3, z^4, z^5, z, 1, 0, z^6, z^5, 0, z, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z, 0, z^2, z^2, z^5, z^6, 1, z^6, z, z, 
0, 0, 0, 0, 0, 0, 0, 0, z, 0, z^4, z, z^5, z, 1, z^5, z^3, 1, 0, 0, 0, 0, 0, 0, 
0, 0, z^4, 0, z^5, z^6, z^4, z^5, z, z^6, z^2, z^3, 0, 0, 0, 0, 0, 0, 0, 0, z, 
0, z^2, z^2, z, z^2, z^5, z^2, z^6, z^6, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, z, z^2, 
z^3, z^4, 0, z^5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z, 0, z^4, z, z, z^4, z^5, z, z,
z^5, 0, 0, 0, 0, 0, 0, 0, 0, z^4, 0, z^5, z^5, 1, z, 0, z, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, z^4, 0, 1, z^4, 1, z^3, 0, 1, 0, 0 ]>;

c:=x;
d:=y;