/*
L3(8) as 9 x 9 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<9,F|
[ 1, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 1, 0, 0, 0, 0, 0, z^3, 0, z^6, 1, 1, 0, 0, 0, 
z^2, z^3, z^3, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 
z^6, 1, 1, z^6, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 
0, 0, 0, 0, 0, z^6, 1, 1 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0 ]>;

a:=x;
b:=y;