/*
A 2-generator presentation for L2(17) x 3.
Generators map on to standard (ie (2,3,17)-) generators for L2(17).
*/

G<x,y>:=Group<x,y|
x^2,
y^3,
(x*y)^4*(x*y^-1)^2*x*y*(x*y*x*y^-1)^2*(x*y)^2*(x*y^-1)^2
>;

H:=sub<G|x,(y*x)^6*y^-1*x*y>;
H2:=sub<G|x,y*x*y*x*y^-1*x*y^-1*x*y*(x*y)^17>;