/*
L2(32) presented on its (2,3,33F/G/H/I/J;33)-generators.
So xyxyxy^-1 has order 31.
*/

G<x,y>:=Group<x,y|
x^2,
y^3,
// (x*y)^5*x*y^-1*(x*y)^5*(x*y^-1)^3*(x*y)^2*(x*y^-1)^3, // Is redundant.
(x*y*x*y*x*y^-1)^3*(x*y^-1*x*y)^4*(x*y^-1)^2
>;

M1:=sub<G|x,y*x*y*x*y*x*y^-1*x*y*x*y^-1>;
M2:=sub<G|x,x^y>;
M3:=sub<G|x,x^(y*x*y)>;