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

G<x,y>:=Group<x,y|
x^2,
y^3,
// (x*y)^31,
((x*y)^4*x*y^-1*(x*y)^3*x*y^-1*x*y^-1)^2,
// ((x*y*x*y*x*y^-1)^2*(x*y*x*y^-1)^2)^2,
// (x*y*x*y*(x*y*x*y*x*y^-1)^3)^2,
// (x*y)^4*(x*y^-1)^3*x*y*x*y^-1*(x*y)^2*(x*y^-1)^3*(x*y)^2*x*y^-1*x*y*(x*y^-1)^3,
(x*y)^7*x*y^-1*(x^-1*y)^7*(x*y^-1)^2*(x*y)^2*(x*y^-1)^2
>;

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

H1:=sub<G|x,x^(y*x*y*x*y)>;