/*
L2(32) presented on its (2,3,31K/L/M/N/O;31)-generators.
So xyxyxy^-1 has order 11.
*/

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

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