/*
2"J2 presented on its standard generators.
*/

G<x,y>:=Group<x,y|
x^4,
(x^2,y),
y^3,
(x*y)^7,
(x,y)^12,
// (x*y*x*y*x*y^-1*x*y*x*y^-1)^6, // Is redundant.
x^-2*(x*y*x*y*x*y^-1*x*y*x*y^-1*x*y^-1*x*y*x*y*x*y^-1*x*y^-1*x*y*x*y^-1)^3
>;

A:=x;B:=y;

M1:=sub<G|y,x^-1*y*x*y*x*y^-1*x*y*x>;
// U3(3), of index 200.

MM1:=sub<G|y,x*y*x*y*x*y^-1*x*y*x>;
// U3(3) x 2, of index 100.