/*
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
// 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
>;
// Rel x^-2*(x*y*...*x*y^-1)^3 is redundant.

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.

/*
NB: x^2 is obviously a central involution, and G/<x^2> has presentation
given in http://www.mat.bham.ac.uk/atlas/v2.0/spor/J2/J2G1-P2.M
*/