/*
2"J2"2 (the ATLAS 2.J2.2) presented on its standard generators.
*/

G<x,y>:=Group<x,y|
x^4,
(x^2,y),
y^5,
x^-2*(x*y)^14,
(x,y)^7,
// (y,x*y*x*y^2*x*y^-1*x*y^2*x*y*x), // redundant but useful.
x^-2*(x*y*x*y*x*y^-2*x*y^-2)^3,
// x^-2*(x*y*x*y*x*y^-2)^4, // redundant.
x^-2*(x,y*x*y)^3, // also redundant, but too good to lose.
x^-2*(x*y*x*y*x*y^2)^3*x*y^-1*x*y*x*y*x*y^-1*x*y^2
// x^-2*(x,y*x*y^2)^3 // redundant.
>;

c:=x;d:=y;

M1:=sub<G|(x,y^-1),x*x^(y*x*y)>;
// U3(3), of index 400.