/*
2^4"A8 presented on its standard generators.
*/

G<x,y>:=Group<x,y|
x^3,
y^7,
(x*y)^6,
(x,y)^2,
(x*y^-3*x*y^-3*x*y^-2)^2, // Redundant but useful.
x*y*x*y^2*x^-1*y*x*y^-2*x*y^3*x*y^-3*x*y^-3
>;

a:=x;b:=y;

/*
Normal 2^4 generated (under normal closure) by (x*x^(y*x*y))^2.
*/