/*
A presentation for M12:2 in terms of standard generators.
SGens are (2C,3A,12A)-generators.
Equivalently, they are (2C,3A,12;11)-generators.
*/

G<x,y>:=Group<x,y|
x^2,
y^3,
(x*y)^12,
// (x,y*x*y)^5,
// (x*y*x*y*(x*y*x*y^-1)^4)^2,
// (x*y*x*y*x*y*x*y*x*y^-1)^4,
(x*y)^5*x*y^-1*x*y*(x*y^-1)^3*(x*y)^2*x*y^-1*x*y*x*y^-1*(x*y)^2*(x*y^-1)^3*x*y*x*y^-1
>;

M0:=sub<G|y,y^x>;
// M0 = M12.
M1:=sub<G|x,y^(x*y)>;
// M1 = PGL2(11), the novelty version.

H1:=sub<G|y,x*y*x*y*x*y*x*y*x*y^-1*x>;
// H1 = M11.