G.<x,y> = FreeGroup();G
G.rank()
R = [x^2, y^3, x*y*x*y^(-1)];R
K = G/R; K
A = matrix([[1,2],[0,1]]); B = matrix([[1,0],[2,1]])
#Gamma_2.<A,B> = FreeGroup();Gamma_2
Gamma(2)
Gamma(2).generators(algorithm = "farey")
Gamma(2).as_permutation_group()
Gamma(2).ngens()
Gamma(2).index()





%gap G := FreeGroup( "x", "y" );
%gap x := G.1;; y:= G.2;
%gap H := G / [ x^2, y^3 ]
%gap K := G / [ x^2, y^3, x*y*x*y^(-1)];
#%gap tab := CosetTable(H, K);
#%gap Display(tab);