S5
r0 := (1,2);
r1 := (2,3);
r2 := (3,4);
r3 := (3,5);
F := FreeGroup(4);
r0 := F.1;; r1 := F.2;; r2 := F.3;; r3 := F.4;;
G := F/[ r1^2, r0^2, r2^2, r3^2, (r3*r0)^2, (r2*r0)^2, (r3*r1)^3, (r2*r1)^3, (r0*r1)^3, (r3*r2*r1*r2)^2 ];;
type 0: 5 elements
type 1: 10 elements
type 2: 5 elements
type 3: 5 elements
Leaf [ 0, 1 ]