((C2 x C2 x C2 x C2) : C3) : C2
r0 := (1,2)(3,5)(4,6)(7,8);
r1 := (1,2)(3,7)(4,5)(6,8);
r2 := (1,3)(2,5)(4,8)(6,7);
r3 := (1,4)(2,6)(3,8)(5,7);
F := FreeGroup(4);
r0 := F.1;; r1 := F.2;; r2 := F.3;; r3 := F.4;;
G := F/[ r0^2, r1^2, r2^2, r3^2, (r0*r3)^2, (r2*r0)^2, (r0*r1)^3, (r1*r0*r3)^3, (r1*r2*r1*r3*r2)^2, r3*r0*r1*r2*r1*r0*r2*r3*r1*r2*r1 ];;
type 0: 3 elements
type 1: 12 elements
type 2: 4 elements
type 3: 4 elements