C2 x (((C2 x C2 x C2 x C2) : C3) : C2)
r0 := (2,3)(4,6)(5,7)(8,11)(10,12);
r1 := (1,2)(4,8)(5,9)(6,10)(11,12);
r2 := (2,4)(3,6)(5,8)(7,11)(10,12);
r3 := (2,5)(3,7)(4,8)(6,11);
F := FreeGroup(4);
r0 := F.1;; r1 := F.2;; r2 := F.3;; r3 := F.4;;
G := F/[ r0^2, r2^2, r3^2, r1^2, (r3*r2)^2, (r0*r3)^2, (r0*r2)^2, (r1*r0)^3, r3*r1*r2*(r1*r3)^2*r2*r1, (r1*r2*r3*r1*r2*r1*r0)^2, ((r1*r2)^3*r3)^2 ];;
type 0: 4 elements
type 1: 24 elements
type 2: 8 elements
type 3: 4 elements