(A4 x A4) : C2
r0 := (1,2)(3,5)(4,8)(6,11)(7,10)(9,12);
r1 := (2,4)(3,6)(5,7)(9,10)(11,12);
r2 := (1,3)(2,5)(4,9)(6,11)(8,12);
r3 := (3,7)(4,8)(5,10)(6,9)(11,12);
F := FreeGroup(4);
r0 := F.1;; r1 := F.2;; r2 := F.3;; r3 := F.4;;
G := F/[ r1^2, r3^2, r0^2, r2^2, (r0*r2)^2, (r0*r3)^2, (r1*r3)^3, (r3*r2)^3, r0*(r1*r0*r1*r2)^2, r0*r1*r3*r0*r1*r0*r3*r1*r3, (r2*r3*r1*r2*r1)^2, r2*r3*r1*r0*r2*r3*r0*r2*r1*r2*r3*r2*r1*r3 ];;
type 0: 4 elements
type 1: 24 elements
type 2: 12 elements
type 3: 6 elements