(C2 x C2 x ((C2 x C2 x C2) : (C2 x C2))) : C2
r0 := (1,2)(3,5)(4,7)(6,10)(8,13)(9,12)(11,17)(14,18)(15,19)(16,22)(20,26)(21,27)(23,29)(24,28)(25,30)(31,32);
r1 := (1,3)(2,4)(5,9)(6,11)(7,12)(8,14)(10,16)(13,20)(15,21)(17,23)(18,24)(19,25)(22,29)(26,28)(27,31)(30,32);
r2 := (3,4)(5,7)(6,8)(10,13)(21,25)(23,24)(27,30)(28,29);
r3 := (3,6)(4,8)(5,10)(7,13)(9,15)(11,18)(12,19)(14,17)(21,28)(23,30)(24,27)(25,29);
F := FreeGroup(4);
r0 := F.1;; r1 := F.2;; r2 := F.3;; r3 := F.4;;
G := F/[ r2^2, r3^2, r0^2, r1^2, (r2*r3)^2, (r0*r3)^2, (r2*r0)^2, (r3*r1*r2*r1)^2, (r2*r1)^4, (r0*r1)^4, (r1*r2*r1*r0)^2, ((r1*r3)^2*r0)^2 ];;
type 0: 4 elements
type 1: 32 elements
type 2: 4 elements
type 3: 8 elements