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