((C2 x C2) : ((C3 x C3 x C3) : C3)) : C2
r0 := (1,2)(3,6)(4,7)(5,12)(8,19)(9,16)(10,22)(11,18)(13,23)(14,24)(15,25)(17,27)(20,34)(21,35)(26,31)(28,32)(29,33)(30,36);
r1 := (2,5)(3,8)(4,10)(6,15)(7,17)(9,21)(11,20)(13,25)(14,27)(16,30)(18,33)(19,23)(22,24)(26,35)(28,34)(29,32)(31,36);
r2 := (1,3)(2,6)(4,11)(5,13)(7,18)(9,10)(12,23)(14,28)(15,25)(16,22)(17,31)(20,21)(24,32)(26,27)(29,30)(33,36)(34,35);
r3 := (1,4)(2,7)(3,9)(5,14)(6,16)(8,20)(10,11)(12,24)(13,26)(15,29)(17,32)(18,22)(19,34)(23,31)(25,33)(27,28)(30,36);
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, (r0*r2)^2, (r2*r3)^3, (r1*r2)^3, (r0*r2*r1)^3, r0*r1*r3*(r1*r0)^2*r3*r1, (r3*r1*r3*r2)^2*r1*r3*r1*r2 ];;
type 0: 4 elements
type 1: 54 elements
type 2: 9 elements
type 3: 27 elements