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