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