(((C3 x C3) : C3) : (C2 x C2)) x S3
r0 := (1,2)(3,5)(4,6)(7,10)(8,11)(9,13)(12,17)(14,16)(15,18);
r1 := (1,3)(2,5)(4,9)(6,12)(7,13)(8,11)(10,15)(14,17)(16,18);
r2 := (1,4)(2,6)(3,7)(5,10)(8,14)(9,13)(11,16)(12,15)(17,18);
r3 := (1,2)(3,8)(4,6)(5,11)(7,14)(9,13)(10,16)(12,15)(17,18);
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, (r2*r3)^2, (r3*r0)^2, (r2*r0)^2, (r1*r2)^3, (r0*r1*r3*r1)^2, (r2*(r1*r3)^2)^2, (r1*r3*r0)^6, ((r0*r2*r1)^3*r3)^2 ];;
type 0: 18 elements
type 1: 81 elements
type 2: 9 elements
type 3: 6 elements