SmallGroup(64,17)

Definition
This group can be defined by the following presentation:

$$G := \langle a_1,a_2,a_3 \mid a_1^8 = a_2^4 = a_3^2 = e, [a_1,a_2] = a_3, [a_1,a_3] = [a_2,a_3] = e \rangle$$

where $$e$$ denotes the identity element and $$[, ]$$ stands for the commutator of two elements (the isomorphism type of the group is independent of the choice of convention -- left versus right-- for the commutator map, though the specific presentations differ).

Description by presentation
gap> F := FreeGroup(3);  gap> G := F/[F.1^8,F.2^4,F.3^2,Comm(F.1,F.2)*F.3^(-1),Comm(F.1,F.3),Comm(F.2,F.3)];  gap> IdGroup(G); [ 64, 17 ]