SmallGroup(64,114)

Definition
This group is defined by the following presentation:

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

The square braces denote the commutator of two elements. It does not matter if we use the left or right action conventions -- though the specific presentations are different, they define isomorphic groups.

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