SmallGroup(64,113)

Definition
This group of order 64 is defined by the following presentation:

$$G := \langle a_1,a_2,a_3,a_4 \mid a_1^2 = a_2^8 = a_3^4 = e, [a_1,a_2] = a_3^2, [a_1,a_3] = e, [a_2,a_3] = a_2^4 \rangle$$

Description by presentation
gap> F := FreeGroup(3);  gap> G := F/[F.1^2,F.2^8,F.3^4,Comm(F.1,F.2)*F.3^(-2),Comm(F.1,F.3),Comm(F.2,F.3)*F.2^(-4)];  gap> IdGroup(G); [ 64, 113 ]