Semidirect product of Z8 and Z8 of M-type

Definition
The group is defined by means of the presentation:

$$\! G := \langle a,b \mid a^8 = b^8 = e, bab^{-1} = a^5 \rangle$$

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