Semidirect product of Z16 and Z4 via fifth power map

Definition
This group is defined as the external semidirect product with base normal subgroup cyclic group:Z16 and acting quotient group cyclic group:Z4, where the generator of the latter acts as the fifth power map.

Equivalently, it is given by the following presentation:

$$G := \langle a,b \mid a^{16} = b^4 = e, bab^{-1} = a^5 \rangle$$

Here, $$e$$ denotes the identity element.

Description by presentation
gap> F := FreeGroup(2);  gap> G := F/[F.1^(16),F.2^4,F.2*F.1*F.2^(-1)*F.1^(-5)];  gap> IdGroup(G); [ 64, 28 ]