Semidirect product of Z16 and Z4 of M-type

Definition
This group is defined as the external semidirect product of cyclic group:Z16 by cyclic group:Z4 acting by the $$9^{th}$$ power map. Explicitly, it is given by the presentation:

$$G := \langle a,b \mid a^{16} = b^4 = e, bab^{-1} = a^9 \rangle$$

Description by presentation
The group can be defined using a presentation as follows:

gap> F := FreeGroup(2);  gap> G := F/[F.1^(16),F.2^4,F.2*F.1*F.2^(-1)*F.1^(-9)]; 