Semidirect product of Z5 and Z8 via square map

Definition
This group of order 40 is defined by means of the following presentation (here, $$e$$ is used to denote the identity element):

$$G := \langle a,b \mid a^5 = b^8 = e, bab^{-1} = a^2 \rangle$$

Description by presentation
We can use the presentation to define the group in GAP:

gap> F := FreeGroup(2);  gap> G := F/[F.1^5,F.2^8,F.2*F.1*F.2^(-1)*F.1^(-2)]; 

To verify that this is the correct group:

gap> IdGroup(G); [ 40, 3 ]