Nontrivial semidirect product of Z4 and Z4

A presentation as a metacyclic group
The group can be defined by:

$$G := \langle x,y \mid x^4 = y^4 = e, yxy^{-1} = x^3 \rangle$$.

Other descriptions
gap> G := F/[F.1^2, F.2^4, F.1*F.2*F.1^(-1)*F.2^(-1),F.3^4,F.3*F.1*F.3^(-1)*F.1^(-1),F.3*F.2*F.3^(-1)*F.2^(-1)*F.1^(-1), F.3^2 * F.2^2];  gap> IdGroup(G); [ 16, 4 ]