Nontrivial semidirect product of Z9 and Z9

Definition
This group is defined by the following presentation (here, $$e$$ denotes the identity element):

$$\langle x,y \mid x^9 = y^9 = e, yxy^{-1} = x^4 \rangle$$

It is the case $$p = 3$$ of the nontrivial semidirect product of cyclic groups of prime-square order.