When studying about the semidirect product, $G=(\mathbb{Z}_p \times \mathbb{Z}_p)\rtimes_{\phi} \mathbb{Z}_q$, I understood that, for some semidirect products by considering a minimal generating set $S=\{s,t\}$, where $|s|=q, |t|=p$, an action of $s$ on $\mathbb{Z}_p \times \mathbb{Z}_p$ can be defined.
For $\phi: \mathbb{Z}_q \rightarrow Aut(\mathbb{Z}_p \times \mathbb{Z}_p)$, let $\phi(s)=\phi_s$. Then, $\phi_s(v) = s^{-1}vs$, $v \in \mathbb{Z}_p \times \mathbb{Z}_p$ (action of $s$). This defines the semidirect product.
When considering a group like, $(\mathbb{Z}_p \times \mathbb{Z}_p)\rtimes_h (\mathbb{Z}_q \times \mathbb{Z}_q)$, let $h:(\mathbb{Z}_q \times \mathbb{Z}_q) \rightarrow Aut(\mathbb{Z}_p \times \mathbb{Z}_p)$. Then can there be instances where we have to mention two actions by two generating elements, say $s_1,s_2 \in (\mathbb{Z}_q \times \mathbb{Z}_q)$ of order $q$, to define $h$? (i.e. to define the semidirect product)
Thanks a lot in advance.