I'm wondering how to specify to GAP which homomorphism to use when constructing a semidirect product. I'm trying to have it construct $\left(\mathbb{Z}_p\times\mathbb{Z}_p\right)\rtimes_\varphi S_3$. Since $\mathrm{Aut}\left(\mathbb{Z}_p\times\mathbb{Z}_p\right)\cong GL_2(\mathbb{F}_p)$, I want to specify $\varphi:S_3\rightarrow\mathrm{Aut}\left(\mathbb{Z}_p\times\mathbb{Z}_p\right)$ as $\varphi:S_3\rightarrow GL_2(\mathbb{F}_p)$ element by element (i.e. give a 2x2 matrix for each element of $S_3$).
I want to do this just to do group element multiplications quickly. I'll obviously specify $p$ when necessary.
I'm fairly new to GAP so a low-level answer (or reference) would be appreciated.