In the (xi) group of the classification of groups of order $p^4$ given by W.Burnside in his book," Theory of Groups Of Finite Order". The group ($\mathbb{Z_{p^{2}}}\rtimes \mathbb{Z_{p^{}}}) \rtimes_{\phi}\mathbb{Z_{p^{}}} $, have presentation $$<a,b,c : a^{p^{2}}=b^p=c^p=e, ab=ba^{1+p},ac=cab,bc=cb>$$
I was trying to explore about the representation(must be faithful) of the above group in $GL(4,F_p)$, i.e. group of $4\times 4$ invertible matrices , taken over $F_p$. Please guide me in the right direction, from where to start or if my statement mathematically correct or not ?