  In this article, we study rational matrix representations of VZ $p$-groups
($p$ is any prime). Utilizing our findings on VZ $p$-groups, we explicitly
obtain all inequivalent irreducible rational matrix representations of all
$p$-groups of order $\leq p^4$. Furthermore, we establish combinatorial
formulas to determine the Wedderburn decompositions of rational group algebras
for VZ $p$-groups and all $p$-groups of order $\leq p^4$, ensuring simplicity
in the process.
