We know all 2-transitive simple groups by Dixon's book (Permutation groups). 
Now let $G$ be finite simple group $2$-transitive and $p(p^{2}-1)/2$ divides
order $G$ and also $\pi (p(p^{2}-1))\subseteq \pi (L_{2}(p))$. Is it true $G$
isomorphic to $L_{2}(p)$?