Nonsplit extensions of Abelian $p$-groups by $L_2(p^n)$ and general theorems on extensions of finite groups

Let a group $\widetilde G$ be a nonsplit extension of an elementary Abelian $p$-group $V$ by the group $G=L_2(p^n)$ such that the action of $G$ on $V$ is irreducible. In the present article, we classify (up to isomorphism) such groups $\widetilde G$ with $p^n\ne3^4$.
The main part of the article consists of proofs of numerous general assertions on representations, cohomologies, and extensions of finite groups. Further, we use these results in our study of extensions by $L_2(q)$.