Finite groups with an irreducible character large degree

We study a finite nontrivial group $G$ with an irreducible complex character $ \Theta $ such that $|G|\leq 2\Theta (1)^2$ and ‚$ \Theta (1)=p^2q$, where $p > q$ and $p, q$ are different primes. In this case we prove that $G$ is solvable groups with abelian normal subgroup $M$ of index $p^{2}q$. We use the classification of finite simple groups and prove that the group with abelian Sylow p-subgroup $P\neq1$ whose order less than $p^2$ and $2|P|^{3}>|G|$ is isomorphic to $L_{2}(q)$.