Finite Groups with Large Irreducible Character

In the general case, the order of a finite nonidentity group $G$ is substantially larger than the squared degree of every irreducible character $\Theta$ of $G$, i.e., $\Theta(1)^2<|G|$. In the present paper, we study finite groups with an irreducible character $\Theta$ such that
$$ |G|\le 2\Theta(1)^2. $$