  For a character $\chi$ of a finite group $G$, the number
cod$(\chi):=|G:\mathrm{ker}(\chi)|/\chi(1)$ is called the codegree of $\chi$.In
this paper, we give a solvability criterion for a finite group $G$ depending on
the minimum of the ratio $\chi(1)^2 /\mathrm{cod}(\chi )$, when $\chi $ varies
among the irreducible characters of $G$.
