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Let $G\in\{p,q\}^*$ be a finite group with trivial center, where$p,q\in\pi(G)$ and $p>q>5$. In the present paper it is proved that$|G|_{\{p,q\}}=|G||_{\{p,q\}}$; in particular $C_G(g)\cap C_G(h)=1$ for every$p$-element $g$ and every $q$-element $h$.

On a connection between the order of a finite group and the set of conjugacy classes size