let $g$ be a finite group and $pi_{e}(g)$ be the set of element orders of $g$. let $k in pi_{e}(g)$ and $m_{k}$ be the number of elements of order $k$ in $g$. set nse($g$):=${ m_{k} | k in pi_{e}(g)}$. in this paper, we prove that if $g$ is a group such that nse($g$)=nse($psl(2, 25)$), then $g cong psl(2, 25) $.