After classification of finite simple groups, the researchers dissucced about groups characterization by property. Properties, such as element order, the set of elements with the same order, graphs,etc. In other words if $G$ be a finite group and $M$ be a property then we say the group $G$ is characterized by property $M$ if by isomorphic $G$ be a only group by property $M$. One of the methods, is group characterization by largest element order. In other wrds, we say the group $G$ is characterized by largest element order $k(G)$ and order of $G$ if there exists the group $H$, so that if $k(G)=k(H)$ and $|G|=|H|$, then $G\cong H$. In this paper, we prove that the simple $K_5$-groups $PSL(6,2)$ and $PSU(6,2)$ can be uniquely determined by their order and the largest order of elements.
