Recognition of the Group $E_6(2)$ by Gruenberg-Kegel Graph

The Gruenberg-Kegel graph (or the prime graph) of a finite group $G$ is a simple graph $\Gamma(G)$ whose vertices are the prime divisors of the order of $G$, and two distinct vertices $p$ and $q$ are adjacent in $\Gamma(G)$ if and only if $G$ contains an element of order $pq$. A finite group is called recognizable by Gruenberg-Kegel graph if it is uniquely determined up to isomorphism in the class of finite groups by its Gruenberg-Kegel graph. In this paper, we prove that the finite simple exceptional group of Lie type $E_6(2)$ is recognizable by its Gruenberg-Kegel graph.