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The Gruenberg--Kegel graph (or the prime graph) $\Gamma(G)$ of a finite group$G$ is defined as follows. The vertex set of $\Gamma(G)$ is the set of allprime divisors of the order of $G$. Two distinct primes $r$ and $s$ regarded asvertices are adjacent in $\Gamma(G)$ if and only if there exists an element oforder $rs$ in $G$. Suppose that $L\cong E_6(3)$ or $L\cong{}^2E_6(3)$. We provethat if $G$ is a finite group such that $\Gamma(G)=\Gamma(L)$, then $G\cong L$.

Characterization of groups $E_6(3)$ and ${^2}E_6(3)$ by Gruenberg--Kegel graph