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The prime graph of a finite group $G$ is denoted by $\ga(G)$ whose vertex setis $\pi(G)$ and two distinct primes $p$ and $q$ are adjacent in $\ga(G)$,whenever $G$ contains an element with order $pq$. We say that $G$ isunrecognizable by prime graph if there is a finite group $H$ with$\ga(H)=\ga(G)$, in while $H\not\cong G$. In this paper, we consider finitegroups with the same prime graph as the almost simple group$\textrm{PGL}(2,49)$. Moreover, we construct some Frobenius groups whose theirprime graph coincide with $\ga(\textrm{PGL}(2,49))$, in particular, we get that$\textrm{PGL}(2,49)$ is unrecognizable by prime graph.

On some Frobenius groups with the same prime graph as the almost simple group PGL(2,49)