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

The prime graph of a nite group G is denoted by (G) whose vertex set is (G) and two distinct primes p and q are adjacent in (G), whenever G contains an element with order pq.We say that G is unrecognizable by prime graph if there is a nite group H with 􀀀(H) = (G), in while H ̸= G. In this paper, we consider nite groups with the same prime graph as the almost simple group PGL(2; 49). Moreover, we construct some Frobenius groups whose prime graphs coincide with (PGL(2; 49)), in particular, we get that PGL(2; 49) is unrecognizable by its prime graph.