OD-characterization of U3(9) and its group of automorphisms

Let L = U3(9) be the simple projective unitary group in dimension 3 over a field with 92 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to L. Since Aut(L) = Z4 hence almost simple groups related to L are L, L : 2 or L : 4. In fact, we prove that L, L : 2 and L : 4 are OD-characterizable.