Automorphism Groups and Uniqueness of Holomorphic Vertex Operator Algebras of Central Charge 24

We describe the automorphism groups of all holomorphic vertex operator algebras of central charge 24 with non-trivial weight one Lie algebras by using their constructions as simple current extensions. We also confirm a conjecture of G. Hohn on the numbers of holomorphic vertex operator algebras of central charge 24 obtained as inequivalent simple current extensions of certain vertex operator algebras, which gives another proof of the uniqueness of holomorphic vertex operator algebras of central charge 24 with non-trivial weight one Lie algebras.