Automorphism groups of cyclic orbifold vertex operator algebras associated with the Leech lattice and some non-prime isometries

We determine the automorphism groups of the cyclic orbifold vertex operator algebras associated with coinvariant lattices for isometries of the Leech lattice in the conjugacy classes 4 C , 6 E , 6 G , 8 E and 10 F . As a consequence, we have determined the automorphism groups of all the 10 vertex operator algebras in [Hö], which are useful to analyze holomorphic vertex operator algebras of central charge 24.