Non-abelian orbifolds of lattice vertex operator algebras

We construct orbifolds of holomorphic lattice vertex operator algebras for non-abelian finite automorphism groups G. To this end, we twisted modules automorphisms g together with the projective representation centralizer on module. This allows us to extract irreducible fixed-point VOA VG, and compute their characters modular transformation properties. then VOAs by adjoining such VG. Applying these methods extremal lattices in d=48 d=72, more than fifty new central charge 48 72, many which have a very small number light states.