S3-permutation orbifolds of Virasoro vertex algebras

In this paper, a continuation of [24], we investigate the S3-orbifold subalgebra (Vc)⊗3, that is, consider S3-fixed point vertex tensor product three copies universal Virasoro operator algebras Vc. Our main result is construction minimal, strong set generators for any generic values c. More precisely, show algebra type (2,4,62,82,9,102,11,123). We also two prominent examples simple corresponding to central charges c=12 (Ising model) and c=−225 (i.e. (2,5)-minimal model). prove former new unitary W-algebra (2,4,6,8) latter isomorphic affine G2 at non-admissible level −196. provide another version isomorphism using coming from subregular nilpotent element.