All rank 6 modular categories with Galois group (012)(345) have modular data conjugate to one of two explicit families, one of which is nonunitarizable.
Creamer, A computational approach to classifying modular tensor cat egories, Texas A&M University, 2018
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Classification of Rank 6 Modular Categories with Galois Group $\langle (012)(345)\rangle$
All rank 6 modular categories with Galois group (012)(345) have modular data conjugate to one of two explicit families, one of which is nonunitarizable.