Quantum symmetries and nimreps for an exotic exceptional modular invariant of F4 at level 6

We revisit an old non-diagonal modular invariant of $F_4$ at level $6$, discovered in 1989. At the time of its discovery, it was noticed that it could not be obtained from a conformal embedding of affine Lie algebras. Later, it was shown that it can be obtained from an extension of a vertex operator