These fusion categories are all weakly integral, each with an FPdim less than 84, and therefore, they are all weakly group-theoretical by [this paper](https://doi.org/10.1016/j.aim.2010.06.009). Consequently, they can all be described using models that are, to varying degrees, derived from finite group theory.  

The first category is recognized as  N°3 of rank 6 in [this paper](https://doi.org/10.1007/s11005-022-01542-1), and has a model from zesting.