Open questions

Liftings over non-cyclic groups, and $u_{q}(\mathfrak{sl}_{2})$ at a seventh root of unity (dimension 343).
Abelian extensions of order 32, and twists by larger abelian subgroups (the isocategorical pairs start at order 64).
Merges by invariants that the isomorphism search leaves undecided.
An exact backend for Rep(H), which is numeric today.
Non-split commutative algebras (Galois descent), and mixed profiles such as $\mathrm{Mat}_{2} \oplus K$ in the search.
The weak Hopf structures on $\mathrm{Mat}_{n}$ with a given noncommutative counital subalgebra, and the weak bialgebra structures on $\mathrm{Mat}_{3}$ .