Precise values of the Davenport constant beyond known cases

Determine the precise value of the large Davenport constant D(G) for finite groups beyond currently settled cases, including abelian groups of rank at least three.

Background

The Davenport constant is a central combinatorial invariant tied to factorization and invariant theory. The authors state that its exact value remains unknown for most finite groups and that even in the abelian case results are largely confined to rank at most two, with further classes only partially resolved.

This underscores a broad unresolved program to compute D(G) across wider families of groups, particularly abelian groups of higher rank and non-abelian groups.