In this talk, we explore several zero-sum invariants for a finite group G: the small Davenport constant d(G), the ordered Davenport constant Dₒ(G), and the Loewy length L(G). We see that Dₒ(G) = d(G) + 1 = d(A) + 2 for every non-abelian group of the form G = A ⋊₋₁ C₂, where A is any finite abelian group. In addition, Dimitrov conjectured in 2004 that Dₒ(G) = L(G) for every finite non-abelian p-group G. We provide explicit families of finite non-abelian p-groups for which Dimitrov's conjecture holds.