Gao–Li conjecture on the Gao constant of finite non-cyclic groups

Let $G$ be a finite group. Write $|G|$ for its order and let $\mathsf{E}(G)$ denote its Gao constant, namely the least integer such that every sequence over $G$ of that length contains a product-one subsequence of length $|G|$. Gao–Li's conjecture. For every finite non-cyclic group $G$,

$$\mathsf{E}(G) \leq \frac{3}{2}|G|.$$

Han proved the conjecture for all finite non-cyclic nilpotent groups, and Gao, Li, and Qu proved the stronger bound $\mathsf{E}(G) \leq \frac{3}{2}(|G|-1)$ for finite non-cyclic groups of odd order greater than $9$. The conjecture remains open in general.