Harada–Chigira's conjecture on the divisibility of Harada's number

Let $G$ be a finite group, let $G'$ denote its commutator subgroup, and let $h(G)$ be the Harada number

$$h(G):=\frac{\prod_{i=1}^{s}|K_i|}{\prod_{i=1}^{s}\chi_i(1)},$$

where $K_1,\ldots,K_s$ are the conjugacy classes of $G$ and $\chi_1,\ldots,\chi_s$ are its irreducible complex characters. Harada–Chigira's conjecture. For every finite group $G$,

$$\frac{h(G)}{|G'|}\in\mathbb{Z}.$$

This is stated as a stronger conjecture than Harada's conjecture II, imposing divisibility by the order of the commutator subgroup. The source does not report a resolution.