Union restoration conjecture for commutator conductors

Let $G$ be a finite group, let $G'$ denote its commutator subgroup, and for each commutator weight $w$ let $\operatorname{C_{\mathrm{comm}}}(w)$ be the associated commutator conductor. Then Union restoration conjecture.

$$\operatorname{rad}(|G'|)\subseteq\bigcup_w\operatorname{C_{\mathrm{comm}}}(w),$$

the union being over commutator weights. The conjecture asserts that every prime divisor of the commutator subgroup occurs in at least one commutator-weight conductor; it survived all ten groups tested, but its general validity remains open.