Abelianization of the unit group of an integral group ring

For a finite group $G$ and $U: = U(\mathbb{Z}G)$, the of units integral ring $G$, we study implications structure on abelianization $U/U'$ $U$. We pose questions connections between exponent $G/G'$ as well ranks torsion-free parts $Z(U)$, center $U$, $U/U'$. show that originating from known generic constructions in $\mathbb{Z}G$ are well-behaved under projection $U$ to our have positive answer for many examples. then exhibit an explicit example which shows general statement part does not hold, also answers [BJJ$^+$18].