When does an integral group ring have finite global dimension?

Question

Let $G$ be a finite group and $R=\mathbb{Z}[G]$ the integral group ring. If $G$ is such that $R$ is Noetherian (so $G$ polycyclic-by-finite) when does $R$ have finite global dimension? Another way of asking the question is, when is $R$ regular?

Answer 1

The answer is short: if $G$ is non-trivial, then never. I have just answered it in this other question. (If $G=\{1\}$, then $\mathbb Z G=\mathbb Z$ has global dimension 1)