Group delay of non differentiable unwrapped phase
If there are phase discontinuities after all $2\pi$-jumps have been removed, then these discontinuities are usually caused by zeros of the frequency response. The phase jumps by $\pi$ at these frequencies, and the group delay doesn't exist, or, if one prefers, is non-finite. Note that the group delay is meaningless anyway at frequencies where the frequency response is zero.