  Let $G$ be a finite group, and let $\pi$ be a set of primes. The aim of this
paper is to obtain some results concerning how much information about the
$\pi$-structure of $G$ can be gathered from the knowledge of the lengths of
conjugacy classes of its $\pi$-elements and of their multiplicities. Among
other results, we prove that this multiset of class lengths determine whether
$G$ has a hypercentral Hall $\pi$-subgroup.
