  For a wide family of formations $\mathfrak{F}$ (which includes Baer-local
formations) it is proved that the $ \mathfrak{F}$-hypercenter of a permutation
finite group can be computed in polynomial time. In particular, the algorithms
for computing the $\mathfrak{F}$-hypercenter for the following classes of
groups are suggested: hereditary local formations with the Shemetkov property,
rank formations, formations of all quasinilpotent, Sylow tower, $p$-nilpotent,
supersoluble, $w$-supersoluble and $SC$-groups. For some of these formations
algorithms for the computation of the intersection of all maximal
$\mathfrak{F}$-subgroups are suggested.
