  We show that if one of various cycle types occurs in the permutation action
of a finite group on the cosets of a given subgroup, then every almost
conjugate subgroup is conjugate. As a number theoretic application,
corresponding decomposition types of primes effect that a number field is
determined by the Dedekind zeta function. As a geometric application, coverings
of Riemannian manifolds with certain geodesic lifting behaviors must be
isometric.
