  We present the first study of the dynamical evolution of a star cluster that
combines a significant population of primordial binaries with the presence of a
central black hole. We use direct N-body simulations, with a black hole mass of
about one percent of the total mass of the cluster.
  The evolution of the binary population is strongly influenced by the presence
of the black hole, which gives the cluster a large core with a central density
cusp. Starting from a Plummer profile, we first encounter a phase, that last
approximately 10 half-mass relaxation times, in which binaries are disrupted
faster compared to analogous simulations without a black hole. Subsequently,
however, binary disruption slows down significantly, due to the large core
size.
  The dynamical interplay between the primordial binaries and the black hole
thus introduces new features with respect to the scenarios investigated so far,
where the influence of the black hole and of the binaries have been considered
separately. Specifically, the pattern of binary destruction by an
intermediate-mass black hole may leave a fingerprint that could be detected
observationally.
