  Riera proved at arXiv:1412.6964 that the diffeomorphism group of particular
compact manifolds are not Jordan by exhibiting subgroups isomorphic to
extra-special $p$-groups of exponent $p$ for primes $p$ satisfying some
conditions. Generalising the methods of that paper, we construct a compact
connected smooth real manifold for every natural number $r$ whose
diffeomorphism group contains not only every extra-special $p$-group, but also
every special $p$-group of order $p^r$ independently of its exponent for every
prime $p$. We obtain a similar statement about finite Heisenberg groups as well
as we display a very explicit counterexample to the conjecture of Ghys about
Jordan property of diffeomorphism group of compact manifolds.
