  The center of our Galaxy is known to host a massive compact object, Sgr
A$^*$, which is commonly considered as a super-massive black hole of $\sim
4\times 10^6$ M$_\odot$. It is surrounded by a dense and massive nuclear star
cluster, with a half mass radius about $5$~pc and a mass larger than $10^{7}$
M$_\odot$.
  In this paper we studied the evolutionary fate of a very dense cluster of
intermediate mass black holes, possible remnants of the dissipative orbital
evolution of massive globular cluster hosts. We performed a set of high
precision $N$-body simulations taking into account deviations from pure
Newtonian gravitational interaction via a Post Newtonian development up to
$2.5$ order, which is the one accounting for energy release by gravitational
wave emission. The violent dynamics of the system leads to various successive
merger events such to grow a single object containing $\sim 25$ per cent of the
total cluster mass before partial dispersal of the cluster, and such to
generate, in different bursts, a significant quantity of gravitational waves
emission. If generalized, the present results suggest a mechanism of mass
growth up to the scale of a super massive black hole.
