  We simulate the star cluster, made of stars in the main sequence and
different black hole (BH) remnants, around SgrA* at the center of the Milky Way
galaxy. Tracking stellar evolution, we find the BH remnant masses and construct
the BH mass function. We sample 4 BH species and consider the impact of the
mass-function in the dynamical evolution of system. Starting from an initial 6
dimensional family of parameters and using an MCMC approach, we find the best
fits to various parameters of model by directly comparing the results of the
simulations after $t = 10.5$ Gyrs with current observations of the stellar
surface density, stellar mass profile and the mass of SgrA*. Using these
parameters, we study the dynamical evolution of system in detail. We also
explore the mass-growth of SgrA* due to tidally disrupted stars and swallowed
BHs. We show that the consumed mass is dominated for the BH component with
larger initial normalization as given by the BH mass-function. Assuming that
about 10% of the tidally disrupted stars contribute in the growth of SgrA*
mass, stars make up the second dominant effect in enhancing the mass of SgrA*.
We consider the detectability of the GW signal from inspiralling stellar mass
BHs around SgrA* with LISA. Computing the fraction of the lifetime of every BH
species in the LISA band, with signal to noise ratio $\gtrsim 8$, to their
entire lifetime, and rescaling this number with the total number of BHs in the
system, we find that the total expected rate of inspirals per Milky-Way sized
galaxy per year is $10^{-5}$. Quite interestingly, the rate is dominated for
the BH component with larger initial normalization as dictated by the BH
mass-function. We interpret it as the second signature of the BH mass-function.
