  The supermassive black hole at the center of the Milky Way plays host to a
massive, young cluster that may have formed in one of the most inhospitable
environments in the Galaxy. We present new measurements of the global
properties of this cluster, including the initial mass function (IMF), age, and
cluster mass. These results are based on Keck laser-guide-star adaptive optics
observations used to identify the young stars and measure their Kp-band
luminosity function as presented in Do et al. 2013. A Bayesian inference
methodology is developed to simultaneously fit the global properties of the
cluster utilizing the observations and extensive simulations of synthetic star
clusters. We find that the slope of the mass function for this cluster is
\alpha = 1.7 +/- 0.2, which is steeper than previously reported, but still
flatter than the traditional Salpeter slope of 2.35. The age of the cluster is
between 2.5-5.8 Myr with 95% confidence, which is a younger age than typically
adopted but consistent within the uncertainties of past measurements. The exact
age of the cluster is difficult to determine since our results show two
distinct age solutions (3.9 Myr and 2.8 Myr) due to model degeneracies in the
relative number of Wolf-Rayet and OB stars. The total cluster mass is between
14,000 - 37,000 \msun above 1 \msun and it is necessary to include multiple
star systems in order to fit the observed luminosity function and the number of
observed Wolf-Rayet stars. The new IMF slope measurement is now consistent with
X-ray observations indicating a factor of 10 fewer X-ray emitting
pre-main-sequence stars than expected when compared with a Salpeter IMF. The
young cluster at the Galactic center is one of the few definitive examples of
an IMF that deviates significantly from the near-universal IMFs found in the
solar neighborhood.
