We report on the structure of the nuclear star cluster in the innermost 0.16pc of the Galaxy as measured by the number density profile of late-type giants. Using laser guide star adaptive optics in conjunction with the integral field spectrograph, OSIRIS, at the Keck II telescope, we are able to differentiate between the older, late-type (~1Gyr) stars, which are presumed to be dynamically relaxed, and the unrelaxed young (~6Myr) population. This distinction is crucial for testing models of stellar cusp formation in the vicinity of a black hole, as the models assume that the cusp stars are in dynamical equilibrium in the black hole potential. In the survey region, we classified 60 stars as early-type (O and early B; 22 newly identified) and 74 stars as late-type (K and M; 61 newly identified). We find that contamination from young stars is significant, with more than twice as many young stars as old stars in our sensitivity range (K'<15.5) within the central arcsecond.