  The aims of this work are to provide accurate photometry in multiple
near-infrared broadband filters, to determine the power-law index of the
extinction-law toward the central parsec of the Galaxy, to provide measurements
of the absolute extinction toward the Galactic center, and finally to measure
the spatial variability of extinction on arcsecond scales.We use adaptive
optics observations of the central parsec of the Milky Way. Absolute values for
the extinction in the H, Ks, and L'-bands as well as of the power-law indices
of the H to Ks and Ks to L' extinction-laws are measured based on the
well-known properties of red clump stars. Extinction maps are derived based on
H-Ks and Ks-L' colors. We present Ks-band photometry for ~7700 stars (H and L'
photometry for a subset). From a number of recently published values we compute
a mean distance of the Galactic center of R_0=8.03+-0.15 kpc, which has an
uncertainty of just 2%. Based on this R_0 and on the RC method, we derive
absolute mean extinction values toward the central parsec of the Galaxy of
A_H=4.48+-0.13 mag, A_Ks=2.54+-0.12$ mag, and A_L'=1.27+-0.18 mag. We estimate
values of the power-law indices of the extinction-law of
alpha_{H-Ks}=2.21+-0.24 and alpha_{Ks-L'}=1.34+-0.29. A Ks-band extinction map
for the Galactic center is computed based on this extinction law and on stellar
H-Ks colors. Mean extinction values in a circular region with 0.5" radius
centered on Sagittarius A* are A_{H, SgrA*}=4.35+-0.12, A_{Ks,
SgrA*}=2.46+-0.03, and A_{L', SgrA*}=1.23+-0.08.
