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The aims of this work are to provide accurate photometry in multiplenear-infrared broadband filters, to determine the power-law index of theextinction-law toward the central parsec of the Galaxy, to provide measurementsof the absolute extinction toward the Galactic center, and finally to measurethe spatial variability of extinction on arcsecond scales.We use adaptiveoptics observations of the central parsec of the Milky Way. Absolute values forthe extinction in the H, Ks, and L'-bands as well as of the power-law indicesof the H to Ks and Ks to L' extinction-laws are measured based on thewell-known properties of red clump stars. Extinction maps are derived based onH-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 computea mean distance of the Galactic center of R_0=8.03+-0.15 kpc, which has anuncertainty of just 2%. Based on this R_0 and on the RC method, we deriveabsolute mean extinction values toward the central parsec of the Galaxy ofA_H=4.48+-0.13 mag, A_Ks=2.54+-0.12$ mag, and A_L'=1.27+-0.18 mag. We estimatevalues of the power-law indices of the extinction-law ofalpha_{H-Ks}=2.21+-0.24 and alpha_{Ks-L'}=1.34+-0.29. A Ks-band extinction mapfor the Galactic center is computed based on this extinction law and on stellarH-Ks colors. Mean extinction values in a circular region with 0.5" radiuscentered 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.

Peering through the veil: near-infrared photometry and extinction for the Galactic nuclear star cluster