Photonic crystal point-defect cavities were fabricated in a GaN free-standing photonic crystal slab. The cavities are based on the popular L3 design, which was optimized using an automated process based on a genetic algorithm, in order to maximize the quality factor. Optical characterization of several individual cavity replicas resulted in an average unloaded quality factor Q = 16 900 at the resonant wavelength lambda similar to 1.3 mu m, with a maximal measured Q value of 22 500. The statistics of both the quality factor and the resonant wavelength are well explained by first-principles simulations including fabrication disorder and background optical absorption. (C) 2014 AIP Publishing LLC.