A bulk GaN half-wave (lambda /2) cavity is grown on Si(Ill) substrate by molecular beam epitaxy. It is embedded between twelve AlN/(Al,Ga)N quaterwave stacks and the silicon substrate, which acts as a metallic bottom mirror in the investigated wavelength range. A (4 lambda - lambda /4) buffer layer has been inserted just above the silicon substrate in order to accommodate the strain, experienced by the GaN layer. and to satisfy the resonance condition of the cavity. Reflectivity experiments at low temperature (T = 5 K) reveal a cavity mode centered around 355 nm with a spectral width of 3.6 nm. The modeling of the reflectivity spectrum accounts well for the experiment. By recording both the photoluminescence and reflectivity signals at the same position, it is shown that the emission is controlled by the cavity mode. The splitting due to strong exciton-photon coupling is not observed, which could be clue to the large spectral width of GaN emission.