The XXL Survey. XXII. The XXL-North spectrophotometric sample and galaxy stellar mass function in X-ray detected groups and clusters

Context. The fraction of galaxies bound in groups in the nearby Universe is high (50% at z ~ 0). Systematic studies of galaxy properties in groups are important in order to improve our understanding of the evolution of galaxies and of the physical phenomena occurring within this environment. Aims. We have built a complete spectrophotometric sample of galaxies within X-ray detected, optically spectroscopically confirmed groups and clusters (G&C), covering a wide range of halo masses at z ≤ 0.6. Methods. In the context of the XXL survey, we analyse a sample of 164 G&C in the XXL-North region (XXL-N), at z ≤ 0.6, with a wide range of virial masses (1.24 x 10^13 ≤ M_500, scal(M_⊙) ≤ 6.63 x 10^14) and X-ray luminosities (2.27 x 10^41 ≤ L^XXL _500, scal(erg s^-1) ≤ 2.15 x 10^44). The G&C are X-ray selected and spectroscopically confirmed. We describe the membership assignment and the spectroscopic completeness analysis, and compute stellar masses. As a first scientific exploitation of the sample, we study the dependence of the galaxy stellar mass function (GSMF) on global environment. Results. We present a spectrophotometric characterisation of the G&C and their galaxies. The final sample contains 132 G&C, 22 111 field galaxies and 2225 G&C galaxies with r-band magnitude