We report on a quantitative analysis of the band gap of hexagonal GaN epilayers in terms of the joint contributions;of the actual wurtzite symmetry on the one hand and of residual strain fields on the other hand. This investigation leads to revision of the previous modelings based on quasicubic descriptions of the valence-band physics and gives Delta(1)=10+/-0.1 meV, Delta(2)=6.2+/-0.1 meV, and Delta(3)=5.5+/-0.1 meV. Last we propose a set of deformation potentials for the hexagonal GaN semiconductor.