Magnetoluminescence of the exciton bound to a neutral acceptor was measured to investigate the electronic structure of a shallow acceptor center in GaN. The application of magnetic fields along different directions with respect to the crystal c axis allowed us to determine the symmetry of the ground (Gamma(9)) and the first excited state (Gamma(7)) of the acceptor. The observed Zeeman splitting pattern has axial symmetry but can be explained well only by assuming a significant reduction of the spin-orbit interaction for this acceptor state. Because of this reduction, the energy structure of the neutral acceptor is found to be very sensitive to any local, axial perturbation.