The Gay-Berne potential is proving to be a valuable model with which to investigate the behavior of liquid crystals using computer simulation techniques. The potential contains four independent parameters which control the anisotropy in the attractive and repulsive interactions. The choice of these parameters is not straightforward and it would seem that those employed in some simulations are not strictly appropriate for mesogenic rodlike molecules. Here we report a detailed computer simulation study of Gay-Berne particles interacting via a potential parametrized to reflect the anisotropic forces based on a fit to a realistic mesogenic molecule. The behavior of the phases and the transitions between them have been investigated for a system of 2000 particles using isothermal-isobaric Monte Carlo simulations. At low pressures, this Gay-Berne mesogen exhibits isotropic, smectic A and smectic B phases but, as the pressure is increased, so a nematic phase is added to the sequence. The nature of the phase transitions and the phase diagram are compared where possible with those of real mesogens. The structures of the four phases have been investigated in detail for a larger system of 16 000 particles using canonical molecular dynamics simulations at state points taken from the phase diagram determined from the Monte Carlo simulations. A wide range of singlet and pair distribution functions were evaluated together with orientational correlation coefficients and, for the smectic phases, a bond orientation correlation function. The results for these properties were used to identify the phases, to consider their structure at a quantitative level and, where possible, to make contact with experimental studies and the predictions of theories of liquid crystals. It would appear that with this parametrization, the Gay-Berne potential provides a powerful tool with which to understand the behavior of real liquid crystals and to test the predictions of theory.