We have measured the magnetization and magnetostriction of Mn3GaC in pulsed high magnetic fields up to 37 T and the magnetization under steady magnetic field and pressure up to 0.82 GPa. Mn3GaC is antiferromagnetic (AF) at low temperatures. It exhibits successive transitions to an intermediate (I), to a ferromagnetic (F) and to a paramagnetic phase. The transition between the AF and I phases is first order and the others are second order. The transition temperature between the I and F phases does not change greatly with increasing magnetic field. At low temperatures, a metamagnetic transition from the AF to the I state is observed. Volume magnetostriction measurement at 4.2 K indicates that the volume is abruptly decreased by the metamagnetic transition and then gradually shrinks with increasing field. High pressure stabilizes the F phase and enhances the Mn moment.