Laser spectroscopy was performed on the Ga-72,Ga-74,Ga-76,Ga-78 isotopes at On-Line Isotope Mass Separator (ISOLDE) facility, CERN. Ground-state nuclear spins and moments were extracted from the measured hyperfine spectra. The results are compared to shell-model calculations, which provide a detailed probe of the nuclear wave function. The spin is established from the shape of the hyperfine structure and the parity inferred from a comparison of shell-model calculations with the measured nuclear moments. The ground states of Ga-76,Ga-78 are both assigned a spin and parity of I-pi = 2(-), while Ga-74 is tentatively assigned as I-pi = 3(-). For Ga-72, the results are consistent with the previous I = 3 assignment.