We explore the radial distribution of star formation in galaxies in the SAMI Galaxy Survey as a function of their local group environment. Using a sample of galaxies in groups (with halo masses less than $ simeq 10^{14} , mathrm{M_{odot}}$) from the Galaxy And Mass Assembly Survey, we find signatures of environmental quenching in high-mass groups ($M_{G} > 10^{12.5} , mathrm{M_{odot}}$). The mean integrated specific star formation rate of star-forming galaxies in high-mass groups is lower than for galaxies in low-mass groups or that are ungrouped, with $Delta log(sSFR/mathrm{yr^{-1}}) = 0.45 pm 0.07$. This difference is seen at all galaxy stellar masses. In high-mass groups, star-forming galaxies more massive than $M_{*} sim 10^{10} , mathrm{M_{odot}}$ have centrally-concentrated star formation. These galaxies also lie below the star-formation main sequence, suggesting they may be undergoing outside-in quenching. Lower mass galaxies in high-mass groups do not show evidence of concentrated star formation. In groups less massive than $M_{G} = 10^{12.5} , mathrm{M_{odot}}$ we do not observe these trends. In this regime we find a modest correlation between centrally-concentrated star formation and an enhancement in total star formation rate, consistent with triggered star formation in these galaxies.