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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 (⁠|$M_{\mathrm{ G}}\, \gt\, 10^{12.5} \, \mathrm{M_{\odot }}$|⁠). The mean integrated specific star formation rate (sSFR) of star-forming galaxies in high-mass groups is lower than for galaxies in low-mass groups or those that are ungrouped, with |$\Delta \log (\mathrm{ sSFR}/\mathrm{yr^{-1}}) \,=\, 0.45 \pm 0.07$|⁠. 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, which suggests 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 |$M_{\mathrm{ G}} = 10^{12.5} \, \mathrm{M_{\odot }}$|⁠, we do not observe these trends. In this regime, we find a modest correlation between centrally concentrated star formation and an enhancement in the total star formation rate, consistent with triggered star formation in these galaxies. [ABSTRACT FROM AUTHOR]