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ABSTRACT We study environmental quenching using the spatial distribution of current star formation and stellar population ages with the full SAMI Galaxy Survey. By using a star formation concentration index [C-index, defined as log10(r50, H α/r50, cont)], we separate our sample into regular galaxies (C-index ≥−0.2) and galaxies with centrally concentrated star formation (SF-concentrated; C-index <−0.2). Concentrated star formation is a potential indicator of galaxies currently undergoing ‘outside-in’ quenching. Our environments cover ungrouped galaxies, low-mass groups (M200 ≤ 1012.5M⊙), high-mass groups (M200 in the range 1012.5–14 M⊙) and clusters (M200 > 1014M⊙). We find the fraction of SF-concentrated galaxies increases as halo mass increases by 9 ± 2 per cent, 8 ± 3 per cent, 19 ± 4 per cent, and 29 ± 4 per cent for ungrouped galaxies, low-mass groups, high-mass groups, and clusters, respectively. We interpret these results as evidence for ‘outside-in’ quenching in groups and clusters. To investigate the quenching time-scale in SF-concentrated galaxies, we calculate light-weighted age (AgeL) and mass-weighted age (AgeM) using full spectral fitting, as well as the Dn4000 and HδA indices. We assume that the average galaxy age radial profile before entering a group or cluster is similar to ungrouped regular galaxies. At large radius (1–2 Re), SF-concentrated galaxies in high-mass groups have older ages than ungrouped regular galaxies with an age difference of 1.83 ± 0.38 Gyr for AgeL and 1.34 ± 0.56 Gyr for AgeM. This suggests that while ‘outside-in’ quenching can be effective in groups, the process will not quickly quench the entire galaxy. In contrast, the ages at 1–2 Re of cluster SF-concentrated galaxies and ungrouped regular galaxies are consistent (difference of 0.19 ± 0.21 Gyr for AgeL, 0.40 ± 0.61 Gyr for AgeM), suggesting the quenching process must be rapid.