Does the environment of a galaxy directly influence the quenching history of a galaxy? Here we investigate the detailed morphological structures and star formation histories of a sample of SDSS group galaxies with both classifications from Galaxy Zoo 2 and NUV detections in GALEX. We use the optical and NUV colours to infer the quenching time and rate describing a simple exponentially declining SFH for each galaxy, along with a control sample of field galaxies. We find that the time since quenching and the rate of quenching do not correlate with the relative velocity of a satellite but are correlated with the group potential. This quenching occurs within an average quenching timescale of $sim2.5~rm{Gyr}$ from star forming to complete quiescence, during an average infall time (from $sim 10R_{200}$ to $0.01R_{200}$) of $sim 2.6~rm{Gyr}$. Our results suggest that the environment does play a direct role in galaxy quenching through quenching mechanisms which are correlated with the group potential, such as harassment, interactions or starvation. Environmental quenching mechanisms which are correlated with satellite velocity, such as ram pressure stripping, are not the main cause of quenching in the group environment. We find that no single mechanism dominates over another, except in the most extreme environments or masses. Instead an interplay of mergers, mass & morphological quenching and environment driven quenching mechanisms dependent on the group potential drive galaxy evolution in groups.
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