  Cluster galaxies exhibit substantially lower star formation rates than field
galaxies today, but it is conceivable that clusters were sites of more active
star formation in the early universe. Herein, we present an interpretation of
the star formation history (SFH) of group/cluster galaxies based on the
large-scale cosmological hydrodynamic simulation, Horizon-AGN. We find that
massive galaxies in general have small values of e-folding timescales of star
formation decay (i.e., ``mass quenching'') regardless of their environment,
whilst low-mass galaxies exhibit prominent environmental dependence. In massive
host halos (i.e., clusters), the e-folding timescales of low-mass galaxies are
further decreased if they reside in such halos for a longer period of time.
This ``environmental quenching'' trend is consistent with the theoretical
expectation from ram pressure stripping. Furthermore, we define a ``transition
epoch'' as where cluster galaxies become less star-forming than field galaxies.
The transition epoch of group/cluster galaxies varies according to their
stellar and host cluster halo masses. Low-mass galaxies in massive clusters
show the earliest transition epoch of $\sim 7.6$ Gyr ago in lookback time.
However, it decreases to $\sim 5.2$ Gyr for massive galaxies in low-mass
clusters. Based on our findings, we can describe cluster galaxy's SFH with
regard to the cluster halo-to-stellar mass ratio.
