  We use the Herschel ATLAS (H-ATLAS) Phase I data to study the conditional
luminosity function of far-IR (250 um) selected galaxies in optically-selected
galaxy groups from the GAMA spectroscopic survey, as well as environmental
effects on the far-IR-to-optical colour. We applied two methods, which gave
consistent results for the far-IR conditional luminosity functions. The direct
matching method matches H-ATLAS sources to GAMA/SDSS galaxies, then links the
optical counterparts to GAMA groups. The stacking method counts the number of
far-IR sources within the projected radii of GAMA groups, subtracting the local
background. We investigated the dependence of the far-IR (250 um) luminosity
function on group mass in the range 10d12 < M_h < 10d14Msun/h and on redshift
in the range 0 < z < 0.4, using a sample of 3000 groups containing H-ATLAS
sources with GAMA redshifts over an area of 126 sq. deg. We find that the
characteristic 250 um luminosity, L^*(250), increases with group mass up to M_h
~ 10d13Msun/h, but is roughly constant above this, while it increases with
redshift at high group masses, but less so at low masses. We also find that the
group far-IR luminosity-to-mass ratio L(250)/M_h increases with redshift and is
higher in low-mass groups. We estimate that around 70% of the 250 um luminosity
density in the local universe is contributed by groups with M_h > 10d12Msun/h.
We also find that the far-IR-to-optical colours of H-ATLAS galaxies are
independent of group mass over the range 10d12 < M_h <10d14Msun/h in the local
universe. We also compare our observational results with recent semi-analytical
models, and find that none of these galaxy formation model can reproduce the
conditional far-IR luminosity functions of galaxy groups.
