  Previous observations of the environments of the lensing galaxies in
gravitational lens systems suggest that many of the lensing galaxies are
associated with small groups of galaxies. As a result, we have begun a
coordinated program to study the local environments of all known gravitational
lens systems. In this paper, we present results on the gravitational lens
system CLASS B0712+472, which has previously measured source and lens redshifts
of (z_l,z_s) = (0.4060,1.339). Although we have not found a galaxy group
associated with the primary lensing galaxy, we have found a foreground group
which is spatially coincident with the lens system. Based on multi-object
spectroscopy taken at the Keck 10-m telescope, we have confirmed ten group
members with a mean redshift of <z> = 0.2909. The resulting velocity dispersion
and estimated virial mass are 306(+110/-58) km/s and 3.0(+2.2/-1.2) x 10^13
h^-1 M_sun, respectively, for (Omega_m,Omega_Lambda) = (0.2,0.0). The dynamical
properties of this moderate-redshift group are completely consistent with the
range of values found in nearby groups of galaxies. Five of the group members
are red, elliptical-like galaxies, while the remaining five are active,
star-forming galaxies. Based on the spectroscopic results and the
publically-available HST imaging of nine group members, we find that the
early-type fraction is 40%. We estimate that the effect of this foreground
group on the gravitational lensing potential of B0712+472 is small, producing
an external shear which is only a few percent, although the shear could be
larger if the group centroid is significantly closer to the lens system than it
appears to be.
