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Previous observations of the environments of the lensing galaxies ingravitational lens systems suggest that many of the lensing galaxies areassociated with small groups of galaxies. As a result, we have begun acoordinated program to study the local environments of all known gravitationallens systems. In this paper, we present results on the gravitational lenssystem CLASS B0712+472, which has previously measured source and lens redshiftsof (z_l,z_s) = (0.4060,1.339). Although we have not found a galaxy groupassociated with the primary lensing galaxy, we have found a foreground groupwhich is spatially coincident with the lens system. Based on multi-objectspectroscopy taken at the Keck 10-m telescope, we have confirmed ten groupmembers with a mean redshift of <z> = 0.2909. The resulting velocity dispersionand estimated virial mass are 306(+110/-58) km/s and 3.0(+2.2/-1.2) x 10^13h^-1 M_sun, respectively, for (Omega_m,Omega_Lambda) = (0.2,0.0). The dynamicalproperties of this moderate-redshift group are completely consistent with therange of values found in nearby groups of galaxies. Five of the group membersare red, elliptical-like galaxies, while the remaining five are active,star-forming galaxies. Based on the spectroscopic results and thepublically-available HST imaging of nine group members, we find that theearly-type fraction is 40%. We estimate that the effect of this foregroundgroup on the gravitational lensing potential of B0712+472 is small, producingan external shear which is only a few percent, although the shear could belarger if the group centroid is significantly closer to the lens system than itappears to be.Comment: Accepted for publication in the Astronomical Journal. 16 pages, 7  figure

The Gravitational Lens–Galaxy Group Connection. I. Discovery of a Group Coincident with CLASS B0712+472