  We present the results of a spectroscopic survey of galaxies in the vicinity
of an ultra-strong MgII \lambda\lambda 2786,2803 absorber of rest-frame
absorption equivalent width W_r(2796)=4.2\AA\ at z=0.5624. This absorber was
originally found at projected separation \rho=246 kpc of a luminous red galaxy
(LRG) at z=0.5604. Magellan IMACs spectroscopy has revealed two galaxies at
\rho < 60 kpc (z=0.5623 and z=0.5621) and a third one at \rho=209 kpc
(z=0.5623) near the redshift of the absorber.These findings indicate that the
absorbing gas resides in a group environment. Combining SDSS broadband
photometry with additional B-, K_s-band images and optical spectroscopy, we
perform a stellar population synthesis analysis of the group members to
characterize their star formation histories, on-going star formation rates
(SFR), and stellar masses. We find that the two group members at \rho < 60 kpc
are best characterized by old stellar populations (>1 Gyr) and little on-going
star formation activity (SFR<2.9 \msun/yr), while the third object at \rho=209
kpc exhibit [OII]- and continuum-derived SFR consistent with SFR>3.0 \msun/yr.
Including the two ultra-strong MgII absorbers analyzed by Nestor et al. (2011),
this is the third ultra-strong MgII absorber for which a detailed study of the
galactic environment is available. All three aborbers are found in galaxy
groups. We examine different physical mechanisms giving rise to the absorbing
gas including starburst driven-outflows, cold filaments, extended rotating
disks, and stripped gas. We argue that the large equivalent width observed in
these absorbers is more likely due to the gas dynamics of the intragroup medium
rather than driven by starburst outflows.
