In a ongoing programme aimed at studying galaxy counterparts of Damped Ly \alpha Absorbers ( DLAs ) we have obtained high resolution deep I-band imaging data of the field around the z _ { em } = 0.457 BAL QSO Q2112+059 .
In the literature this QSO is listed to have a candidate DLA at z _ { abs } = 0.2039 along the line of sight .
After subtraction of the QSO Point Spread Function ( PSF ) we detect a galaxy centred on the position of Q2112+059 .
To help answer whether this galaxy is the DLA or the QSO host galaxy we retrieved a GHRS spectrum of Q2112+059 from the HST-archive .
This spectrum shows that there is no Ly \alpha absorption line at z _ { abs } = 0.2039 .
This fact in combination with the perfect alignment on the sky of the galaxy and Q2112+059 lead us to the conclusion that the galaxy must be the host galaxy of Q2112+059 .

The host galaxy of Q2112+059 is bright ( M _ { I } ^ { obs } = -23.6 ) , and has a radial profile well fitted by a modified Hubble + de Vaucouleurs profile with R _ { c } = 0.5 kpc and R _ { e } = 3.6 kpc .
Our results are well in line with the conclusion of earlier work done at lower redshifts , that bright low redshift QSOs preferentially reside in luminous , elliptical galaxies .
The host of Q2112+059 is however , despite it ’ s brightness , very compact when compared to early type galaxies at lower redshifts .