  Context. Ultra-compact dwarfs (UCDs) are stellar systems displaying colours
and metallicities between those of globular clusters (GCs) and early-type dwarf
galaxies, as well as sizes of Reff <= 100 pc and luminosities in the range
-13.5 < MV < -11 mag. Although their origin is still subject of debate, the
most popular scenarios suggest that they are massive star clusters or the
nuclei of tidally stripped dwarf galaxies. Aims. NGC 5044 is the central
massive elliptical galaxy of the NGC 5044 group. Its GC/UCD system is
completely unexplored. Methods. In Gemini+GMOS deep images of several fields
around NGC 5044 and in spectroscopic multi-object data of one of these fields,
we detected an unresolved source with g'~20.6 mag, compatible with being an
UCD. Its radial velocity was obtained with FXCOR and the penalized
pixel-fitting (pPXF) code. To study its stellar population content, we measured
the Lick/IDS indices and compared them with predictions of single stellar
population models, and we used the full spectral fitting technique. Results.
The spectroscopic analysis of the UCD revealed a radial velocity that agrees
with the velocity of the elliptical galaxy NGC 5044. From the Lick/IDS indices,
we have obtained a luminosity-weighted age and metallicity of 11.7+/-1.4 Gyr
and [Z/H] = -0.79 +/- 0.04 dex, respectively, as well as [alpha/Fe] = 0.30 +/-
0.06. From the full spectral fitting technique, we measured a lower age (8.52
Gyr) and a similar total metallicity ([Z/H] = -0.86 dex). Conclusions. Our
results indicate that NGC 5044-UCD1 is most likely an extreme GC (MV ~ -12.5
mag) belonging to the GC system of the elliptical galaxy NGC 5044.
