The fate of cooling gas in the centers of galaxy clusters and groups is still not well understood, as is also the case for the complex processes of triggering star formation in central dominant galaxies, reheating of cooled gas by active galactic nuclei (AGN), and the triggering or "feeding" of supermassive black hole outbursts. We present CO observations of the early-type galaxy NGC 5044, which resides at the center of an X-ray bright group with a moderate cooling flow. For our analysis we combine CO(2-1) data from the 7 m antennae of the Atacama Compact Array (ACA) and the ACA total power array (TP). We demonstrate, using the 7 m array data, that we can recover the total flux inferred from IRAM 30 m single-dish observations, which corresponds to a total molecular mass of about 4 × 107M☉. Most of the recovered flux is blueshifted with respect to the galaxy rest frame and is extended on kiloparsec-scales, suggesting low filling factor dispersed clouds. We find eight concentrations of molecular gas out to a radius of 10″ (1.5 kpc), which we identify with giant molecular clouds. The total molecular gas mass is more centrally concentrated than the X-ray emitting gas, but is extended in the northeast-southwest direction beyond the IRAM 30 m beam. We also compare the spatial extent of the molecular gas to the Hα emission: The CO emission coincides with the very bright Hα region in the center. We do not detect CO emission in the fainter Hα regions. Furthermore, we find two CO absorption features spatially located at the center of the galaxy, within 5 pc projected distance of the AGN, infalling at 255 and 265 km s-1 relative to the AGN. This indicates that the two giant molecular clouds seen in absorption are most likely within the sphere of influence of the supermassive black hole.
