An ALMA observation of the early-type galaxy NGC 5044, which resides at the center of an X-ray bright group with a moderate cooling flow, detected 24 molecular structures within the central 2.5 kpc. The masses of the molecular structures vary from 3 × 105 M ? to 107 M ? and the CO(2-1) linewidths vary from 15 to 65 km s-1. Given the large CO(2-1) linewidths, the observed structures are likely giant molecular associations (GMAs) and not individual giant molecular clouds (GMCs). Only a few of the GMAs are spatially resolved and the average density of these GMAs yields a GMC volume filling factor of about 15%. The masses of the resolved GMAs are insufficient for them to be gravitationally bound, however, the most massive GMA does contain a less massive component with a linewidth of 5.5 km s-1 (typical of an individual virialized GMC). We also show that the GMAs cannot be pressure confined by the hot gas. Given the CO(2-1) linewidths of the GMAs (i.e., the velocity dispersion of the embedded GMCs) they should disperse on a timescale of about 12 Myr. No disk-like molecular structures are detected and all indications suggest that the molecular gas follows ballistic trajectories after condensing out of the thermally unstable hot gas. The 230 GHz luminosity of the central continuum source is 500 times greater than its low frequency radio luminosity and probably reflects a recent accretion event. The spectrum of the central continuum source also exhibits an absorption feature with a linewidth typical of an individual GMC and an infalling velocity of 250 km s-1.
