We aim to create a large sample of local post-starburst (PSB) galaxies to study their characteristic properties, particularly morphological features indicative of gravitational distortions and indications for active galactic nuclei (AGNs). The selection is based on a huge Kohonen self-organising map (SOM) of about one million SDSS spectra. The SOM is made fully available for the astronomical community, in combination with an interactive user interface. We compiled a catalogue of 2665 PSB galaxies with redshifts z < 0.4. In the colour-mass diagram, the PSB sample is found to be clearly concentrated towards the region between the red and the blue cloud, in agreement with the idea that PSB galaxies represent the transitioning phase between actively and passively evolving galaxies. The relative frequency of morphologically distorted PSB galaxies is at least 57%, significantly higher than in a comparison sample. The search for AGNs based on conventional selection criteria in the radio and MIR results in a low AGN fraction of 2 - 3%. We confirm an MIR excess in the mean SED of the PSB galaxy sample that may indicate hidden AGNs, though other sources are also possible. (Abstract modified to match the arXiv format.)
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