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Here we analyze radio, optical, and X-ray data for the peculiar cluster Abell 578. This cluster is not fully relaxed and consists of two merging sub-systems. The brightest cluster galaxy (BCG), CGPG 0719.8+6704, is a pair of interacting ellipticals with projected separation ~10 kpc, the brighter of which hosts the radio source 4C+67.13. The Fanaroff–Riley type-II radio morphology of 4C+67.13 is unusual for central radio galaxies in local Abell clusters. Our new optical spectroscopy revealed that both nuclei of the CGPG 0719.8+6704 pair are active, albeit at low accretion rates corresponding to the Eddington ratio $$\sim {{10}^{-4}}$$ (for the estimatedmore » black hole masses of $$\sim 3\times {{10}^{8}}\;{{M}_{\odot }}$$ and $$\sim {{10}^{9}}\;{{M}_{\odot }}$$). The gathered X-ray (Chandra) data allowed us to confirm and to quantify robustly the previously noted elongation of the gaseous atmosphere in the dominant sub-cluster, as well as a large spatial offset (~60 kpc projected) between the position of the BCG and the cluster center inferred from the modeling of the X-ray surface brightness distribution. Detailed analysis of the brightness profiles and temperature revealed also that the cluster gas in the vicinity of 4C+67.13 is compressed (by a factor of about ~1.4) and heated (from $$\simeq 2.0$$ keV up to 2.7 keV), consistent with the presence of a weak shock (Mach number ~1.3) driven by the expanding jet cocoon. As a result, this would then require the jet kinetic power of the order of $$\sim {{10}^{45}}$$ erg s^–1, implying either a very high efficiency of the jet production for the current accretion rate, or a highly modulated jet/accretion activity in the system.« less