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ABSTRACT Abell 407 (A407) is a unique galaxy cluster hosting a central compact group of nine galaxies (named as ‘Zwicky’s Nonet’; G1–G9 in this work) within a 30 kpc radius region. The cluster core also hosts a luminous radio active galactic nucleus (AGN), 4C 35.06 with helically twisted jets extending over 200 kpc. With a 44 ks Chandra observation of A407, we characterize the X-ray properties of its intracluster medium and central galaxies. The mean X-ray temperature of A407 is 2.7 keV and the M200 is $$1.9 \times 10^{14}\, {\mathrm{M}_{\odot }}$$. We suggest that A407 has a weak cool core at r < 60 kpc scales and at its very centre, <1–2 kpc radius, a small galaxy corona associated with the strong radio AGN. We also conclude that the AGN 4C 35.06 host galaxy is most likely G3. We suggest that the central group of galaxies is undergoing a ‘slow merge’ procedure. The range of the merging time-scale is 0.3 ∼ 2.3 Gyr and the stellar mass of the future brightest cluster galaxy (BCG) will be $$7.4\times 10^{11} \, \mathrm{M}_{\odot }$$. We find that the regions that overlap with the radio jets have higher temperature and metallicity. This is consistent with AGN feedback activity. The central entropy is higher than that for other clusters, which may be due to the AGN feedback and/or merging activity. With all these facts, we suggest that A407 is a unique and rare system in the local universe that could help us to understand the formation of a massive BCG.