Context. Galaxy groups are more susceptible to feedback from the central active galactic nuclei (AGNs) due to their lower gravitational binding energy compared to clusters. This makes them ideal laboratories to study feedback effects on the overall energy and baryonic mass budget. Aims. We study the LOFAR-detected galaxy group Nest200047, where there is clear evidence of multiple generations of radio lobes from the AGN. Using 140 ks Chandra and 25 ks XMM-Newton data, we investigated thermodynamic properties of the intragroup medium, including any excess energy due to the central AGN. We also investigated the X-ray properties of the central black hole and constrained the 2‑10 keV X-ray flux. Methods. We used spectral analysis techniques to measure various thermodynamic profiles across the whole field of view. We also used both imaging and spectral analysis to detect and estimated the energy deposited by potential shocks and cavities. Due to the faint emission from the object beyond the core, various background effects were considered. Results. Nest200047 has significant excess entropy, and the AGN likely contributes to a part of it. There is an excess energy of (5‑6.5)×1060 erg within 400 kpc, exceeding the binding energy. The pressure profile indicates that gas is likely being ejected from the system, resulting in a baryon fraction of ∼4% inside r500. From scaling relations, we estimated a black hole mass of (1‑4)×109 M⊙. An upper limit of 2.1×1040 erg s‑1 was derived on the black hole bolometric luminosity, which is ∼2.5% of the Bondi accretion power. Conclusions. Nest200047 is likely part of a class of over-heated galaxy groups, such as ESO 3060170, AWM 4, and AWM 5. Such excessive heating may lead to high quenching of star formation. Moreover, the faint X-ray nuclear emission in Nest is likely due to the accretion energy being converted into jets rather than radiation.
