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We estimate the total amount of diffuse ionised gas to be of the order of (~5 \u00b1 3) \u00d7 10<jats:sup>10<\/jats:sup> <jats:italic>M<\/jats:italic><jats:sub>\u2299<\/jats:sub> and explore its physical properties to understand its origin and the source(s) of the ionisation. The MUSE data allow the identification of a dozen group members that are embedded in this structure through emission and absorption lines. We extracted spectra from small apertures defined for both the diffuse ionised gas and the galaxies. We investigated the kinematics and ionisation properties of the various galaxies and extended gas regions through line diagnostics (R23, O32, and [O\u2009<jats:sc>iii<\/jats:sc>]\/H<jats:italic>\u03b2<\/jats:italic>) that are available within the MUSE wavelength range. We compared these diagnostics to photo-ionisation models and shock models. The structure is divided into two kinematically distinct sub-structures. The most extended sub-structure of ionised gas is likely rotating around a massive galaxy and displays filamentary patterns that link some galaxies. The second sub-structure links another massive galaxy that hosts an active galactic nucleus (AGN) to a low-mass galaxy, but it also extends orthogonally to the AGN host disc over ~ 35 kpc. This extent is likely ionised by the AGN itself. The location of small diffuse regions in the R23 vs. O32 diagram is compatible with photo-ionisation. However, the location of three of these regions in this diagram (low O32, high R23) can also be explained by shocks, which is supported by their high velocity dispersions. One edge-on galaxy shares the same properties and may be a source of shocks. Regardless of the hypothesis, the extended gas seems to be non-primordial. 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