  We report the discovery of a 10^4 kpc^2 gaseous structure detected in [OII]
in an over-dense region of the COSMOS-Gr30 galaxy group at z~0.725 thanks to
deep MUSE Guaranteed Time Observations. We estimate the total amount of diffuse
ionised gas to be of the order of (~5+-3)x10^10 Msun 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 of group members embedded in this
structure from 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 thanks to line diagnostics (R23, O32 and
[OIII]/H\beta) available within the MUSE wavelength range. We compared these
diagnostics to photo-ionisation models and shock models. The structure is
divided in two kinematically distinct sub-structures. The most extended
sub-structure of ionised gas is likely rotating around a massive galaxy and
displays filamentary patterns linking some galaxies. The second sub-structure
links another massive galaxy hosting an Active Galactic Nucleus to a low mass
galaxy but also extends orthogonally to the AGN host disk 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 large
velocity dispersions. One edge-on galaxy shares the same properties and may be
a source of shocks. Whatever the hypothesis, the extended gas seems to be non
primordial. We favour a scenario where the gas has been extracted from galaxies
by tidal forces and AGN triggered by interactions between at least the two
sub-structures.
