We present Hubble Space Telescope Cosmic Origin Spectrograph (COS) UV line spectroscopy and integral-field unit (IFU) observations of the intragroup medium in Stephan's Quintet (SQ). SQ hosts a 30 kpc long shocked ridge triggered by a galaxy collision at a relative velocity of 1000 km s −1 , where large amounts of molecular gas coexist with a hot, X-ray-emitting, plasma. COS spectroscopy at five positions sampling the diverse environments of the SQ intragroup medium reveals very broad (≈2000 km s −1) Lyα line emission with complex line shapes. The Lyα line profiles are similar to or much broader than those of Hβ, [C II]157.7 μm, and CO (1-0) emission. The extreme breadth of the Lyα emission, compared with Hβ, implies resonance scattering within the observed structure. Scattering indicates that the neutral gas of the intragroup medium is clumpy, with a significant surface covering factor. We observe significant variations in the Lyα/Hβ flux ratio between positions and velocity components. From the mean line ratio averaged over positions and velocities, we estimate the effective escape fraction of Lyα photons to be ≈10%-30%. Remarkably, over more than four orders of magnitude in temperature, the powers radiated by X-rays, Lyα, H 2 , and [C II] are comparable within a factor of a few, assuming that the ratio of the Lyα to H 2 fluxes over the whole shocked intragroup medium stay in line with those observed at those five positions. Both shocks and mixing layers could contribute to the energy dissipation associated with a turbulent energy cascade. Our results may be relevant for the cooling of gas at high redshifts, where the metal content is lower than in this local system, and a high amplitude of turbulence is more common. Unified Astronomy Thesaurus concepts: Galaxy groups (597); Hickson compact group (729); Galaxy mergers (608); Galaxy interactions (600); Interacting galaxies (802); Intergalactic medium phases (814); Intergalactic medium (813); Cool intergalactic medium (303); Galaxy evolution (594); Galaxy processes (614); Galaxy quenching (2040); Interstellar dust (836)