The invention concerns a hydraulic pump (6, 7) for a clutch mechanism (1) of a vehicle transmission, the hydraulic pump (6, 7) comprising a body (60, 70) in which there are formed a chamber (61, 71), an inlet opening (62, 72) through which a hydraulic fluid can enter the chamber (61, 71), and an outlet opening (63, 73) through which the hydraulic fluid can leave the chamber (61, 71), the chamber (61, 71) receiving at least one hydraulic wheel of the hydraulic pump (6, 7), the inlet opening (62, 72) and the outlet opening (63, 73) each opening into the chamber (61, 71) of the body (60, 70), the body (60, 70) of the hydraulic pump (6, 7) being delimited by an outer edge (80) on which at least one peripheral groove (81, 82) is formed, configured to receive a gasket (83, 84), the gasket (83, 84) being intended to provide contact sealing between the body (60, 70) of the hydraulic pump (6, 7) and a hydraulic connection interface (4) of the clutch mechanism (1).