A friction clutch having a clutch ring and having two clutch disks, which are mounted so as to be rotatable about a clutch axis of rotation and on which friction surfaces are formed, is presented. In this case, the clutch ring and the clutch disks can be moved parallel to the clutch axis of rotation and relative to one another in such a way that, for torque transmission, first friction surfaces on each of the clutch disks can be moved into frictional surface contact with a respective second friction surface on the clutch ring. A first and a second friction surface in each case are matched to one another as a friction surface pair, having in each case a friction surface curved convexly in the direction of the clutch axis of rotation and a friction surface curved concavely in the direction of the clutch axis of rotation.