A double clutch of a double clutch transmission is described and illustrated, and can include an inner clutch which is connected to an inner shaft and has an inner disk carrier for inner disks; an outer clutch which is connected to a hollow shaft arranged co-axially with respect to the inner shaft and has an outer disk carrier for outer disks; and a drive member arranged on a drive shaft and having inner and outer drive disks which can be operatively connected to the inner or outer disks and which form an inner clutch pack or an outer clutch pack together with the disks; wherein a common disk carrier for both clutch packs is attached to the drive member; the disk carrier includes two hubs associated with the clutch packs and engaged within one another; and each hub comprises a plurality of teeth.