The locking cylinder has a basic code which can be changed using at least one change key (17, 17′). A rotor (3) is mounted in a cylinder housing (2a, 2b) and has a keyway (4) into which a shank of a standard key which is provided with control surfaces 18 can be pushed in order to position the tumblers which are arranged in three first rows (A, B, C). Further tumblers have coding elements (13) which are arranged in further bores in the cylinder housing (2a, 2b) in a programming position of the rotor (3). The change key (17, 17′) interacts with three further rows (D, E, F) of tumblers in the programming position, these tumblers being arranged in slides. These further rows (D, E, F) each contain tumblers having coding elements (C). The locking cylinder can be produced with a smaller outside diameter and be installed in a particularly cost-effective manner.