An apparatus, clustered computer system, and program product rely on cluster-private group names to perform accesses to groups that are resident in a clustered computer system. Thus, for a cluster-accessible group, all nodes capable of participating in a cluster are configured to map to the same cluster-private group name for that group, so that any external user that has access to the clustered computer system can access the group name and utilize the group name to initiate operations by the group.