The auto-generated groups are the ones the system automatically creates when you create a new Delegated Administration role. The groups created share the same name as the Delegated Administration role.
These groups are similar to the Default Group and cannot be edited by design. The only way to edit permissions of these groups is by creating other groups in the management role, and then add or remove users to and from those other groups. The only way to remove auto-generated groups in management roles is to delete the management role entirely.