I’m not sure exactly what you mean by the question. If you want a profile that will be used by the helpdesk or some other group for profile maintenance, I would create individuals profiles that have the *SECADM special authority, *LMTCPB *YES, and a menu option that guides them through profile creation, admin or deletion steps. Latest greatest security practice says special authorities should not be granted to group profiles but to individuals. Those same standards recommend against using IBM supplied profiles for group profiles because they are well known and more likely to be attacked by hackers or malicious programmers.
If you mean that you want to create a group profile to base other profiles on, any profile you create will become a group if you create another profile with that profile as the group profile.
One strategy is to make your object owner for an app, say the profile OBJOWNR that owns a library and all of the objects in it, the group profile for the business group that owns the application and the data. The library and objects can then have an authorization list that grants other group profiles lower levels of object authority. This way you can have a group without existence rights so they can’t delete objects, or in todays SOX and HIPAA world you will probably want a programmer group such as PGMR(you create that) that has read only rights so they can do research without being able to update production.