Sage Peopleself service People Groups use Sage People Permission Sets to grant users an appropriate level of access to People Groups features.
Self service Groups extend the existing Sage People Groups feature, which previously relied on Profiles only. If you have a long-standing org, this means you may need to manually adjust standard Profiles to ensure all users have appropriate access to People Groups as determined by the Permission Sets. If you have cloned standard Sage People Profiles as a basis for your custom Profiles, you should check and adjust the cloned Profiles too.
Profiles and permission sets provides more information about Profiles and Permission Sets in general. See Adjusting Profiles for People Groups for information about the checks you should make and how to adjust the Profiles.