I am trying to create a group the App and Games group API, using the Graph API explorer. I am getting the following error. Do you have to be an approved app center app to be able to use this feature?
(#3) App must be on whitelist
Yes, there's a note to this effect on the App and Game Groups documentation:
Your app must be in the App Center to be able to use Game Groups.
And on the blog post which announced the feature:
To ensure a high quality experience for users, we're making this feature available as a beta to all apps and games listed in App Center, and will continue to iterate over time. You can get started now by reading our concepts and reference documentation.