We have had some success with User creation thanks to the previous thread, we now need to know how to do the following:

Creation of a new group via API? We always get 'you do not have permission to create a group' (or words to that effect) even though we used UserManager.Authenticateuser()

How do we send out a manually-created invitation via the API using the group of users created in the previous step?

Any sample code for this would be greatly appreciated.