I dont think any of the billing plugins go as deep as per group, i know they do the billing memberships but not as far as per group level.
For now you may have to rely on making group pages and setting up individual paypal buttons for each group page.
For example you could create a page thru admin called group1_membership and then on that page display a paypal hosted saved button called grp1 . Then the members of that group1 are given the group1_membership page link as part of their group info.
When they pay you take them back to a generic thank you page (or generic cancel page if the cancel) and on that page you tell them that their account will be updated within 24hours as paid.
do the same for group2 and so on.. (but all use the same thank you and cancel page)
Thats all i can think of to do at this time until someone dev a plugin that will bill on the group level.