Also, I forgot. Make sure you share the folder with the group first, and then push it to their Drive. It's easy to do in Drive, but can be done in GAM too.
Add group to folder.
gam user <folder owner email> add drivefileacl drivefile id <folder ID> group <group address> role <commenter|editor|organizer|owner|reader|writer>
Push folder to group users' My Drive.
gam group <email address of your group here> update drivefile id <The ID of your folder here> parentid root