Yes , Facebook groups are really great for your customer relationships !
This is a fantastic paper from socialmediaexaminer.com, explaining how you can use Facebook groups for business, engaging customers, finding hidden opportunities, generating qualified leads, getting real customer feedback and supporting your community ! And if you have the right analytical tool to do the job for you , well, just imagine.
http://www.socialmediaexaminer.com/facebook-groups-enhance-customer-relationships/
Enjoy it.