As far as I know, there is no plan to set up an official facebook group. The company that owns this site, IB, bought it as a commercial venture. Creating a facebook group would draw members away from this site and there would be no benefit to IB - just loss. The current fb page is designed to send traffic to the site, not pull it away.
I belong to a few fb groups and they are fun
If you want to create one, you can do it and invite members here that you know. But you would not be able to use the 3fc name due to the trademark. I would suggest posting it in general chatter.
Thanks for asking