How to embed a facebook group (Not a regular page) into iframe on wordpress?
There's a couple of great plugins for this. One is called "Feed Them Social", and it does everything you're asking for. There's a free and paid version, and they support FB groups. You can search for it in the "Add Plugin" option page in Wordpress.
Option two is the one I have installed in one of my sites, called "Custom Facebook Feed", by Smash Balloon. Again, you can search for it on the "Add Plugin" page of your site. This one is free and works great, and it even displays your group's header and FB faces!