Confusingly, there is no direct facility to delete a Facebook Group. However, a Group that has no members is automatically deleted. So to delete a Facebook Group, first remove all of the members, and then leave the Group yourself.
View the How To Delete A Facebook Group presentation on Scribd.
Slide 1 – Remove Members
Navigate to the Group admin page, then the Members tab. Delete all the members leaving only yourself.
Slide 2 – Leave Group
Navigate to the Group page and click Leave Group.