How to delete Facebook group
Step 1:
Navigate to the main page for the Group you intend to delete by clicking the group name on the left navigation panel.
Step 2:
Click on the Settings icon. It's the small gear at the top right of the group page.
Step 3:
Click on the About tab. To the left of the "Find a Member" entry field, click on the menu and select All Members. 
Step 4:
Remove members. One at a time, click on the gear icon under the group member's name, and from the menu, select Remove from Group. NB: Make sure you don't remove yourself till the very end.
Step 5:
When you're the last person, Remove Yourself.
Facebook will ask you to verify that you wish to leave, and that the group will closed if you do so.
If you're sure this is what you want, go ahead and leave the group.
The group will be deleted.
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