Blocking a group on Facebook will prevent you from seeing any posts made by the group or any users who have joined that group. In order to block a group on Facebook, visit your account settings page, and then follow These Steps:
1) Scroll down to the Apps section under Account Settings.
2) Click edit next to Manage Your Groups
3) Choose the group you wish to block
4) Click Block Group at the bottom of the page
5) Click Confirm Block
Find The Group
You can find the name of a group by clicking the Groups tab in your newsfeed. Once you click, search for the name of the group you want to block. You will then see a list of people that are members of that particular group and how many members there are. Click on Report Group to report it as spam or abuse, which will remove it from your newsfeed and make it so you cannot join.
Open Group Notifications Tab
This tab is a list of all the groups you are currently subscribed to. If you want to unsubscribe from a group, click Leave Group which will be located at the top right corner of the screen. To block an entire group from contacting you, click More Actions and then Block Group. You will be asked to confirm your decision by clicking Yes. This is how to block a group on Facebook.