A guest cannot leave a group. If there is only a group admin, he cannot leave the group.
To leave a group:
Click on the group's Settings icon
Click on Leave this group
When you leave a group:
The group no longer appears in the in the left-hand navigation menu, but you can join it again by clicking on Join in the left-hand menu
The group's content no longer appears in your news feed
You can no longer participate within the group (posting, comments, voting)
You will no longer appear as a group member
You can still view the content of an open group without being a member.