Members of groups are delegated to one of three different roles: Admin, Moderator, or Member. To modify the level of authority of a user within your group, or a group in which you are an admin, simply find that user in the “+members” page of the group. Click the cog icon beside their channel link, and you may modify their level of authority. You may also choose to remove a user from the group via this menu.
Member - Post content to feed or conversations, join gatherings, vote, comment, remind
Moderator - All member controls, plus ability to accept/reject posts to feed (if group is moderated), accept/reject requests to join (if group is closed), remove any unwanted users or content
Admin - All moderator controls, plus ability to edit group description, banner and avatar, appoint moderators and admins