There are 5 ranks in Groups, from highest to lowest they are Leader, CoLeader, Elder, Officer and Member.

Every Group rank above 'Member' can Promote, Demote, Kick, and Accept.

There are some limits to the Promote, Demote, and Kick actions that can be done by anyone higher than Member rank. Promote can only be done by a player up to their own rank, while Demote, and Kick can only be done by a player to anyone of a lower rank. 

The Leader/Co-Leader only permissions are to edit the Group description, and switch the Group between Open or Closed.