From Online Manual
Group Moderators are members that can manage a membergroup. Group moderators have access to the moderation center from where adding and removing members can be carried out. From the moderation center, group moderators can accept and decline requests to join a membergroup (Profile > Group Membership).
Please note that for a member to be able to request membership for a group, that group must be set to request in the membergroup settings.
Although being able to add and remove members, group moderators do not have the ability to change a group's name and online (or display) color. These permissions stay solely with the administrators.