Within the App the Group Leader has the ability to do the following:
Edit the Group Info page About section
View the list of members in the group
Add/remove members to/from the group
Add/remove leader status from a group member (unlimited number of leaders)
Make a member a leader/remove leader status from a member
Invite others to the Group via SMS (or other App on - this would be a lookup from the leader's contacts in their phone)
When someone requests to join a Private Group, Leaders will receive notifications and can Accept or Decline the new member. If approved, members will receive a notification that they have been added to the group.