When creating a group, you have the ability to assign a group admin and a group leader.
Group Admin
A group admin is a position that any member of the group can be assigned. A member does not need to be the leader of a group to be a group admin.
See here for how to update a member's position.
A group admin has the following abilities with their group:
Can send e-mails to groups members through the member listing page
Can upload and delete group files
Can start group discussions
Can delete group discussion threads and messages
Can see notes inside a group
A group admin can NOT:
Edit group details
Delete groups
A group admin is easily identified from the member listing with the admin banner.
Note
A group admin will also have these permissions over any subgroup under the group that they are an admin of.
If the membership of a group is set to Approval Required, group admins are emailed to decide whether the person should be approved or denied membership.
Group Leader
A Group Leader doesn't get any special access or permissions. It's simply a way to denote who the leader is and they get a special place where they are listed online.
If someone is not a group admin, then permission-wise within the group, they are no different than any other group member.
A leader can also optionally be an admin, but that's not always desired. This is why Is Admin? is a separate setting.
In other words, besides a label, leaders have the same access rights as a normal group member (assuming they aren't set as a group admin).
Special Permissions
Non-admin group members can be granted special access to help manage portions of the group. When editing a group member, an Access tab is available.
Only group admins and users with Limited Write Groups are able to set special permissions for group members. Available options:
Can manage events — Add, edit, and delete group events.
Can manage member roster and positions — Add, edit, and delete group members and positions. This will not allow them to edit any group admins or modify member permissions. Group members with this access will not be able to edit other group admins nor will they be able to set permissions for any members. They also will not be able to grant group admin access to any members.
Can manage attendance — Enter and edit group attendance. While this permission allows them to create group events, they will not be able to edit the event itself unless they have the Can manage events permission as well. Member will not be made an organizer of any events created for attendance.
Can manage files — Upload and delete group files.
Can manage discussions — Start discussions and delete individual messages.
Can manage notes — Add, edit, and delete group notes.
A filter is part of the group listing named Has Special Access? which will help return members with elevated access to the group. Members with special permissions will also have a yellow special access label within the Type column. Clicking on this will open the Edit Member pop up with the Access tab already opened.