The Group object cannot be reported on. You can view and edit the lists from Setup but you can pull a list in Salesforce Developer Console that will include the members of each Group.
To open the Developer Console, click on Setup (gear icon) and choose Developer Console. Be sure the Query Editor tab is highlighted.
Here are some SOQL queries to help:
Get All Group Names
Enter the following in the Query Editor.
Select ID, Group.name from Group where type = ‘Regular’
Click the Execute button
Get User Information for All Members of a Group
Enter the following in the Query Editor and replace <GroupName> with the name of your Public Group.
select id, name, email, isactive, profile.name, userrole.name, usertype
from user
where id in
(select userorgroupid from groupmember where group.name = ‘<Group Name>’)
Click the Execute button.
Get All Groups for a User
Enter the following in the Query Editor and replace <Username> with the name of the user.
SELECT Id, Group.name
FROM GroupMember
WHERE UserOrGroupId IN (SELECT Id FROM User where name = ‘<UserName>’)
Click the Execute button.
