Create Google app with redirect URL and have your client ID and client secret
If your CiviCRM is already connected to Google app, you have to delete the access token in setting table in order to connect to new Google App.
Installation
Install the extension manually in CiviCRM. More details here about installing extensions in CiviCRM.
Fill in GOOGLE_CLIENT_KEY and GOOGLE_SECERT_KEY in googlegroup.php
Configure Google Group details in Mailings >> Googlegroup Settings(civicrm/googlegroup/settings?reset=1)
Usage
Warning: Contacts in CiviCRM will exactly match in Google Group after sync. That means contacts which are not in CiviCRM but in Google Group will be removed during the sync to keep contacts same in both
Sync CiviCRM with Google group in Mailings >> Sync Civi Contacts To Googlegroup