After logging in to your Carthage Google account (Gmail, Drive, etc.), click on the apps icon in the upper right corner. Choose the "My Account" option or go to https://aboutme.google.com.
Choose "Personal Info & Privacy" and then "Your personal info."
Under "Your personal info" click on "About You."
Click the pink "+" symbol on the bottom right.
Click the pencil icon next to the "Work contact info" section to edit. Click "OK" to save.
Now you want to share this information only within the Carthage domain, rather than making it public. Click the bottom of the "Work contact info" box where it defaults to "Private." Then click "Your Organization." The changes are saved automatically.
After completing the steps, people with the @carthage.edu address should now be able to see your newly shared information within Google contacts.