As of September, 2016, the following procedure can be used to create a Group in Google’s Contacts App. This is the one feature of Google Apps that seems to be a little harder to do than it should be. We hope they fix it..
Let's say you want a Group for all the Elementary Teachers and one for all the Middle and High School teachers.
Sadly, there seems to be no way at this time to export groups or share groups. I'm betting this is a feature that will be added in the future. Google is continuously improving their products.
To illustrate the the steps, here’s what it currently looks like in the left side bar where you create a new group:
Here is a picture of the Directory listing for our domain. You can see the check boxes that appear on the left-most column in place of the user’s icon when you mouse over it or whenever you are actively making selections. Ater all your selections have been made, you can see the “Add to Contacts” icon in the top bar. This icon is the first in that set of buttons in the upper-right corner of the picture and looks like a silhouette of a person with a plus sign.
This image shows a list of “All Contacts” from which I can open the contact’s cards one at a time to assign their group membership.:
And, finally, here is what a contact card looks like. Note the icon in the bottom left that shows Andrea Sewell is a member of the Faculty group. A contact who belonged to no group would have the “Add to Group” icon instead. Also note the left pointing arrow in the upper left corner of the card. Click this arrow to go back to the Contacts screen.