Apple's announcemnt on TestFlight Groups says:
Organize your testers into groups to quickly send builds, provide separate instructions on where to focus, and apply an action to several testers at once in TestFlight
How do I do this? I have my groups set up, my build has been uploaded and passed Beta App Store review. But I can't figure out how to send the load to a specific group.
It's somewhat misleading. You can only create a single list of testers for an app, and you send the build to those testers. If you want to change who gets it for the next build you send, you can modify the list, but you cannot send out multiple builds to different groups at once.
Groups only come into play as a filtering mechanism when you're adding external testers to the tester list for your app. So, if you have a group set up and you want to send a build to that group, you'd do this:
My guess is that isn't what you were hoping to do, but that's all the 'Groups' functionality does for you - it's just a way to tag your testers. I only see it being helpful if you've got multiple apps with different sets of testers, and you want to be able to easily maintain the separate lists of testers.