Adding a class to a button in a button group

I need to apply some styling to buttons within a button group. Ideally this would be a reusable CSS class, so different button styles may be used across the site and within different button groups without having to set each different individual property each time you want to use a different button style, or to implement styling not available from the editor.

When editing a button in a button group, there is no ‘Advanced’ tab (such as what a single button has), which allows you to apply a class. I don’t see a way to apply a class directly to any buttons within a button group.

You could apply a class to the group itself of course, and then target the buttons within it, but that does not promote reusable button styles, or the ability to use different button styles within different button groups.

Is there something that I’m missing here? Or is there a way to get the ‘Advanced’ tab for buttons within a button group, so that I may individually apply a class?