We don't currently have a way to break down specific response data by group. Since contacts could exist across multiple groups that a mailing might have been sent to, that creates a unique challenge in calculating the response data for those groups (i.e. does that address count in just one of the groups or in all of the groups, etc.)
One thing you could do, if you're looking for specific information on a groups response to a particular mailing is to use our Segmenting tool to find people "in Group X" who "opened Mailing Z" or "clicked on Mailing Z" . That would give you an exportable list of folks within a specific group who opened or clicked on a specific mailing, depending on how you set that up.
Does that help you find the information you're looking for?