It's easy to add an image (small and large) to a control in a group but I can't find where to set images for the group itself. I can add entire group to the quick access toolbar but since i never set an image on the group it always appears as a broken icon.
By default, the tool representing the RibbonGroup in the QAT (the PopupRibbonGroupTool) uses the Image set on the RibbonGroup.Settings.CollapsedAppearance. This is the image that would display if the RibbonGroup needed to collapse down to a drop down button to save space.