Where Broadcast setup and processing is more the exception, Group definition (linking) and Group messages are the norm. Whenever devices are linked together Insteon uses Group command protocol exclusively. In most houses I would guess that 95% of Insteon traffic is Group related, device controlling device. I say that only to put Group processing in perspective. It is the most tested most exercised aspect of Insteon. If Group processing is not working something in the setup or definition is amiss.
After a Factory Reset all EZIOxx Inputs have no Group numbers assigned and no link records in the link database. In the simplest definition when using the Set button to link an EZIOxx device as a Controller to a Responder the Input is identified by the number of times the Set button is tapped. When done with the Set button Input 1 is assigned Group 1, Input 2 is assigned Group 2, etc so Group number to Input number is predictable. If software/firmware is defining the linkage any Group number convention can be established. For example, the ISY assigns Group 9 to the first Input, incrementing the Group number by one for each subsequent Input. So long as the Controller device and the Responder device use the same Group number in related link records any Group number can be used. Just so someone does not jump in and correct that statement there are some limitations. Group 0 cannot be used, Group 255 cannot be used as that is reserved for All On/All Off but in general any Group number between 1 and 254 is okay so long as the same Group number is used in the “Controller of” link record in the Controller and the “Responder to” link record in the Responder and that Group number has been assigned to the respective Input.
If you are thinking about using the SHN Utility to verify what information has been stored in an EZIOxx device I can guide you through the process.