Group travel earns miles the same way regular travel does, it totally depends on the booking class. I was just on a group travel with SQ but the booking class was heavily discounted booking class G so no miles earned.
Same with upgrading. First, depending on if the booking class is upgrade-able. But also the catch is that all travelers on the same booking have to be upgraded at the same time. So either you upgrade everyone, or contact the airline to split the booking and get yourself a new reservation reference number just for you, then you can try to upgrade just yourself.
In my experience, these group travel tickets are usually very low or no mileage earning because of their low price, and so don't have your hopes up too much for a big earn or upgrade possibility.