What is the difference in SR gained when playing solo vs a group?
As far as I understand things from numerous different Blizzard statements:
There's a consecutive win bonus on SR. The more consecutive games you win, the more SR you get. Although I'm not sure about the following, it would appear that the consecutive bonus is different for different group sizes. That's why you weren't getting as much with a larger party than all by yourself.
Another point worth mentioning is how much SR you get has absolutely nothing to do with group size, how well you did, how well any of the group members did, etc. The game takes how well you performed and compares you to other players of the same hero in a similar MMR (Match Making Rank) to yours. This means if you're an above average player with a given hero, you'll get more SR if I played the same hero, and the game ended in exactly the same way.