Seems to be a couple of ways to do this:
Option A: Groups are non-hierarchical. A character has a set of groups (one might be himself only), and derives his net opinion from the opinion of all his groups, all groups being treated equally.
Option B: Same as A but each group has an associated affinity factor, which determines how much weight that group's opinion bears on the character's net opinion.
Option C: Hierarchical groups. A character again has a set of groups, but each group has an optional parent group. The ancestral distance of a group reduces the weight of its influence on the character.
The equation becomes more complicated when you consider that a character must not only account for the opinion of all of his own groups, he must consider those opinions about all of the groups of the subject in question!
In other games its typical for characters to be in one and only one group, and for the player to be in his own group. That makes it very simple to figure out opinions. And it seems like a reasonable simplification, so I'll go with that.
So...