Do not show any initials.
The concept of profile for single persons and groups is entirely different, so you shouldn't show the initials for people in the group.
Think about this: you're adding a lot of friction, in visual terms this is really confusing, and in terms of usability nobody would get what all that noise means. It's really important to understand whether you're dealing with an individual or a group, so you shouldn't try to disguise the group as an individual.
But if the reasons above are not enough, think about lack of versatility. Take a look at a very common case you will face:
Group A was formed by AB, CD, EF
and thus you show the initials for these individuals.
Now GH and IJ
join the group, while AB and CD
leave it.
Now the group is.... ABCDEF
even though AB and CD
are not part of the group. Furthermore, GH and IJ
are not represented, which makes no sense at all.
So.... you can change the group to EFGHIJ
. Easy, right? Well, think twice: now anyone that interacted with ABCDEF
will not know who is EFGHIJ
!
In short: get rid of those initials: they're really bad UX, they bring a lot of problems, and they bring no benefit at all!
PS: Also, aren't you allowing your users to name a group any way they want?