Finding to which server a group belongs

Aloha everyone,

I have a problem that puzzles me and I hope there is a simple
answer that I've overlooked.

Okay, I'm in a group summary buffer, say INBOX.  I poll
several IMAP servers.  I want to know from which server this
group was populated.

It's sometime possible to figure it out from the variable
gnus-summary-buffer, but not always; for instance
nnimap+fastmail:Archive is easy but INBOX is not, especially
as several servers provide INBOX with no further clues in the
name.

So how do I programmatically determine the 'parent' server of
the group?

Mahalo in advance for any ideas,

-- 
Bob Newell
Honolulu, Hawai`i

- Via GNU-Linux/Emacs/Gnus/BBDB