Comment 4 for bug 72732

"Group name" is slightly incorrect: if a window's in a group, it has a field pointing to a(nother) window's ID, and all the windows which have that ID are in the group. The window which is pointed to is called the "group leader" and doesn't even have to be mapped.

xwininfo doesn't know about groups, but xprop does:

tthurman@haematite:~$ xprop|grep group
  window id # of group leader: 0x2400001

(where I clicked on Firefox in between.)

Specs for this are at http://tronche.com/gui/x/icccm/sec-4.html -- search throughout for "group".

Hope this helps!