Try exploding something into 500 pieces (or less) and have it on auto, and you'll see lots of barycenters that exist for a brief amount of time.
Anyways, at this time, there is one barycenter in the save I attatched (it's already zoomed in), although there were four earlier. They tend to come and go. Turn on labels and parent > child gravitational relationships for understanding of why the barycenter is there.
Edit: Actually, heres a jupiter that I exploded into 500+ pieces, turn on labels and you'll see there are a lot of barycenters. Granted theres a ton of bodies compacted near each other, which is why they are there, but they'll dissapear after a while.