Based on their documentation—which, albeit, I know has many classes omitted—Unreal Engine has ~6900 classes. That number probably gets greatly multiplied, though, if you count generated classes.
And it's managed in git.
I can't find the link, but I remember an Epic engineer saying that they use Perforce internally and do a 2 way sync with Github.
Correct, it is managed in Perforce and MIRRORED onto Github.