Is Wall of Stone suppressed by Antimagic Field?

I noticed that the Wall of Stone spell includes this interesting tidbit in its first sentence (emphasized in bold):

A nonmagical wall of solid stone springs into existence at a point you choose within range.

The remainder of the spell mainly deals with how the wall can be shaped, and what happens to trapped creatures. The other relevant bit is the last paragraph:

If you maintain your concentration on this spell for its whole duration, the wall becomes permanent and can’t be dispelled. Otherwise, the wall disappears when the spell ends.

So, the wall of stone is nonmagical, but the spell can be dispelled, which causes the wall to disappear. So, is the wall magic or not? What happens if another wizard casts Antimagic Field around the wall? Will it suppress the spell within the region? And if so, what does that mean for the "nonmagical" wall created and maintained by the non-nonmagical spell?

And even though I’m pretty sure I know the answer for this one, I’ll ask it for the sake of completeness: what effect does Antimagic Field have on a wall of stone that has already been made permanent by concentrating on it for the full duration of the spell?