I think this should be `Power.precedence` that is 590.

It's not that well documented, but I found:
"Forms such [`Integrate[a, b]`] as have an "outer" precedence just below Power, as indicated in the table above, but an "inner" precedence just above [`Sum`]. The outer precedence determines when  needs to be parenthesized; the inner precedence determines when  needs to be parenthesized.", which doesn't much sense to me, but I checked

`s = Infix[{a, b, c}, "\[Precedes]\[Succeeds]"]; Table[{k, PrecedenceForm[s, k]^2}, {k, 580, 600}]`

and found that at precedence 590 is when the parentheses are removed from the result (`Precedence[Power]` is 590).

Sorry if I've explained this badly.