Day 24: The Missing Digit

Rudolph was tired of pulling the sleigh everywhere.

So, using his awesome intellect, he calculated \(2015!\) and then wrote his answer down on a piece of paper. But unfortunately he missed out one digit and then couldn't remember what it was.

His (also intelligent) friend tried to help him and found that the sum of the digits was 23514.

What is the missing digit?

This problem is part of the Advent Calendar 2015.

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