Missing digits in 19!

\[\large 19! = \overline{12164510{\color{blue}a}4{\color{blue}a}8832000} \]

Determine the digit \({\color{blue}a}\).

Note: \( 19 ! = 19 \times 18 \times 17 \times \cdots \times 2 \times 1 \)

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