It is given that \( 19!\) equals \[\overline{121\, 645\, 100\, 408\, abc\, 000}. \]

Determine the value of \( \overline{abc} \).

**Details and assumptions:**

- \( \overline{abc}\) means \( 100a + 10b + 1c\), as opposed to \( a \times b \times c\). As an explicit example, for \(a=2, b=3, c=4\), \(\overline{abc} = 234\) and not \( 2 \times 3 \times 4 = 24\).

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