# Sylow and 168

Let $G$ be a simple group with 168 elements. How many elements of order 7 does $G$ contain?

Notation: An element $g\in G$ has order 7 if $g^7 = 1$ but $g^x \ne 1$ for any positive integer $x<7.$ (Here $1$ is the identity of the group $G.$)

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