Sylow and 168

Algebra Level 5

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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