# Sylow and 168

Algebra Level 4

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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