S8S_8 inside AnA_n

Algebra Level 5

What is the smallest positive integer nn such that there is an injective homomorphism ϕ ⁣:S8An \phi \colon S_8 \to A_n?

Notation: S8S_8 is the symmetric group on 8 symbols, and AnA_n is the alternating group consisting of the even permutations on n n symbols.

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