# $$S_8$$ inside $$A_n$$

Algebra Level 5

What is the smallest positive integer $$n$$ such that there is an injective homomorphism $$\phi \colon S_8 \to A_n$$?

Notation: $$S_8$$ is the symmetric group on 8 symbols, and $$A_n$$ is the alternating group consisting of the even permutations on $$n$$ symbols.

×