We study the values of the Möbius function $μ$ of intervals in the containment poset of permutations. We construct a sequence of permutations $π_n$ of size $2n-2$ for which $μ(1,π_n)$ is given by a polynomial in $n$ of degree 7. This construction provides the fastest known growth of $|μ(1,π)|$ in terms of $|π|$, improving a previous quadratic bound by Smith. Our approach is based on a formula expressing the Möbius function of an arbitrary permutation interval $[α,β]$ in terms of the number of embeddings of the elements of the interval into $β$.