Sylow branching coefficients for symmetric groups

Let $p\ge 5$ be a prime and let $n$ be a natural number. In this article we describe the irreducible constituents of the induced characters $\varphi {\uparrow }^{{\mathfrak{S}}_n}$ for arbitrary linear characters $\varphi$ of a Sylow $p$-subgroup of the symmetric group ${\mathfrak{S}}_n$, generalising earlier results of the authors. By doing so, we introduce Sylow branching coefficients for symmetric groups.