 Young subgroup

For a composition $\lambda$ of $n$, a Young subgroup permutes independently the blocks of a set partition of $\{1,\dots ,n\}$ with sizes ${\lambda }_i$, and is isomorphic to $S_{{\lambda }_1}\times \cdots \times S_{{\lambda }_r}$. Reordering the block sizes gives a conjugate subgroup. Inducing its trivial representation gives a Young permutation module.