→Relationship between irreducibles and those of subgroups: Frobenius reciprocity
===Relationship between irreducibles and those of subgroups: Frobenius reciprocity===
Here, the rows correspond to irreducible representations of the whole group, and the columns correspond to irreducible representations of the
subgrop. The number in a cell is the multiplicity of the column representation in the restriction of the row representation to the subgroup; equivalently, it is the multiplicity of the row representation in the [[induced representation]] from the column representation of the subgroup to the whole group. These numbers are equal by [[Frobenius reciprocity]].
Between the whole group and its 3-Sylow subgroup: