 Irreducible characters separate conjugacy classes (source code)

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= Irreducible characters separate conjugacy classes
{title2=$(\forall\chi\in\operatorname{Irr}(G),\ \chi(g)=\chi(h))\Longleftrightarrow g\sim_Gh$}

The <irreducible characters> of a <finite group> form a basis of its complex <class functions>. Equality of every irreducible character value therefore forces equality of every class-function value, including indicators of <conjugacy classes>, and hence conjugacy. The converse follows from the class-function property.

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