# Semantic search

Character determines representation in characteristic zero, Degree of irreducible representation divides order of group, Equivalent linear representations of finite group over field are equivalent over subfield in characteristic zero, Irreducible character of degree greater than one takes value zero on some conjugacy class, Orthogonal projection formula, Regular representation over splitting field has multiplicity of each irreducible representation equal to its degree, Splitting implies characters form a basis for space of class functions, Sum of squares of degrees of irreducible representations equals order of group