Degree of induced representation from subgroup is product of degree of original representation and index of subgroup

From Groupprops
Jump to: navigation, search

Statement

Suppose G is a group, H is a subgroup of G, and \varphi is a linear representation of H over a field K. Denote by \operatorname{Ind}_H^G\varphi the induced representation of \varphi from H to G. Then, the degree of \operatorname{Ind}_H^G\varphi is the product of the degree of \varphi and the index of H in G.

Related facts