# Induced class function from conjugacy-closed normal subgroup is index of subgroup times class function inside the subgroup and zero outside the subgroup

From Groupprops

## Statement

Suppose is a finite group and is a Conjugacy-closed normal subgroup (?) (i.e., is both a conjugacy-closed subgroup and normal subgroup) of . Suppose is a Class function (?) on with values in a field . Then, the Induced class function (?) is as follows:

Here, is the index of in .

In particular, any Direct factor (?) or any Central factor (?) is a conjugacy-closed normal subgroup, so the above applies.