# Number of conjugacy classes in extension group is bounded by product of number of conjugacy classes in normal subgroup and quotient group

From Groupprops

## Statement

### Statement in terms of conjugacy classes

Suppose is a finite group and is a normal subgroup of with quotient group . Denote by respectively the number of conjugacy classes in respectively. Then, we have the relation:

### Statement in terms of conjugacy classes

Suppose is a finite group and is a normal subgroup of with quotient group . Denote by respectively the commuting fractions of respectively. Then, we have the relation: