# Commuting fraction in quotient group is at least as much as in whole group

From Groupprops

## Statement

Suppose is a finite group and is a normal subgroup. Let be the quotient group. Then, the following are true:

- The Commuting fraction (?) (i.e., the fraction of pairs of elements that commute) in is at least as much as in .
- The Number of conjugacy classes (?) in is bounded from below by the quotient of the number of conjugacy classes in by the size of .

## Related facts

### Similar facts

- Commuting fraction in subgroup is at least as much as in whole group
- Number of conjugacy classes in a subgroup may be more than in the whole group