# Quasirandom degree of quotient group is bounded below by quasirandom degree of whole group

From Groupprops

## Contents

## Statement

Suppose is a finite group and is a normal subgroup of . The quasirandom degree of is *at least* as much as the quasirandom degree of the quotient group .

Here, quasirandom degree refers to the minimum possible degree of a nontrivial irreducible linear representation over the complex numbers.

## Related facts

## Facts used

## Proof

The proof follows directly from Fact (1).