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

Statement
Suppose $$G$$ is a finite group and $$N$$ is a normal subgroup of $$G$$. The quasirandom degree of $$G$$ is at least as much as the quasirandom degree of the quotient group $$G/N$$.

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

Related facts

 * Quasirandom degree of extension group is bounded by maximum of quasirandom degrees of normal subgroup and quotient group

Facts used

 * 1) uses::Degrees of irreducible representations of quotient group are contained in degrees of irreducible representations of group

Proof
The proof follows directly from Fact (1).