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

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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

Facts used

  1. Degrees of irreducible representations of quotient group are contained in degrees of irreducible representations of group

Proof

The proof follows directly from Fact (1).