Maximum degree of irreducible real representation is at most twice maximum degree of irreducible complex representation

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Statement

The maximum of the Degrees of irreducible representations (?) over the reals for a finite group G is at most twice the maximum of the degrees of irreducible representations over the complex numbers.

Related facts

Similar facts

Combination applications

Facts used

  1. Degree of irreducible real representation either equals or is twice of degree of irreducible complex representation

Proof

The proof is a straightforward application of fact (1).