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

From Groupprops

## Contents

## Statement

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

## Related facts

### Similar facts

### Combination applications

- Combining with square bound (order of inner automorphism group bounds square of degree of irreducible representation): Combined with the fact that the maximum of the degrees of irreducible representations over the complex numbers is bounded by , the maximum of the degrees of irreducible representations over the real numbers is bounded by .

## Facts used

## Proof

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