Square of degree of irreducible representation need not divide group order

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This fact is related to: linear representation theory
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Statement

It is possible to have a finite group G such that the square of one of its Degrees of irreducible representations (?) (i.e., the degree of an irreducible linear representation over an algebraically closed field of characteristic zero) does not divide the order of the group.

Related facts

Similar facts

Opposite facts

Additive, rather than divisibility, bounds:

Divisibility facts:

Proof

Further information: linear representation theory of symmetric group:S3

The simplest example is that of symmetric group:S3, a group of order 6 that has an irreducible linear representation of degree 2, even though 2^2 does not divide 6.