Degrees of irreducible representations need not determine nilpotency class

From Groupprops
Jump to: navigation, search

Statement

It is possible to have two finite nilpotent groups G_1 and G_2 of the same order and with the same Degrees of irreducible representations (?) over a splitting field but with different nilpotency class values.

Related facts

Similar facts

Opposite facts

Proof

Further information: linear representation theory of groups of order 32#Degrees of irreducible representations, linear representation theory of groups of prime-fifth order#Degrees of irreducible representations

There are many examples among groups of order p^5 for p a prime number. For instance, for order 2^5 = 32, there are groups of nilpotency class both 2 and 3 with the following degrees of irreducible representations: 8 of degree 1, 6 of degree 2.