Degrees of irreducible representations need not determine derived length

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It is possible to have two finite solvable 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 derived length values.

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See linear representation theory of groups of order 128#Degrees of irreducible representations, and note that there do exist collections of degrees of irreducible representations that occur in groups of derived length 2 as well as 3.