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Representations and Characters of Groups, Second Edition by Martin Liebeck, Gordon James

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26

Characters of some p-groups

Throughout this chapter, p will be a prime number. We shall show how to obtain the character tables of all groups of order pn for n image 4. The method consists of examining the characters of those p-groups which contain an abelian subgroup of index p, and before explaining the method, we show that all groups of order pn with 1 image n image 4 do, indeed, have an abelian subgroup of index p. We later give explicitly the irreducible ...

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