# Classification of finite p-groups with self-centralizing cyclic normal subgroup

From Groupprops

This article gives a classification statement for certain kinds of groups of prime power order, subject to additional constraints.

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## Statement

A finite -group (a group of prime power order) , with a self-centralizing cyclic normal subgroup , could be either of the following:

- If is an odd prime, it is a faithful semidirect product of cyclic p-groups: it is the semidirect product of with a cyclic subgroup of the automorphism group of .
- If , there are a number of possibilities:
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