We determine the order of the automorphism group $\operatorname{Aut}(W)$ for each member $W$ of an important family of finite $p$-groups that may be constructed as iterated regular wreath products of cyclic groups. We use a method based on representation theory.

MSC Classifications:

20D45, 20D15, 20E22 show english descriptions Automorphisms
Nilpotent groups, $p$-groups
Extensions, wreath products, and other compositions [See also 20J05] 20D45 - Automorphisms
20D15 - Nilpotent groups, $p$-groups
20E22 - Extensions, wreath products, and other compositions [See also 20J05]

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