Element structure of wreath product of groups of order p

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Contents

This article gives specific information, namely, element structure, about a family of groups, namely: wreath product of groups of order p.
View element structure of group families | View other specific information about wreath product of groups of order p

Summary

Item Value
number of conjugacy classes in the whole group p^{p-1} + p^2 - 1 (equals number of irreducible representations; see number of irreducible representations equals number of conjugacy classes and linear representation theory of wreath product of groups of order p)
order of the group p^{p+1}
conjugacy class sizes 1 (occurs p times), p (occurs p^{p-1} - 1 times), p^{p-1} (occurs p^2 - p times).
order statistics order 1: 1 conjugacy class of size 1 (total 1 element)
order p: p - 1 conjugacy classes of size 1, p^{p-1} - 1 conjugacy classes of size p, p - 1 conjugacy classes of size p^{p-1} (total: 2p^p - p^{p-1} - 1 elements)
order p^2: (p - 1)^2 conjugacy classes of size p^{p-1} (total p^{p+1} - 2p^p + p^{p-1} elements)