Element structure of wreath product of groups of order p

This article gives specific information, namely, element structure, about a family of groups, namely: wreath product of groups of order p.
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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)