Element structure of unitriangular matrix group:UT(3,Z4)

This article gives specific information, namely, element structure, about a particular group, namely: unitriangular matrix group:UT(3,Z4).
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This article describes the element structure of unitriangular matrix group:UT(3,Z4).

Summary

Item	Value
number of conjugacy classes	22
order	64 As $UT(n,R),n=3,|R|=4$: $|R|^{n(n-1)/2}=4^{3(2)/2}=4^{3}=64$
exponent	8
conjugacy class size statistics	size 1 (4 classes), size 2 (6 classes), size 4 (12 classes)
order statistics	order 1 (1 element), order 2 (7 elements), order 4 (40 elements), order 8 (16 elements)

Conjugacy class structure

Interpretation as unitriangular matrix group of degree three

Compare with element structure of unitriangular matrix group of degree three over a finite discrete valuation ring#Conjugacy class structure