# Linear representation theory of groups of order 3^n

This article gives specific information, namely, linear representation theory, about a family of groups, namely: groups of order 3^n.
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This article describes the linear representation theory of groups of order 3^n, i.e., groups whose order is a power of $3$. $n$ $3^n$ Number of groups of order $3^n$ Information on groups Information on linear representation theory
0 1 1 trivial group linear representation theory of trivial group
1 3 1 cyclic group:Z3 linear representation theory of cyclic group:Z3
2 9 2 groups of order 9 (see specifically cyclic group:Z9 and elementary abelian group:E9) linear representation theory of groups of order 9 (see specifically linear representation theory of cyclic group:Z9 and linear representation theory of elementary abelian group:E9)
3 27 5 groups of order 27 linear representation theory of groups of order 27, see also linear representation theory of groups of prime-cube order
4 81 15 groups of order 81 linear representation theory of groups of order 81, see also linear representation theory of groups of prime-fourth order
5 243 67 groups of order 243 linear representation theory of groups of order 243
6 729 504 groups of order 729 linear representation theory of groups of order 729
7 2187 9310 groups of order 2187 linear representation theory of groups of order 2187