Dihedral Group

A dihedral group

D_{n}

is a group of order

2 n

containing an element

a

of order

n

and an element

b

of order

2

such that

b a b = a^{- 1}

Elements of a Dihedral Group

Suppose that

D_{n}

is a dihedral group, then it's elements are given by

{e, a^{1}, a^{2}, \dots, a^{n - 1}, b e, b a^{1}, b a^{2}, \dots, b a^{n - 1}}

Caley Table for D _ 4

\begin{matrix} A & B & C & D & E & F & G & H \\ A & A & B & C & D & E & F & G & H \\ B & B & C & D & A & H & G & E & F \\ C & C & D & A & B & F & E & H & G \\ D & D & A & B & C & G & H & F & E \\ E & E & G & F & H & A & C & B & D \\ F & F & H & E & G & C & A & D & B \\ G & G & F & H & E & D & B & A & C \\ H & H & E & G & F & B & D & C & A \end{matrix}