左右反転も含んだ回転置換群
\(\iota =\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\ 1 & 2 & 3 & 4 & 5 & 6 \end{pmatrix}\\ \sigma =\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\ 6 & 1 & 2 & 3 & 4 & 5 \end{pmatrix}\\ \tau =\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\ 6 & 5 & 4 & 3 & 2 & 1 \end{pmatrix}\)
\(\begin{matrix} \iota \cdot \tau =\tau \cdot \iota \quad & =\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\ 6 & 5 & 4 & 3 & 2 & 1 \end{pmatrix} \\ \sigma \cdot \tau =\tau \cdot { \sigma }^{ 5 } & =\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\ 5 & 4 & 3 & 2 & 1 & 6 \end{pmatrix} \\ { \sigma }^{ 2 }\cdot \tau =\tau \cdot { \sigma }^{ 4 } & =\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\ 4 & 3 & 2 & 1 & 6 & 5 \end{pmatrix} \\ { \sigma }^{ 3 }\cdot \tau =\tau \cdot { \sigma }^{ 3 } & =\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\ 3 & 2 & 1 & 6 & 5 & 4 \end{pmatrix} \\ { \sigma }^{ 4 }\cdot \tau =\tau \cdot { \sigma }^{ 2 } & =\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\ 2 & 1 & 6 & 5 & 4 & 3 \end{pmatrix} \\ { \sigma }^{ 5 }\cdot \tau =\tau \cdot { \sigma } & =\begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\ 1 & 6 & 5 & 4 & 3 & 2 \end{pmatrix} \end{matrix}\\ \\ T=\left\{ \iota ,\sigma ,{ \sigma }^{ 2 },{ \sigma }^{ 3 },{ \sigma }^{ 4 },{ \sigma }^{ 5 },\tau ,\tau \sigma ,\tau { \sigma }^{ 2 },\tau { \sigma }^{ 3 },\tau { \sigma }^{ 4 },\tau { \sigma }^{ 5 } \right\} \)