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List all the elements of symmetries of a square and construct the
group multiplication table. Use the multiplication table construct the class
multiplication rules.}
Notation:Name the group elements as follows.
- Anticlockwise rotation about \(z\)- axis by angle \(\pi/2\) \(:\to 4_z\).
- Anticlockwise rotation about \(z\)- axis by angle \(\pi\)\(:\to 4_z^2\).
- Anticlockwise rotation about \(z\)- axis by angle \(3\pi/2\)\(:\to 4_z^3\).
- Reflection in a plane perpendicular to \(X\)- axis \(:\to m_x\)
- Reflection in a plane perpendicular to \(Y\)- axis \(:\to m_y\)
- Reflection in plane containing \(Z\)- axis and diagonal 13 \(:\to m_{13}\)
- Reflection in plane containing \(Z\)- axis and diagonal 24 \(:\to m_{24}\)
The classes are given to be\\
\begin{equation*} \begin{array}{ll} C_1=\{e\}.& \\ C_2 =\{4_z^2\} &C_3 =\{4_z,
4_z^3\} \\ C_4=\{m_x, m_y\} &C_5 =\{m_{13}, m_{24}\} \end{array}\end{equation*}
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4727:Diamond Point
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