- #1
LagrangeEuler
- 717
- 20
Homework Statement
##e = \begin{bmatrix}
1 & 0 \\[0.3em]
0 & 1 \\[0.3em]
\end{bmatrix}##,
##a =\frac{1}{2} \begin{bmatrix}
1 & -\sqrt{3} \\[0.3em]
-\sqrt{3} & -1 \\[0.3em]
\end{bmatrix}##.
##b =\frac{1}{2} \begin{bmatrix}
1 & \sqrt{3} \\[0.3em]
\sqrt{3} & -1 \\[0.3em]
\end{bmatrix}##
##c= \begin{bmatrix}
-1 & 0 \\[0.3em]
0 & 1 \\[0.3em]
\end{bmatrix}##
##d=\frac{1}{2} \begin{bmatrix}
-1 & \sqrt{3} \\[0.3em]
-\sqrt{3} & -1 \\[0.3em]
\end{bmatrix}##
##f=\frac{1}{2} \begin{bmatrix}
-1 & -\sqrt{3} \\[0.3em]
\sqrt{3} & -1 \\[0.3em]
\end{bmatrix}##
Find classes of group.
Homework Equations
The Attempt at a Solution
Classes are ##\{e\}##,##\{a,b,c\},\{d,f\}##.
My problem is what is easiest way to find them? I think by watching characters. Am I right? ##\{e\}## is only element with character ##2##. Elements ##\{a,b,c\}## have character ##0##, and elements ##\{d,f\}## have character ##-1##. What is the other way to search this classes?
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