Difference between revisions of "Aufgaben:Problem 7"
From Ferienserie MMP2
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See Here [https://unapologetic.wordpress.com/2010/11/08/the-character-table-of-s4/] | See Here [https://unapologetic.wordpress.com/2010/11/08/the-character-table-of-s4/] | ||
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| + | {| class="wikitable" style="text-align:center" | ||
| + | ! style="width:40px" | \(S_4\) | ||
| + | ! style="width:40px" | \(e\) | ||
| + | ! style="width:40px" | \(6C_2\) | ||
| + | ! style="width:40px" | \(8C_3\) | ||
| + | ! style="width:40px" | \(6C_4\) | ||
| + | ! style="width:40px" | \(3C_{2,2}\) | ||
| + | |- | ||
| + | | \(U\) || 1 || 1 || 1 || 1 || 1 | ||
| + | |- | ||
| + | | \(U'\) || 1 || -1 || 1 || -1 || 1 | ||
| + | |- | ||
| + | | \(V\) || 3 || 1 || 0 || -1 || -1 | ||
| + | |- | ||
| + | | \(V'\) || 3 || -1 || 0 || 1 || -1 | ||
| + | |- | ||
| + | | \(W\) || 2 || 0 || -1 || 0 || 2 | ||
| + | |} | ||
Revision as of 08:51, 15 June 2015
Exercise
Compute the character table of \(S_4\)
Solution
See Here [1]
| \(S_4\) | \(e\) | \(6C_2\) | \(8C_3\) | \(6C_4\) | \(3C_{2,2}\) |
|---|---|---|---|---|---|
| \(U\) | 1 | 1 | 1 | 1 | 1 |
| \(U'\) | 1 | -1 | 1 | -1 | 1 |
| \(V\) | 3 | 1 | 0 | -1 | -1 |
| \(V'\) | 3 | -1 | 0 | 1 | -1 |
| \(W\) | 2 | 0 | -1 | 0 | 2 |
