Name: | $D_6$ |
Order: | $12$ |
Abelian: | no |
Generators: | $\begin{bmatrix}\zeta_{12}&0&0&0\\0&\zeta_{12}^{11}&0&0\\0&0&\zeta_{12}^{11}&0\\0&0&0&\zeta_{12}\end{bmatrix}, \begin{bmatrix}0&1&0&0\\-1&0&0&0\\0&0&0&1\\0&0&-1&0\end{bmatrix}$ |
$x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
$a_1$ |
$1$ |
$0$ |
$2$ |
$0$ |
$18$ |
$0$ |
$200$ |
$0$ |
$2450$ |
$0$ |
$31752$ |
$0$ |
$427812$ |
$a_2$ |
$1$ |
$1$ |
$5$ |
$16$ |
$77$ |
$356$ |
$1803$ |
$9262$ |
$48933$ |
$262372$ |
$1427255$ |
$7850822$ |
$43608271$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=2\right)\colon$ |
$1$ |
$2$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=4\right)\colon$ |
$5$ |
$8$ |
$18$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=6\right)\colon$ |
$16$ |
$36$ |
$84$ |
$200$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=8\right)\colon$ |
$77$ |
$172$ |
$412$ |
$1000$ |
$2450$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=10\right)\colon$ |
$356$ |
$856$ |
$2088$ |
$5140$ |
$12740$ |
$31752$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=12\right)\colon$ |
$1803$ |
$4386$ |
$10842$ |
$26980$ |
$67494$ |
$169596$ |
$427812$ |
$\mathrm{E}\left[\chi_i\chi_j\right] = \begin{bmatrix}1&0&0&1&0&2&0&1&0&0\\0&2&0&0&4&0&4&0&6&0\\0&0&4&2&0&1&0&9&0&8\\1&0&2&7&0&7&0&12&0&6\\0&4&0&0&12&0&12&0&20&0\\2&0&1&7&0&12&0&12&0&5\\0&4&0&0&12&0&14&0&22&0\\1&0&9&12&0&12&0&39&0&29\\0&6&0&0&20&0&22&0&40&0\\0&0&8&6&0&5&0&29&0&29\end{bmatrix}$
$\ \ \ \mathrm{E}\left[\chi_i^2\right] = \begin{bmatrix}1&2&4&7&12&12&14&39&40&29\end{bmatrix}$
| $-$ | $a_2\in\mathbb{Z}$ | $a_2=-2$ | $a_2=-1$ | $a_2=0$ | $a_2=1$ | $a_2=2$ |
---|
$-$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
---|
$a_1=0$ | $7/12$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
---|