Name: | $D_6$ |
Order: | $12$ |
Abelian: | no |
Generators: | $\begin{bmatrix}\zeta_{12}&0&0&0\\0&\zeta_{12}&0&0\\0&0&\zeta_{12}^{11}&0\\0&0&0&\zeta_{12}^{11}\end{bmatrix}, \begin{bmatrix}0&0&0&1\\0&0&-1&0\\0&-1&0&0\\1&0&0&0\end{bmatrix}$ |
$x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
$a_1$ |
$1$ |
$0$ |
$1$ |
$0$ |
$6$ |
$0$ |
$50$ |
$0$ |
$490$ |
$0$ |
$5292$ |
$0$ |
$61116$ |
$a_2$ |
$1$ |
$1$ |
$3$ |
$7$ |
$25$ |
$91$ |
$387$ |
$1716$ |
$8045$ |
$38821$ |
$192415$ |
$972544$ |
$4999447$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=2\right)\colon$ |
$1$ |
$1$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=4\right)\colon$ |
$3$ |
$3$ |
$6$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=6\right)\colon$ |
$7$ |
$11$ |
$23$ |
$50$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=8\right)\colon$ |
$25$ |
$44$ |
$96$ |
$215$ |
$490$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=10\right)\colon$ |
$91$ |
$188$ |
$423$ |
$970$ |
$2254$ |
$5292$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=12\right)\colon$ |
$387$ |
$843$ |
$1942$ |
$4537$ |
$10710$ |
$25494$ |
$61116$ |
$\mathrm{E}\left[\chi_i\chi_j\right] = \begin{bmatrix}1&0&0&0&0&1&0&0&0&0\\0&1&0&0&1&0&1&0&1&0\\0&0&2&0&0&0&0&2&0&2\\0&0&0&3&0&1&0&2&0&0\\0&1&0&0&3&0&2&0&3&0\\1&0&0&1&0&4&0&1&0&0\\0&1&0&0&2&0&3&0&3&0\\0&0&2&2&0&1&0&7&0&4\\0&1&0&0&3&0&3&0&6&0\\0&0&2&0&0&0&0&4&0&7\end{bmatrix}$
$\ \ \ \mathrm{E}\left[\chi_i^2\right] = \begin{bmatrix}1&1&2&3&3&4&3&7&6&7\end{bmatrix}$
| $-$ | $a_2\in\mathbb{Z}$ | $a_2=-2$ | $a_2=-1$ | $a_2=0$ | $a_2=1$ | $a_2=2$ |
---|
$-$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
---|
$a_1=0$ | $7/12$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
---|