Name: | $C_4^2:C_6$ |
Order: | $96$ |
Abelian: | no |
Generators: | $\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & i & 0 & 0 & 0 & 0 \\0 & 0 & -i & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & -i & 0 \\0 & 0 & 0 & 0 & 0 & i\\\end{bmatrix}, \begin{bmatrix}\zeta_{12}^{1} & 0 & 0 & 0 & 0 & 0 \\0 & \zeta_{12}^{1} & 0 & 0 & 0 & 0 \\0 & 0 & \zeta_{6}^{5} & 0 & 0 & 0 \\0 & 0 & 0 &\zeta_{12}^{11} & 0 & 0 \\0 & 0 & 0 & 0 & \zeta_{12}^{11} & 0 \\0 & 0 & 0 & 0 & 0 & \zeta_{6}^{1} \\\end{bmatrix}, \begin{bmatrix}0 & 0 & 1 & 0 & 0 & 0 \\1 & 0& 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 \\\end{bmatrix}, \begin{bmatrix}0 & 0 & 0 & 1 &0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\-1 & 0 & 0 & 0 & 0 & 0 \\0 & -1 & 0 & 0 & 0 & 0 \\0 & 0 & -1 & 0 & 0 & 0 \\\end{bmatrix}$ |
$x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
$a_1$ |
$1$ |
$0$ |
$1$ |
$0$ |
$15$ |
$0$ |
$310$ |
$0$ |
$7525$ |
$0$ |
$204246$ |
$0$ |
$6017550$ |
$a_2$ |
$1$ |
$1$ |
$5$ |
$35$ |
$322$ |
$3466$ |
$40934$ |
$513850$ |
$6734074$ |
$91012814$ |
$1257365680$ |
$17643361660$ |
$250327558573$ |
$a_3$ |
$1$ |
$0$ |
$6$ |
$0$ |
$828$ |
$0$ |
$199740$ |
$0$ |
$60649596$ |
$0$ |
$20613284436$ |
$0$ |
$7386934420602$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=2\right)\colon$ |
$1$ |
$1$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=4\right)\colon$ |
$5$ |
$2$ |
$7$ |
$15$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=6\right)\colon$ |
$6$ |
$35$ |
$18$ |
$65$ |
$38$ |
$141$ |
$310$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=8\right)\colon$ |
$48$ |
$322$ |
$178$ |
$104$ |
$677$ |
$390$ |
$1501$ |
$860$ |
$3350$ |
$7525$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=10\right)\colon$ |
$502$ |
$3466$ |
$288$ |
$1944$ |
$1108$ |
$7675$ |
$4342$ |
$2468$ |
$17307$ |
$9760$ |
$39230$ |
$22050$ |
$89327$ |
$204246$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=12\right)\colon$ |
$828$ |
$5698$ |
$40934$ |
$3222$ |
$22838$ |
$12822$ |
$92905$ |
$7220$ |
$51840$ |
$29012$ |
$212453$ |
$118220$ |
$65980$ |
$487738$ |
$$ |
$270718$ |
$1123633$ |
$622188$ |
$2596650$ |
$6017550$ |
$\mathrm{E}\left[\chi_i\chi_j\right] = \begin{bmatrix}1&0&0&0&0&0&1&2&0&0&0&1&0&0&2\\0&1&0&1&0&4&0&0&5&0&3&0&7&11&0\\0&0&4&0&2&0&6&10&0&4&0&14&0&0&30\\0&1&0&3&0&6&0&0&9&0&5&0&15&21&0\\0&0&2&0&6&0&10&8&0&10&0&22&0&0&40\\0&4&0&6&0&26&0&0&36&0&18&0&56&84&0\\1&0&6&0&10&0&27&26&0&22&0&55&0&0&118\\2&0&10&0&8&0&26&41&0&23&0&61&0&0&144\\0&5&0&9&0&36&0&0&59&0&27&0&89&139&0\\0&0&4&0&10&0&22&23&0&29&0&51&0&0&120\\0&3&0&5&0&18&0&0&27&0&16&0&42&67&0\\1&0&14&0&22&0&55&61&0&51&0&128&0&0&280\\0&7&0&15&0&56&0&0&89&0&42&0&148&221&0\\0&11&0&21&0&84&0&0&139&0&67&0&221&347&0\\2&0&30&0&40&0&118&144&0&120&0&280&0&0&686\end{bmatrix}$
$\ \ \ \mathrm{E}\left[\chi_i^2\right] = \begin{bmatrix}1&1&4&3&6&26&27&41&59&29&16&128&148&347&686&349&369&866&765&233\end{bmatrix}$
| $-$ | $a_2\in\mathbb{Z}$ | $a_2=-1$ | $a_2=0$ | $a_2=1$ | $a_2=2$ | $a_2=3$ |
---|
$-$ | $1$ | $5/6$ | $0$ | $2/3$ | $0$ | $0$ | $1/6$ |
---|
$a_1=0$ | $5/6$ | $5/6$ | $0$ | $2/3$ | $0$ | $0$ | $1/6$ |
---|
$a_3=0$ | $1/2$ | $1/2$ | $0$ | $1/3$ | $0$ | $0$ | $1/6$ |
---|
$a_1=a_3=0$ | $1/2$ | $1/2$ | $0$ | $1/3$ | $0$ | $0$ | $1/6$ |
---|