| Name: | $C_2\times D_6$ |
| Order: | $24$ |
| Abelian: | no |
| Generators: | $\begin{bmatrix}\zeta_{6}^{1} & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 &0 & \zeta_{6}^{5} & 0 & 0 & 0 \\0 & 0 & 0 & \zeta_{6}^{5} & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & \zeta_{6}^{1} \\\end{bmatrix}, \begin{bmatrix}\zeta_{3}^{2} & 0 & 0 & 0 & 0 & 0 \\0 & \zeta_{6}^{1} & 0 & 0 & 0 & 0 \\0 & 0 & \zeta_{6}^{1} & 0 & 0 & 0 \\0 & 0 & 0 & \zeta_{3}^{1} & 0 & 0 \\0 & 0 & 0 & 0 & \zeta_{6}^{5} & 0 \\0 & 0 & 0 & 0 & 0 & \zeta_{6}^{5} \\\end{bmatrix}, \begin{bmatrix}0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0& 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\-1 & 0 & 0 & 0 & 0 & 0 \\0 & -1 & 0 & 0 & 0 & 0 \\0 & 0 & -1 & 0 & 0 & 0 \\\end{bmatrix}$ |
| Maximal subgroups: | $J(A(2,2))$, $J(A(3,2))$${}^{\times 6}$, $A(6,2)$ |
| Minimal supergroups: | $J(C(6,2))$, $J(B(6,2))$, $J(A(6,6))$ |
| $x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
| $a_1$ |
$1$ |
$0$ |
$3$ |
$0$ |
$45$ |
$0$ |
$930$ |
$0$ |
$23625$ |
$0$ |
$684558$ |
$0$ |
$21406770$ |
| $a_2$ |
$1$ |
$3$ |
$15$ |
$105$ |
$981$ |
$10983$ |
$136332$ |
$1795230$ |
$24478137$ |
$340930707$ |
$4812781770$ |
$68548275480$ |
$982420163484$ |
| $a_3$ |
$1$ |
$0$ |
$16$ |
$0$ |
$2580$ |
$0$ |
$694030$ |
$0$ |
$227757404$ |
$0$ |
$80388358956$ |
$0$ |
$29263011957762$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=2\right)\colon$ |
$3$ |
$3$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=4\right)\colon$ |
$15$ |
$6$ |
$21$ |
$45$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=6\right)\colon$ |
$16$ |
$105$ |
$54$ |
$195$ |
$114$ |
$423$ |
$930$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=8\right)\colon$ |
$144$ |
$981$ |
$540$ |
$315$ |
$2079$ |
$1191$ |
$4644$ |
$2640$ |
$10440$ |
$23625$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=10\right)\colon$ |
$1548$ |
$10983$ |
$882$ |
$6108$ |
$3453$ |
$24627$ |
$13794$ |
$7770$ |
$56178$ |
$31338$ |
$128760$ |
$71526$ |
$296331$ |
$684558$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=12\right)\colon$ |
$2580$ |
$18348$ |
$136332$ |
$10278$ |
$75282$ |
$41829$ |
$313515$ |
$23316$ |
$173061$ |
$95814$ |
$725625$ |
$399396$ |
$220458$ |
$1684710$ |
| $$ |
$924924$ |
$3922191$ |
$2148300$ |
$9153270$ |
$21406770$ |
$\mathrm{E}\left[\chi_i\chi_j\right] = \begin{bmatrix}1&0&2&0&0&0&1&6&0&0&0&3&0&0&8\\0&3&0&3&0&12&0&0&15&0&9&0&21&33&0\\2&0&10&0&6&0&20&30&0&12&0&42&0&0&94\\0&3&0&7&0&20&0&0&27&0&13&0&48&64&0\\0&0&6&0&18&0&30&24&0&33&0&66&0&0&132\\0&12&0&20&0&76&0&0&114&0&56&0&180&272&0\\1&0&20&0&30&0&82&81&0&72&0&177&0&0&404\\6&0&30&0&24&0&81&129&0&81&0&198&0&0&498\\0&15&0&27&0&114&0&0&195&0&90&0&303&480&0\\0&0&12&0&33&0&72&81&0&95&0&180&0&0&436\\0&9&0&13&0&56&0&0&90&0&46&0&138&220&0\\3&0&42&0&66&0&177&198&0&180&0&417&0&0&996\\0&21&0&48&0&180&0&0&303&0&138&0&516&774&0\\0&33&0&64&0&272&0&0&480&0&220&0&774&1225&0\\8&0&94&0&132&0&404&498&0&436&0&996&0&0&2514\end{bmatrix}$
$\ \ \ \mathrm{E}\left[\chi_i^2\right] = \begin{bmatrix}1&3&10&7&18&76&82&129&195&95&46&417&516&1225&2514&1317&1365&3310&2958&899\end{bmatrix}$
| $-$ | $a_2\in\mathbb{Z}$ | $a_2=-1$ | $a_2=0$ | $a_2=1$ | $a_2=2$ | $a_2=3$ |
|---|
| $-$ | $1$ | $7/12$ | $0$ | $1/12$ | $0$ | $0$ | $1/2$ |
|---|
| $a_1=0$ | $7/12$ | $7/12$ | $0$ | $1/12$ | $0$ | $0$ | $1/2$ |
|---|
| $a_3=0$ | $1/2$ | $1/2$ | $0$ | $0$ | $0$ | $0$ | $1/2$ |
|---|
| $a_1=a_3=0$ | $1/2$ | $1/2$ | $0$ | $0$ | $0$ | $0$ | $1/2$ |
|---|
