Name: | $C_2\times A_4$ |
Order: | $24$ |
Abelian: | no |
Generators: | $\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & -1 & 0 & 0 & 0 & 0 \\0 & 0 & -1 & 0& 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & -1 & 0 \\0 & 0 & 0 & 0 & 0 & -1 \\\end{bmatrix}, \begin{bmatrix}\zeta_{6}^{1} & 0 & 0 & 0 & 0 & 0 \\0 & \zeta_{6}^{1} & 0 & 0 & 0 & 0 \\0 & 0 & \zeta_{3}^{2} & 0 & 0 & 0 \\0 & 0 & 0 & \zeta_{6}^{5} & 0 & 0 \\0 & 0 & 0 & 0 & \zeta_{6}^{5} & 0 \\0 & 0 & 0 & 0 & 0 & \zeta_{3}^{1} \\\end{bmatrix}, \begin{bmatrix}0 & 0 & 1 & 0 & 0 & 0 \\1 & 0 & 0& 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 \\\end{bmatrix}, \begin{bmatrix}0 & 0 & 0 & 1 & 0 &0 \\0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\-1 & 0 & 0 & 0 & 0 & 0 \\0 &-1 & 0 & 0 & 0 & 0 \\0 & 0 & -1 & 0 & 0 & 0 \\\end{bmatrix}$ |
Maximal subgroups: | $J(A(2,2))$, $C(2,2)$, $J_s(A(3,1))$ |
Minimal supergroups: | $J(C(4,4))$, $J(C(6,2))$, $J(D(2,2))$ |
$x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
$a_1$ |
$1$ |
$0$ |
$1$ |
$0$ |
$21$ |
$0$ |
$610$ |
$0$ |
$19145$ |
$0$ |
$620046$ |
$0$ |
$20460594$ |
$a_2$ |
$1$ |
$1$ |
$6$ |
$56$ |
$674$ |
$8886$ |
$121305$ |
$1684677$ |
$23652270$ |
$334700786$ |
$4765464551$ |
$68187035247$ |
$979650930593$ |
$a_3$ |
$1$ |
$0$ |
$8$ |
$0$ |
$1972$ |
$0$ |
$644030$ |
$0$ |
$223416284$ |
$0$ |
$79999502268$ |
$0$ |
$29227479221314$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=2\right)\colon$ |
$1$ |
$1$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=4\right)\colon$ |
$6$ |
$2$ |
$9$ |
$21$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=6\right)\colon$ |
$8$ |
$56$ |
$28$ |
$115$ |
$62$ |
$263$ |
$610$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=8\right)\colon$ |
$86$ |
$674$ |
$360$ |
$199$ |
$1519$ |
$831$ |
$3524$ |
$1920$ |
$8200$ |
$19145$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=10\right)\colon$ |
$1136$ |
$8886$ |
$618$ |
$4820$ |
$2629$ |
$20595$ |
$11218$ |
$6122$ |
$48114$ |
$26186$ |
$112632$ |
$61222$ |
$264075$ |
$620046$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}a_3^{e_3}\right]:\sum ie_i=12\right)\colon$ |
$1972$ |
$15352$ |
$121305$ |
$8368$ |
$65874$ |
$35837$ |
$283947$ |
$19496$ |
$154245$ |
$83830$ |
$666489$ |
$361764$ |
$196490$ |
$1566438$ |
$$ |
$849660$ |
$3685647$ |
$1997772$ |
$8680182$ |
$20460594$ |
$\mathrm{E}\left[\chi_i\chi_j\right] = \begin{bmatrix}1&0&0&0&0&0&1&3&0&1&0&2&0&0&6\\0&1&0&1&0&6&0&0&11&0&5&0&15&27&0\\0&0&5&0&3&0&13&19&0&12&0&32&0&0&84\\0&1&0&5&0&12&0&0&21&0&9&0&40&56&0\\0&0&3&0&9&0&19&22&0&26&0&49&0&0&120\\0&6&0&12&0&54&0&0&96&0&42&0&156&246&0\\1&0&13&0&19&0&65&70&0&62&0&151&0&0&378\\3&0&19&0&22&0&70&103&0&82&0&182&0&0&474\\0&11&0&21&0&96&0&0&177&0&80&0&281&456&0\\1&0&12&0&26&0&62&82&0&86&0&166&0&0&420\\0&5&0&9&0&42&0&0&80&0&38&0&124&206&0\\2&0&32&0&49&0&151&182&0&166&0&378&0&0&960\\0&15&0&40&0&156&0&0&281&0&124&0&488&744&0\\0&27&0&56&0&246&0&0&456&0&206&0&744&1193&0\\6&0&84&0&120&0&378&474&0&420&0&960&0&0&2466\end{bmatrix}$
$\ \ \ \mathrm{E}\left[\chi_i^2\right] = \begin{bmatrix}1&1&5&5&9&54&65&103&177&86&38&378&488&1193&2466&1297&1334&3294&2926&895\end{bmatrix}$
| $-$ | $a_2\in\mathbb{Z}$ | $a_2=-1$ | $a_2=0$ | $a_2=1$ | $a_2=2$ | $a_2=3$ |
---|
$-$ | $1$ | $5/6$ | $0$ | $2/3$ | $0$ | $0$ | $1/6$ |
---|
$a_1=0$ | $5/6$ | $5/6$ | $0$ | $2/3$ | $0$ | $0$ | $1/6$ |
---|
$a_3=0$ | $1/2$ | $1/2$ | $0$ | $1/3$ | $0$ | $0$ | $1/6$ |
---|
$a_1=a_3=0$ | $1/2$ | $1/2$ | $0$ | $1/3$ | $0$ | $0$ | $1/6$ |
---|