| Label |
Degree |
Type |
Faithful |
Conductor |
Field of Traces |
$\Q$-character |
Group |
Image |
Image Order |
Kernel |
Kernel Order |
Center |
Center Order |
Center Index |
Schur Index |
| 768.1085882.1a |
$1$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.1a |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_1$ |
$1$ |
1.a1.a1 |
$768$ |
1.a1.a1 |
$768$ |
$1$ |
$1$ |
| 768.1085882.1b |
$1$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.1b |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_2$ |
$2$ |
2.c1.a1 |
$384$ |
1.a1.a1 |
$768$ |
$1$ |
$1$ |
| 768.1085882.1c |
$1$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.1c |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_2$ |
$2$ |
2.b1.a1 |
$384$ |
1.a1.a1 |
$768$ |
$1$ |
$1$ |
| 768.1085882.1d |
$1$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.1d |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_2$ |
$2$ |
2.a1.a1 |
$384$ |
1.a1.a1 |
$768$ |
$1$ |
$1$ |
| 768.1085882.1e1 |
$1$ |
C |
|
$4$ |
\(\Q(\sqrt{-1}) \) |
768.1085882.1e |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_4$ |
$4$ |
4.c1.a1 |
$192$ |
1.a1.a1 |
$768$ |
$1$ |
$1$ |
| 768.1085882.1e2 |
$1$ |
C |
|
$4$ |
\(\Q(\sqrt{-1}) \) |
768.1085882.1e |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_4$ |
$4$ |
4.c1.a1 |
$192$ |
1.a1.a1 |
$768$ |
$1$ |
$1$ |
| 768.1085882.1f1 |
$1$ |
C |
|
$4$ |
\(\Q(\sqrt{-1}) \) |
768.1085882.1f |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_4$ |
$4$ |
4.a1.a1 |
$192$ |
1.a1.a1 |
$768$ |
$1$ |
$1$ |
| 768.1085882.1f2 |
$1$ |
C |
|
$4$ |
\(\Q(\sqrt{-1}) \) |
768.1085882.1f |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_4$ |
$4$ |
4.a1.a1 |
$192$ |
1.a1.a1 |
$768$ |
$1$ |
$1$ |
| 768.1085882.2a |
$2$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.2a |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$S_3$ |
$6$ |
6.a1.a1 |
$128$ |
6.a1.a1 |
$128$ |
$6$ |
$1$ |
| 768.1085882.2b |
$2$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.2b |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$D_4$ |
$8$ |
8.c1.a1 |
$96$ |
4.b1.a1 |
$192$ |
$4$ |
$1$ |
| 768.1085882.2c |
$2$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.2c |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$D_4$ |
$8$ |
8.b1.a1 |
$96$ |
4.b1.a1 |
$192$ |
$4$ |
$1$ |
| 768.1085882.2d |
$2$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.2d |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$D_6$ |
$12$ |
12.b1.a1 |
$64$ |
6.a1.a1 |
$128$ |
$6$ |
$1$ |
| 768.1085882.2e |
$2$ |
S |
|
$1$ |
\(\Q\) |
768.1085882.2e |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_3:C_4$ |
$12$ |
12.c1.a1 |
$64$ |
6.a1.a1 |
$128$ |
$6$ |
$2$ |
| 768.1085882.2f |
$2$ |
S |
|
$1$ |
\(\Q\) |
768.1085882.2f |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_3:C_4$ |
$12$ |
12.a1.a1 |
$64$ |
6.a1.a1 |
$128$ |
$6$ |
$2$ |
| 768.1085882.2g1 |
$2$ |
C |
|
$3$ |
\(\Q(\sqrt{-3}) \) |
768.1085882.2g |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_3:D_4$ |
$24$ |
24.c1.a1 |
$32$ |
12.b1.a1 |
$64$ |
$12$ |
$1$ |
| 768.1085882.2g2 |
$2$ |
C |
|
$3$ |
\(\Q(\sqrt{-3}) \) |
768.1085882.2g |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_3:D_4$ |
$24$ |
24.c1.a1 |
$32$ |
12.b1.a1 |
$64$ |
$12$ |
$1$ |
| 768.1085882.2h1 |
$2$ |
C |
|
$3$ |
\(\Q(\sqrt{-3}) \) |
768.1085882.2h |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_3:D_4$ |
$24$ |
24.b1.a1 |
$32$ |
12.b1.a1 |
$64$ |
$12$ |
$1$ |
| 768.1085882.2h2 |
$2$ |
C |
|
$3$ |
\(\Q(\sqrt{-3}) \) |
768.1085882.2h |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_3:D_4$ |
$24$ |
24.b1.a1 |
$32$ |
12.b1.a1 |
$64$ |
$12$ |
$1$ |
| 768.1085882.3a |
$3$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.3a |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$S_4$ |
$24$ |
24.d1.a1 |
$32$ |
24.d1.a1 |
$32$ |
$24$ |
$1$ |
| 768.1085882.3b |
$3$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.3b |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$S_4$ |
$24$ |
24.d1.a1 |
$32$ |
24.d1.a1 |
$32$ |
$24$ |
$1$ |
| 768.1085882.3c |
$3$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.3c |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_2\times S_4$ |
$48$ |
48.c1.a1 |
$16$ |
24.d1.a1 |
$32$ |
$24$ |
$1$ |
| 768.1085882.3d |
$3$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.3d |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_2\times S_4$ |
$48$ |
48.c1.a1 |
$16$ |
24.d1.a1 |
$32$ |
$24$ |
$1$ |
| 768.1085882.3e1 |
$3$ |
C |
|
$4$ |
\(\Q(\sqrt{-1}) \) |
768.1085882.3e |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$A_4:C_4$ |
$48$ |
48.d1.a1 |
$16$ |
24.d1.a1 |
$32$ |
$24$ |
$1$ |
| 768.1085882.3e2 |
$3$ |
C |
|
$4$ |
\(\Q(\sqrt{-1}) \) |
768.1085882.3e |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$A_4:C_4$ |
$48$ |
48.d1.a1 |
$16$ |
24.d1.a1 |
$32$ |
$24$ |
$1$ |
| 768.1085882.3f1 |
$3$ |
C |
|
$4$ |
\(\Q(\sqrt{-1}) \) |
768.1085882.3f |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$A_4:C_4$ |
$48$ |
48.b1.a1 |
$16$ |
24.d1.a1 |
$32$ |
$24$ |
$1$ |
| 768.1085882.3f2 |
$3$ |
C |
|
$4$ |
\(\Q(\sqrt{-1}) \) |
768.1085882.3f |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$A_4:C_4$ |
$48$ |
48.b1.a1 |
$16$ |
24.d1.a1 |
$32$ |
$24$ |
$1$ |
| 768.1085882.4a |
$4$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.4a |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_2^3:C_4$ |
$32$ |
32.a1.a1 |
$24$ |
16.a1.a1 |
$48$ |
$16$ |
$1$ |
| 768.1085882.4b |
$4$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.4b |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_2\wr C_4$ |
$64$ |
64.a1.a1 |
$12$ |
32.a1.a1 |
$24$ |
$32$ |
$1$ |
| 768.1085882.4c |
$4$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.4c |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_2\wr C_4$ |
$64$ |
64.a1.a1 |
$12$ |
32.a1.a1 |
$24$ |
$32$ |
$1$ |
| 768.1085882.4d1 |
$4$ |
C |
|
$3$ |
\(\Q(\sqrt{-3}) \) |
768.1085882.4d |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_2^3.D_6$ |
$96$ |
96.d1.a1 |
$8$ |
48.a1.a1 |
$16$ |
$48$ |
$1$ |
| 768.1085882.4d2 |
$4$ |
C |
|
$3$ |
\(\Q(\sqrt{-3}) \) |
768.1085882.4d |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_2^3.D_6$ |
$96$ |
96.d1.a1 |
$8$ |
48.a1.a1 |
$16$ |
$48$ |
$1$ |
| 768.1085882.4e1 |
$4$ |
C |
|
$3$ |
\(\Q(\sqrt{-3}) \) |
768.1085882.4e |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$(C_2^3\times C_6):C_4$ |
$192$ |
192.b1.a1 |
$4$ |
96.d1.a1 |
$8$ |
$96$ |
$1$ |
| 768.1085882.4e2 |
$4$ |
C |
|
$3$ |
\(\Q(\sqrt{-3}) \) |
768.1085882.4e |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$(C_2^3\times C_6):C_4$ |
$192$ |
192.b1.a1 |
$4$ |
96.d1.a1 |
$8$ |
$96$ |
$1$ |
| 768.1085882.4f1 |
$4$ |
C |
|
$3$ |
\(\Q(\sqrt{-3}) \) |
768.1085882.4f |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$(C_2^3\times C_6):C_4$ |
$192$ |
192.b1.a1 |
$4$ |
96.d1.a1 |
$8$ |
$96$ |
$1$ |
| 768.1085882.4f2 |
$4$ |
C |
|
$3$ |
\(\Q(\sqrt{-3}) \) |
768.1085882.4f |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$(C_2^3\times C_6):C_4$ |
$192$ |
192.b1.a1 |
$4$ |
96.d1.a1 |
$8$ |
$96$ |
$1$ |
| 768.1085882.6a |
$6$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.6a |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$\GL(2,\mathbb{Z}/4)$ |
$96$ |
96.c1.a1 |
$8$ |
48.c1.a1 |
$16$ |
$48$ |
$1$ |
| 768.1085882.6b |
$6$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.6b |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$\GL(2,\mathbb{Z}/4)$ |
$96$ |
96.b1.a1 |
$8$ |
48.c1.a1 |
$16$ |
$48$ |
$1$ |
| 768.1085882.12a |
$12$ |
R |
|
$1$ |
\(\Q\) |
768.1085882.12a |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_2^2.\GL(2,\mathbb{Z}/4)$ |
$384$ |
384.a1.a1 |
$2$ |
192.a1.a1 |
$4$ |
$192$ |
$1$ |
| 768.1085882.12b |
$12$ |
R |
✓ |
$1$ |
\(\Q\) |
768.1085882.12b |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$768$ |
768.a1.a1 |
$1$ |
384.a1.a1 |
$2$ |
$384$ |
$1$ |
| 768.1085882.12c |
$12$ |
R |
✓ |
$1$ |
\(\Q\) |
768.1085882.12c |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$C_2^3.\GL(2,\mathbb{Z}/4)$ |
$768$ |
768.a1.a1 |
$1$ |
384.a1.a1 |
$2$ |
$384$ |
$1$ |
