Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
3.9.0.1 |
$9$ |
$x^{9} + 2 x^{3} + 2 x^{2} + x + 1$ |
$3$ |
$1$ |
$9$ |
$0$ |
$C_9$ (as 9T1) |
$9$ |
$1$ |
$[\ ]$ |
$[\ ]^{9}$ |
$t^{9} + 2 t^{3} + 2 t^{2} + t + 1$ |
$x - 3$ |
$[0]$ |
$[]$ |
3.9.9.1 |
$9$ |
$x^{9} + 90 x^{7} - 207 x^{6} + 540 x^{5} + 324 x^{4} + 243 x^{3} + 324 x^{2} + 162 x + 27$ |
$3$ |
$3$ |
$3$ |
$9$ |
$S_3\times C_3$ (as 9T4) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 6 t x^{2} + 6 x + 3$ |
$[1, 0]$ |
$[1]$ |
3.9.9.10 |
$9$ |
$x^{9} - 24 x^{8} + 321 x^{7} - 117 x^{6} - 243 x^{5} + 1062 x^{4} + 1053 x^{3} + 135 x^{2} - 27 x + 27$ |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6 t\right) x^{2} + \left(3 t^{2} + 6 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
3.9.9.11 |
$9$ |
$x^{9} + 3 x + 3$ |
$3$ |
$9$ |
$1$ |
$9$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[9/8, 9/8]$ |
$[9/8, 9/8]_{8}^{2}$ |
$t + 1$ |
$x^{9} + 3 x + 3$ |
$[1, 1, 0]$ |
$[1]$ |
3.9.9.12 |
$9$ |
$x^{9} + 6 x + 3$ |
$3$ |
$9$ |
$1$ |
$9$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[9/8, 9/8]$ |
$[9/8, 9/8]_{8}^{2}$ |
$t + 1$ |
$x^{9} + 6 x + 3$ |
$[1, 1, 0]$ |
$[1]$ |
3.9.9.2 |
$9$ |
$x^{9} - 3 x^{7} + 9 x^{6} - 9 x^{5} - 18 x^{4} + 81 x^{3} - 27 x^{2} - 27 x + 27$ |
$3$ |
$3$ |
$3$ |
$9$ |
$C_3^2 : S_3 $ (as 9T13) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
3.9.9.3 |
$9$ |
$x^{9} - 3 x^{8} + 126 x^{7} + 198 x^{6} + 297 x^{5} + 567 x^{4} + 324 x^{3} + 108 x^{2} + 81 x + 27$ |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 6 t + 3\right) x^{2} + \left(3 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
3.9.9.4 |
$9$ |
$x^{9} - 24 x^{8} + 318 x^{7} - 189 x^{6} + 1080 x^{5} + 2826 x^{4} + 1350 x^{3} - 108 x^{2} - 54 x + 27$ |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6 t\right) x^{2} + \left(6 t^{2} + 3 t + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
3.9.9.5 |
$9$ |
$x^{9} - 24 x^{7} + 9 x^{6} + 216 x^{5} - 144 x^{4} + 648 x^{2} - 216 x + 27$ |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 3 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
3.9.9.6 |
$9$ |
$x^{9} - 6 x^{8} + 45 x^{7} + 594 x^{6} + 99 x^{5} + 108 x^{4} - 54 x^{3} + 27 x^{2} + 81 x + 27$ |
$3$ |
$3$ |
$3$ |
$9$ |
$S_3\times C_3$ (as 9T4) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 3 t + 6\right) x^{2} + 3 x + 3$ |
$[1, 0]$ |
$[1]$ |
3.9.9.7 |
$9$ |
$x^{9} - 6 x^{7} + 9 x^{6} - 36 x^{5} - 36 x^{4} + 459 x^{3} - 108 x^{2} - 54 x + 27$ |
$3$ |
$3$ |
$3$ |
$9$ |
$C_3^2 : S_3 $ (as 9T13) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
3.9.9.8 |
$9$ |
$x^{9} + 6 x^{8} + 114 x^{7} + 549 x^{6} + 522 x^{5} + 495 x^{4} + 216 x^{3} + 297 x^{2} - 108 x + 27$ |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 6 t + 6\right) x^{2} + \left(3 t^{2} + 3 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
3.9.9.9 |
$9$ |
$x^{9} + 9 x^{6} + 72 x^{5} - 189 x^{3} + 216 x^{2} + 27$ |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 6 t x + 3$ |
$[1, 0]$ |
$[1]$ |
3.9.10.1 |
$9$ |
$x^{9} + 3 x^{2} + 3$ |
$3$ |
$9$ |
$1$ |
$10$ |
$C_3^2:Q_8$ (as 9T14) |
$2$ |
$4$ |
$[5/4, 5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t + 1$ |
$x^{9} + 3 x^{2} + 3$ |
$[2, 2, 0]$ |
$[2]$ |
3.9.10.2 |
$9$ |
$x^{9} + 6 x^{2} + 3$ |
$3$ |
$9$ |
$1$ |
$10$ |
$S_3^2:C_2$ (as 9T16) |
$2$ |
$4$ |
$[5/4, 5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t + 1$ |
$x^{9} + 6 x^{2} + 3$ |
$[2, 2, 0]$ |
$[1]$ |
3.9.12.1 |
$9$ |
$x^{9} + 18 x^{8} + 108 x^{7} + 225 x^{6} + 108 x^{5} + 324 x^{4} + 675 x^{3} + 4050 x^{2} - 3861$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3^2$ (as 9T2) |
$3$ |
$1$ |
$[2]$ |
$[2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 6 x^{2} + 18 t + 3$ |
$[2, 0]$ |
$[1]$ |
3.9.12.10 |
$9$ |
$x^{9} + 9 x^{8} + 45 x^{7} + 90 x^{6} + 324 x^{5} + 621 x^{4} + 594 x^{3} + 2349 x^{2} + 2943$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t + 3\right) x^{2} + 9 t + 12$ |
$[2, 0]$ |
$[1]$ |
3.9.12.11 |
$9$ |
$x^{9} - 24 x^{8} + 324 x^{7} - 459 x^{6} + 828 x^{5} - 972 x^{4} + 540 x^{3} - 216 x^{2} + 432$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6 t\right) x^{2} + 9 t^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
3.9.12.12 |
$9$ |
$x^{9} + 9 x^{8} + 45 x^{7} + 54 x^{6} + 189 x^{5} + 540 x^{4} + 297 x^{3} + 1944 x^{2} + 3834$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t + 3\right) x^{2} + 9 t^{2} + 9 t + 12$ |
$[2, 0]$ |
$[1]$ |
3.9.12.13 |
$9$ |
$x^{9} - 6 x^{8} + 144 x^{7} + 927 x^{6} + 504 x^{5} + 4320 x^{4} + 1971 x^{3} + 11286 x^{2} + 17037$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6 t + 6\right) x^{2} + 18 t + 21$ |
$[2, 0]$ |
$[1]$ |
3.9.12.14 |
$9$ |
$x^{9} - 6 x^{8} + 144 x^{7} + 900 x^{6} + 612 x^{5} + 3024 x^{4} + 1080 x^{3} + 6264 x^{2} + 3672$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6 t + 6\right) x^{2} + 18 t + 12$ |
$[2, 0]$ |
$[1]$ |
3.9.12.15 |
$9$ |
$x^{9} - 24 x^{8} + 216 x^{7} - 27 x^{6} + 477 x^{5} + 1134 x^{4} + 1026 x^{3} + 3348 x^{2} + 6021$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 3 t\right) x^{2} + 9 t^{2} + 18 t + 12$ |
$[2, 0]$ |
$[1]$ |
3.9.12.16 |
$9$ |
$x^{9} + 9 x^{8} + 27 x^{7} + 36 x^{6} + 54 x^{5} + 81 x^{4} + 675 x^{3} + 2025 x^{2} - 3861$ |
$3$ |
$3$ |
$3$ |
$12$ |
$S_3\times C_3$ (as 9T4) |
$6$ |
$1$ |
$[2]$ |
$[2]^{6}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 3 x^{2} + 18 t + 3$ |
$[2, 0]$ |
$[2]$ |
3.9.12.17 |
$9$ |
$x^{9} - 6 x^{8} - 36 x^{7} + 441 x^{6} + 126 x^{5} + 216 x^{4} + 189 x^{3} + 1404 x^{2} - 216$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3^2 : S_3 $ (as 9T13) |
$6$ |
$1$ |
$[2]$ |
$[2, 2]^{6}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6\right) x^{2} + 9 t + 3$ |
$[2, 0]$ |
$[2]$ |
3.9.12.18 |
$9$ |
$x^{9} - 12 x^{8} + 36 x^{7} + 90 x^{6} - 342 x^{5} + 432 x^{4} + 1971 x^{3} - 1890 x^{2} + 17037$ |
$3$ |
$3$ |
$3$ |
$12$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{6}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 3 t^{2} x^{2} + 18 t + 21$ |
$[2, 0]$ |
$[2]$ |
3.9.12.19 |
$9$ |
$x^{9} + 18 x^{8} + 180 x^{7} + 495 x^{6} + 1188 x^{5} + 4428 x^{4} + 1971 x^{3} + 15066 x^{2} + 17037$ |
$3$ |
$3$ |
$3$ |
$12$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{6}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t + 6\right) x^{2} + 18 t + 21$ |
$[2, 0]$ |
$[2]$ |
3.9.12.2 |
$9$ |
$x^{9} + 18 x^{8} + 108 x^{7} + 243 x^{6} + 324 x^{5} + 972 x^{4} + 1269 x^{3} + 7614 x^{2} + 15984$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9$ (as 9T1) |
$3$ |
$1$ |
$[2]$ |
$[2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 6 x^{2} + 9 t^{2} + 18 t + 21$ |
$[2, 0]$ |
$[1]$ |
3.9.12.20 |
$9$ |
$x^{9} - 12 x^{8} + 81 x^{7} - 45 x^{6} + 117 x^{5} - 162 x^{4} + 189 x^{3} - 270 x^{2} - 216$ |
$3$ |
$3$ |
$3$ |
$12$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{6}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 3 t\right) x^{2} + 9 t + 3$ |
$[2, 0]$ |
$[2]$ |
3.9.12.21 |
$9$ |
$x^{9} + 6 x^{4} + 3$ |
$3$ |
$9$ |
$1$ |
$12$ |
$C_3^2:C_4$ (as 9T9) |
$2$ |
$2$ |
$[3/2, 3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t + 1$ |
$x^{9} + 6 x^{4} + 3$ |
$[4, 4, 0]$ |
$[2]$ |
3.9.12.22 |
$9$ |
$x^{9} + 6 x^{4} + 6 x^{3} + 3$ |
$3$ |
$9$ |
$1$ |
$12$ |
$C_3^2 : C_6$ (as 9T11) |
$3$ |
$2$ |
$[3/2, 3/2]$ |
$[3/2, 3/2]_{2}^{3}$ |
$t + 1$ |
$x^{9} + 6 x^{4} + 6 x^{3} + 3$ |
$[4, 3, 0]$ |
$[3]$ |
3.9.12.23 |
$9$ |
$x^{9} + 6 x^{4} + 3 x^{3} + 3$ |
$3$ |
$9$ |
$1$ |
$12$ |
$C_3^2 : C_6$ (as 9T11) |
$3$ |
$2$ |
$[3/2, 3/2]$ |
$[3/2, 3/2]_{2}^{3}$ |
$t + 1$ |
$x^{9} + 6 x^{4} + 3 x^{3} + 3$ |
$[4, 3, 0]$ |
$[3]$ |
3.9.12.24 |
$9$ |
$x^{9} + 3 x^{4} + 3$ |
$3$ |
$9$ |
$1$ |
$12$ |
$S_3^2$ (as 9T8) |
$2$ |
$2$ |
$[3/2, 3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t + 1$ |
$x^{9} + 3 x^{4} + 3$ |
$[4, 4, 0]$ |
$[2]$ |
3.9.12.25 |
$9$ |
$x^{9} + 3 x^{4} + 6 x^{3} + 3$ |
$3$ |
$9$ |
$1$ |
$12$ |
$C_3^2:C_8$ (as 9T15) |
$4$ |
$2$ |
$[3/2, 3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t + 1$ |
$x^{9} + 3 x^{4} + 6 x^{3} + 3$ |
$[4, 3, 0]$ |
$[4]$ |
3.9.12.26 |
$9$ |
$x^{9} + 3 x^{4} + 3 x^{3} + 3$ |
$3$ |
$9$ |
$1$ |
$12$ |
$C_3^2:C_8$ (as 9T15) |
$4$ |
$2$ |
$[3/2, 3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t + 1$ |
$x^{9} + 3 x^{4} + 3 x^{3} + 3$ |
$[4, 3, 0]$ |
$[4]$ |
3.9.12.3 |
$9$ |
$x^{9} + 18 x^{8} + 108 x^{7} + 153 x^{6} - 756 x^{5} - 2268 x^{4} + 891 x^{3} + 5346 x^{2} + 9099$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9$ (as 9T1) |
$3$ |
$1$ |
$[2]$ |
$[2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 6 x^{2} + 18 t^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
3.9.12.4 |
$9$ |
$x^{9} + 6 x^{8} + 45 x^{7} + 252 x^{6} + 144 x^{5} + 540 x^{4} + 432 x^{3} + 864 x^{2} + 1728$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3^2:C_3$ (as 9T7) |
$3$ |
$1$ |
$[2]$ |
$[2, 2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 3 t + 6\right) x^{2} + 12$ |
$[2, 0]$ |
$[1]$ |
3.9.12.5 |
$9$ |
$x^{9} + 6 x^{8} + 126 x^{7} + 468 x^{6} + 630 x^{5} + 1674 x^{4} + 675 x^{3} - 108 x^{2} - 3861$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9:C_3$ (as 9T6) |
$3$ |
$1$ |
$[2]$ |
$[2, 2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 6 t + 6\right) x^{2} + 18 t + 3$ |
$[2, 0]$ |
$[1]$ |
3.9.12.6 |
$9$ |
$x^{9} - 3 x^{8} - 9 x^{7} + 63 x^{6} + 63 x^{5} + 54 x^{4} + 189 x^{3} + 702 x^{2} - 216$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9:C_3$ (as 9T6) |
$3$ |
$1$ |
$[2]$ |
$[2, 2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 3\right) x^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
3.9.12.7 |
$9$ |
$x^{9} - 6 x^{8} + 36 x^{7} + 621 x^{6} + 477 x^{5} + 3996 x^{4} + 1026 x^{3} + 9504 x^{2} + 6021$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 3 t + 6\right) x^{2} + 9 t^{2} + 18 t + 12$ |
$[2, 0]$ |
$[1]$ |
3.9.12.8 |
$9$ |
$x^{9} - 24 x^{8} + 324 x^{7} - 405 x^{6} - 36 x^{5} + 4860 x^{4} + 540 x^{3} + 6912 x^{2} + 7236$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6 t\right) x^{2} + 9 t^{2} + 9 t + 21$ |
$[2, 0]$ |
$[1]$ |
3.9.12.9 |
$9$ |
$x^{9} + 9 x^{8} + 45 x^{7} + 117 x^{6} + 486 x^{5} + 1026 x^{4} + 1485 x^{3} + 5994 x^{2} + 11934$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t + 3\right) x^{2} + 9 t + 21$ |
$[2, 0]$ |
$[1]$ |
3.9.13.1 |
$9$ |
$x^{9} + 6 x^{5} + 3$ |
$3$ |
$9$ |
$1$ |
$13$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[13/8, 13/8]$ |
$[13/8, 13/8]_{8}^{2}$ |
$t + 1$ |
$x^{9} + 6 x^{5} + 3$ |
$[5, 5, 0]$ |
$[1]$ |
3.9.13.10 |
$9$ |
$x^{9} + 6 x^{6} + 3 x^{5} + 3 x^{3} + 3$ |
$3$ |
$9$ |
$1$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[3/2, 5/3]$ |
$[3/2, 3/2, 5/3]_{2}^{3}$ |
$t + 1$ |
$x^{9} + 6 x^{6} + 3 x^{5} + 3 x^{3} + 3$ |
$[5, 3, 0]$ |
$[1, 1]$ |
3.9.13.2 |
$9$ |
$x^{9} + 6 x^{5} + 3 x^{3} + 3$ |
$3$ |
$9$ |
$1$ |
$13$ |
$C_3^2 : D_{6} $ (as 9T18) |
$2$ |
$2$ |
$[3/2, 5/3]$ |
$[3/2, 3/2, 5/3]_{2}^{2}$ |
$t + 1$ |
$x^{9} + 6 x^{5} + 3 x^{3} + 3$ |
$[5, 3, 0]$ |
$[2, 1]$ |
3.9.13.3 |
$9$ |
$x^{9} + 3 x^{6} + 6 x^{5} + 6 x^{3} + 3$ |
$3$ |
$9$ |
$1$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[3/2, 5/3]$ |
$[3/2, 3/2, 5/3]_{2}^{3}$ |
$t + 1$ |
$x^{9} + 3 x^{6} + 6 x^{5} + 6 x^{3} + 3$ |
$[5, 3, 0]$ |
$[1, 1]$ |
3.9.13.4 |
$9$ |
$x^{9} + 6 x^{5} + 6 x^{3} + 3$ |
$3$ |
$9$ |
$1$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[3/2, 5/3]$ |
$[3/2, 3/2, 5/3]_{2}^{3}$ |
$t + 1$ |
$x^{9} + 6 x^{5} + 6 x^{3} + 3$ |
$[5, 3, 0]$ |
$[1, 1]$ |
3.9.13.5 |
$9$ |
$x^{9} + 6 x^{6} + 6 x^{5} + 6 x^{3} + 3$ |
$3$ |
$9$ |
$1$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[3/2, 5/3]$ |
$[3/2, 3/2, 5/3]_{2}^{3}$ |
$t + 1$ |
$x^{9} + 6 x^{6} + 6 x^{5} + 6 x^{3} + 3$ |
$[5, 3, 0]$ |
$[1, 1]$ |
3.9.13.6 |
$9$ |
$x^{9} + 3 x^{5} + 3$ |
$3$ |
$9$ |
$1$ |
$13$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[13/8, 13/8]$ |
$[13/8, 13/8]_{8}^{2}$ |
$t + 1$ |
$x^{9} + 3 x^{5} + 3$ |
$[5, 5, 0]$ |
$[1]$ |
3.9.13.7 |
$9$ |
$x^{9} + 3 x^{5} + 6 x^{3} + 3$ |
$3$ |
$9$ |
$1$ |
$13$ |
$C_3^2 : D_{6} $ (as 9T18) |
$2$ |
$2$ |
$[3/2, 5/3]$ |
$[3/2, 3/2, 5/3]_{2}^{2}$ |
$t + 1$ |
$x^{9} + 3 x^{5} + 6 x^{3} + 3$ |
$[5, 3, 0]$ |
$[2, 1]$ |
3.9.13.8 |
$9$ |
$x^{9} + 3 x^{5} + 3 x^{3} + 3$ |
$3$ |
$9$ |
$1$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[3/2, 5/3]$ |
$[3/2, 3/2, 5/3]_{2}^{3}$ |
$t + 1$ |
$x^{9} + 3 x^{5} + 3 x^{3} + 3$ |
$[5, 3, 0]$ |
$[1, 1]$ |