Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
12.8.16135716339712.1 |
$x^{12} - 2 x^{11} - 3 x^{10} + 10 x^{9} - 11 x^{8} + 2 x^{7} + 24 x^{6} - 38 x^{5} + 31 x^{4} - 20 x^{3} - 2 x^{2} + 8 x - 1$ |
$12$ |
[8,2] |
$2^{18}\cdot 367^{2}\cdot 457$ |
$3$ |
$12.6080818889$ |
$1158.3401918262182$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$9$ |
$119.057952469$ |
12.8.17497403356237.1 |
$x^{12} - x^{11} - 9 x^{10} + 9 x^{9} + 30 x^{8} - 29 x^{7} - 46 x^{6} + 39 x^{5} + 33 x^{4} - 19 x^{3} - 10 x^{2} + 2 x + 1$ |
$12$ |
[8,2] |
$7^{2}\cdot 373\cdot 30941^{2}$ |
$3$ |
$12.693492584$ |
$8988.156151291543$ |
|
|
✓ |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$9$ |
$124.895743469$ |
12.8.18137291911168.1 |
$x^{12} - 4 x^{10} - 2 x^{9} + 9 x^{8} + 2 x^{7} - 15 x^{6} + 8 x^{5} + 14 x^{4} - 10 x^{3} - 7 x^{2} + 2 x + 1$ |
$12$ |
[8,2] |
$2^{12}\cdot 151\cdot 2237\cdot 13109$ |
$4$ |
$12.7315428744$ |
$244082.97569768157$ |
|
|
✓ |
$S_{12}$ (as 12T301) |
trivial |
$2$ |
$9$ |
$127.640680383$ |
12.8.18172175140625.1 |
$x^{12} - x^{11} - 4 x^{10} + 5 x^{9} - 2 x^{8} + 15 x^{6} - 15 x^{5} - 10 x^{4} + 14 x^{3} - x^{2} - 4 x + 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 11^{2}\cdot 109^{2}\cdot 809$ |
$4$ |
$12.7335816128$ |
$2202.2613378071187$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$9$ |
$127.537100962$ |
12.8.18277154559581.1 |
$x^{12} - 2 x^{11} - 3 x^{10} + 6 x^{9} - 3 x^{7} + 3 x^{6} - x^{5} + 4 x^{4} - 4 x^{3} - 3 x^{2} + 4 x - 1$ |
$12$ |
[8,2] |
$18277154559581$ |
$1$ |
$12.7396955277$ |
$4275178.892114458$ |
|
|
✓ |
$S_{12}$ (as 12T301) |
trivial |
$2$ |
$9$ |
$127.989315487$ |
12.8.18308160781573.1 |
$x^{12} - x^{11} - 7 x^{10} + 7 x^{9} + 10 x^{8} - 14 x^{7} + 2 x^{6} + 19 x^{5} - 8 x^{4} - 17 x^{3} + x^{2} + 5 x + 1$ |
$12$ |
[8,2] |
$13^{2}\cdot 397\cdot 16519^{2}$ |
$3$ |
$12.7414951469$ |
$9233.339536700683$ |
|
|
? |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$9$ |
$128.463455261$ |
12.8.18319482619417.1 |
$x^{12} - x^{11} - 8 x^{10} + 6 x^{9} + 26 x^{8} - 15 x^{7} - 39 x^{6} + 19 x^{5} + 20 x^{4} - 6 x^{3} - 3 x + 1$ |
$12$ |
[8,2] |
$7^{8}\cdot 97\cdot 181^{2}$ |
$3$ |
$12.7421515767$ |
$484.86836299303326$ |
|
|
✓ |
$D_4\wr C_3$ (as 12T222) |
trivial |
$2$ |
$9$ |
$128.232202134$ |
12.8.19063047515625.1 |
$x^{12} - 2 x^{11} - 5 x^{10} + 7 x^{9} + 10 x^{8} + 2 x^{7} - 20 x^{6} - 19 x^{5} + 20 x^{4} + 19 x^{3} - 5 x^{2} - 6 x - 1$ |
$12$ |
[8,2] |
$3^{4}\cdot 5^{6}\cdot 3881^{2}$ |
$3$ |
$12.7844689936$ |
$241.2778481336403$ |
|
|
? |
$S_4\wr C_2$ (as 12T203) |
trivial |
$2$ |
$9$ |
$131.311224905$ |
12.8.20290998443009.1 |
$x^{12} - 2 x^{11} - 7 x^{10} + 10 x^{9} + 21 x^{8} - 18 x^{7} - 24 x^{6} + 16 x^{5} + 7 x^{4} - 10 x^{3} + 4 x + 1$ |
$12$ |
[8,2] |
$7^{8}\cdot 41\cdot 293^{2}$ |
$3$ |
$12.8511487783$ |
$401.0739284602191$ |
|
|
? |
$D_4\wr C_3$ (as 12T222) |
trivial |
$2$ |
$9$ |
$136.470116005$ |
12.8.20802722533376.1 |
$x^{12} - 2 x^{11} - 6 x^{10} + 14 x^{9} + 10 x^{8} - 46 x^{7} - 18 x^{6} + 58 x^{5} + 22 x^{4} - 28 x^{3} - 9 x^{2} + 4 x + 1$ |
$12$ |
[8,2] |
$2^{12}\cdot 7^{8}\cdot 881$ |
$3$ |
$12.8778495812$ |
$365.3331991872269$ |
|
|
? |
$D_4\wr C_3$ (as 12T222) |
trivial |
$2$ |
$9$ |
$138.21501334$ |
12.8.21426070716181.1 |
$x^{12} - 2 x^{11} - 2 x^{10} + 2 x^{9} - x^{8} + 18 x^{7} + 3 x^{6} - 44 x^{5} + x^{4} + 32 x^{3} - 3 x^{2} - 5 x + 1$ |
$12$ |
[8,2] |
$61\cdot 592661^{2}$ |
$2$ |
$12.9095730044$ |
$6012.680018095092$ |
|
|
✓ |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$9$ |
$140.499080957$ |
12.8.24302560546048.1 |
$x^{12} - x^{11} - 4 x^{10} + 10 x^{9} - 5 x^{8} - 26 x^{7} + 29 x^{6} + 10 x^{5} - 23 x^{4} + 12 x^{3} + 2 x^{2} - 5 x + 1$ |
$12$ |
[8,2] |
$2^{8}\cdot 37^{7}$ |
$2$ |
$13.0458086084$ |
$23.81430748424474$ |
|
|
? |
$A_4:C_4$ (as 12T30) |
trivial |
$2$ |
$9$ |
$152.927532449$ |
12.8.24805630328125.1 |
$x^{12} - 3 x^{11} + x^{9} + 5 x^{8} + 8 x^{7} - 8 x^{6} - 8 x^{5} - 5 x^{4} - 2 x^{3} + 6 x^{2} + 5 x + 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 2731\cdot 581311$ |
$3$ |
$13.0681022007$ |
$89094.3415992284$ |
|
|
? |
$S_6\wr C_2$ (as 12T299) |
trivial |
$2$ |
$9$ |
$154.471906261$ |
12.8.24952387024669.1 |
$x^{12} - 6 x^{11} + 14 x^{10} - 15 x^{9} + 24 x^{7} - 30 x^{6} + 9 x^{5} + 13 x^{4} - 16 x^{3} + 3 x^{2} + 3 x - 1$ |
$12$ |
[8,2] |
$13^{10}\cdot 181$ |
$2$ |
$13.0745276594$ |
$114.05791132835279$ |
|
|
✓ |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$9$ |
$154.283337179$ |
12.8.25438761101997.1 |
$x^{12} - 3 x^{10} - x^{9} - 9 x^{8} + 12 x^{7} + 21 x^{6} - 12 x^{5} - 9 x^{4} + x^{3} - 3 x^{2} + 1$ |
$12$ |
[8,2] |
$3^{16}\cdot 19^{2}\cdot 1637$ |
$3$ |
$13.0955777411$ |
$763.0672475840189$ |
|
|
? |
$D_4\wr C_3$ (as 12T222) |
trivial |
$2$ |
$9$ |
$155.078927319$ |
12.8.25641035447233.1 |
$x^{12} - 5 x^{11} + 6 x^{10} + 6 x^{9} - 18 x^{8} + 17 x^{7} - 15 x^{6} + 17 x^{5} - 18 x^{4} + 6 x^{3} + 6 x^{2} - 5 x + 1$ |
$12$ |
[8,2] |
$73\cdot 592661^{2}$ |
$2$ |
$13.1042236499$ |
$6577.556765243459$ |
|
|
✓ |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$9$ |
$156.046592372$ |
12.8.25652742953125.1 |
$x^{12} - 5 x^{11} + 3 x^{10} + 22 x^{9} - 41 x^{8} + 6 x^{7} + 39 x^{6} - 35 x^{5} + 3 x^{4} + 18 x^{3} - 5 x^{2} - 6 x - 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 109\cdot 3881^{2}$ |
$3$ |
$13.1047221532$ |
$1454.3538083973926$ |
|
|
✓ |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$9$ |
$156.335074574$ |
12.8.25652742953125.2 |
$x^{12} - 4 x^{11} + 16 x^{9} - 9 x^{8} - 30 x^{7} + 22 x^{6} + 31 x^{5} - 23 x^{4} - 13 x^{3} + 10 x^{2} + x - 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 109\cdot 3881^{2}$ |
$3$ |
$13.1047221532$ |
$1454.3538083973926$ |
|
|
✓ |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$9$ |
$156.402949424$ |
12.8.26641409828125.1 |
$x^{12} - x^{11} - 2 x^{10} + 6 x^{9} - 4 x^{8} - 2 x^{7} - 4 x^{6} - 10 x^{5} + 20 x^{4} + 7 x^{3} - 11 x^{2} + 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 1705050229$ |
$2$ |
$13.1460849274$ |
$92332.28657950588$ |
|
|
? |
$S_6\wr C_2$ (as 12T299) |
trivial |
$2$ |
$9$ |
$159.465807194$ |
12.8.28866785588221.1 |
$x^{12} - 6 x^{10} - 4 x^{9} + 13 x^{8} + 16 x^{7} - 9 x^{6} - 21 x^{5} - 4 x^{4} + 11 x^{3} + 5 x^{2} - 2 x - 1$ |
$12$ |
[8,2] |
$7^{8}\cdot 5007421$ |
$2$ |
$13.2342662878$ |
$8188.526267478483$ |
|
|
✓ |
$S_4\wr C_3$ (as 12T292) |
trivial |
$2$ |
$9$ |
$168.173115475$ |
12.8.30967526064128.1 |
$x^{12} - 6 x^{10} - 2 x^{9} + 9 x^{8} + 8 x^{7} - x^{6} - 14 x^{5} - 6 x^{4} + 10 x^{3} + 5 x^{2} - 2 x - 1$ |
$12$ |
[8,2] |
$2^{18}\cdot 118131737$ |
$2$ |
$13.3119662942$ |
$30741.728903885676$ |
|
|
✓ |
$S_6\wr C_2$ (as 12T299) |
trivial |
$2$ |
$9$ |
$175.399901193$ |
12.8.31436180453125.1 |
$x^{12} - 2 x^{11} - 2 x^{10} + 2 x^{9} - 7 x^{8} + 6 x^{7} + 23 x^{6} - x^{5} - 24 x^{4} - 9 x^{3} + 9 x^{2} + 4 x - 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 7^{8}\cdot 349$ |
$3$ |
$13.3286392753$ |
$152.86089885109513$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$9$ |
$175.632791501$ |
12.8.34183776846541.1 |
$x^{12} - 4 x^{11} + 3 x^{10} + 2 x^{9} - 7 x^{8} + 11 x^{7} - 11 x^{6} - x^{5} + 21 x^{4} - 9 x^{3} - 8 x^{2} + 2 x + 1$ |
$12$ |
[8,2] |
$7^{8}\cdot 181^{3}$ |
$2$ |
$13.4220340756$ |
$180.57500040015438$ |
|
|
? |
$C_4\wr C_3$ (as 12T94) |
trivial |
$2$ |
$9$ |
$185.527083784$ |
12.8.34282488765625.1 |
$x^{12} - x^{11} - 5 x^{10} + 7 x^{9} + x^{8} - 11 x^{7} + 19 x^{6} - 14 x^{5} - 5 x^{4} + 30 x^{3} - 27 x^{2} + 5 x + 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 31^{2}\cdot 1511^{2}$ |
$3$ |
$13.4252596905$ |
$483.9473111817029$ |
|
|
? |
$S_4\wr C_2$ (as 12T203) |
trivial |
$2$ |
$9$ |
$185.208174005$ |
12.8.34801233152049.1 |
$x^{12} - 3 x^{11} - 4 x^{10} + 16 x^{9} + 4 x^{8} - 24 x^{7} - x^{6} - 4 x^{5} - 10 x^{4} + 26 x^{3} + 31 x^{2} + 10 x + 1$ |
$12$ |
[8,2] |
$3^{6}\cdot 7^{10}\cdot 13^{2}$ |
$3$ |
$13.442072066$ |
$31.606810323667133$ |
|
|
? |
$C_2^2 \times A_4$ (as 12T25) |
trivial |
$2$ |
$9$ |
$185.836401127$ |
12.8.35258133876736.1 |
$x^{12} - 3 x^{10} + x^{8} - 6 x^{6} + 11 x^{4} - 6 x^{2} + 1$ |
$12$ |
[8,2] |
$2^{12}\cdot 92779^{2}$ |
$2$ |
$13.4566909027$ |
$1117.2647207234238$ |
|
|
✓ |
$C_2^5:S_6$ (as 12T285) |
trivial |
$2$ |
$9$ |
$188.34728076$ |
12.8.36472323149824.1 |
$x^{12} - 6 x^{10} + 13 x^{8} - 15 x^{6} + 14 x^{4} - 9 x^{2} + 1$ |
$12$ |
[8,2] |
$2^{12}\cdot 197^{2}\cdot 479^{2}$ |
$3$ |
$13.4947119538$ |
$1126.761791560834$ |
|
|
✓ |
$C_2^5:S_6$ (as 12T285) |
trivial |
$2$ |
$9$ |
$192.752697995$ |
12.8.36767438995456.1 |
$x^{12} - 4 x^{11} - 2 x^{10} + 20 x^{9} + x^{8} - 46 x^{7} - 2 x^{6} + 58 x^{5} + 3 x^{4} - 34 x^{3} + x^{2} + 6 x - 1$ |
$12$ |
[8,2] |
$2^{18}\cdot 13^{2}\cdot 911^{2}$ |
$3$ |
$13.5037777544$ |
$307.80513316057613$ |
|
|
? |
$S_4^2:C_2^2$ (as 12T236) |
trivial |
$2$ |
$9$ |
$196.084738415$ |
12.8.37921581578125.1 |
$x^{12} - x^{11} - 5 x^{10} + 9 x^{9} + 9 x^{8} - 20 x^{7} - 11 x^{6} + 9 x^{5} + 9 x^{4} + 7 x^{3} - x^{2} - 4 x - 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 7^{8}\cdot 421$ |
$3$ |
$13.5386035236$ |
$167.8899668775688$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$9$ |
$196.536532311$ |
12.8.38509781640625.1 |
$x^{12} - x^{11} - 7 x^{10} + 4 x^{9} + 8 x^{8} - 13 x^{7} + 9 x^{6} + 21 x^{5} - 18 x^{4} - 12 x^{3} + 8 x^{2} + 2 x - 1$ |
$12$ |
[8,2] |
$5^{8}\cdot 9929^{2}$ |
$2$ |
$13.5559800598$ |
$333.1810239839254$ |
|
|
? |
$S_4\wr C_2$ (as 12T203) |
trivial |
$2$ |
$9$ |
$198.646945236$ |
12.8.39358370640625.1 |
$x^{12} - 2 x^{11} - 8 x^{10} + 20 x^{9} + 8 x^{8} - 38 x^{7} + 2 x^{6} + 20 x^{5} + 3 x^{4} + x^{3} - 6 x^{2} - x + 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 31^{2}\cdot 1619^{2}$ |
$3$ |
$13.5806250626$ |
$500.9441086588403$ |
|
|
? |
$S_4\wr C_2$ (as 12T203) |
trivial |
$2$ |
$9$ |
$202.073516984$ |
12.8.40147924665121.1 |
$x^{12} - 5 x^{11} + 6 x^{10} + 9 x^{9} - 33 x^{8} + 36 x^{7} + 6 x^{6} - 51 x^{5} + 22 x^{4} + 19 x^{3} - 2 x^{2} - 8 x + 1$ |
$12$ |
[8,2] |
$7^{10}\cdot 13^{2}\cdot 29^{2}$ |
$3$ |
$13.6031219578$ |
$98.26956684930803$ |
|
|
? |
$C_2^2\wr C_3$ (as 12T90) |
trivial |
$2$ |
$9$ |
$209.650751578$ |
12.8.40419192196881.1 |
$x^{12} - 6 x^{11} + 12 x^{10} - 45 x^{8} + 81 x^{7} - 25 x^{6} - 69 x^{5} + 48 x^{4} + 21 x^{3} - 18 x^{2} + 1$ |
$12$ |
[8,2] |
$3^{18}\cdot 17^{2}\cdot 19^{2}$ |
$3$ |
$13.6107576926$ |
$93.38629449764028$ |
|
|
? |
$C_2^2\wr C_3$ (as 12T90) |
trivial |
$2$ |
$9$ |
$210.44327278$ |
12.8.41524582203125.1 |
$x^{12} - 3 x^{11} - 5 x^{10} + 20 x^{9} + 3 x^{8} - 40 x^{7} + 11 x^{6} + 15 x^{5} + 3 x^{4} + 13 x^{3} - 26 x^{2} + 10 x - 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 7^{8}\cdot 461$ |
$3$ |
$13.6413946261$ |
$175.6847877137702$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$9$ |
$208.277047451$ |
12.8.42597674078125.1 |
$x^{12} - x^{11} - 5 x^{10} + 5 x^{9} + 3 x^{8} + x^{7} + 6 x^{6} - 17 x^{5} - 8 x^{4} + 15 x^{3} + 5 x^{2} - 3 x - 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 181\cdot 3881^{2}$ |
$3$ |
$13.6704294268$ |
$1874.114457550552$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$9$ |
$211.394191552$ |
12.8.44804009850925.1 |
$x^{12} - 4 x^{11} + 3 x^{10} + x^{9} - 4 x^{8} + 3 x^{7} + x^{6} + 9 x^{5} + 3 x^{4} - 12 x^{3} - 4 x^{2} + 3 x + 1$ |
$12$ |
[8,2] |
$5^{2}\cdot 13^{11}$ |
$2$ |
$13.7280780714$ |
$23.474683296117743$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$9$ |
$219.591054766$ |
12.8.44962053890625.1 |
$x^{12} - 5 x^{11} + 4 x^{10} + 14 x^{9} - 22 x^{8} - 7 x^{7} + 29 x^{6} - 7 x^{5} - 22 x^{4} + 14 x^{3} + 4 x^{2} - 5 x + 1$ |
$12$ |
[8,2] |
$3^{2}\cdot 5^{6}\cdot 17881^{2}$ |
$3$ |
$13.7321069909$ |
$517.8947769576364$ |
|
|
? |
$S_4^2:C_2^2$ (as 12T236) |
trivial |
$2$ |
$9$ |
$225.044091621$ |
12.8.45358541265625.1 |
$x^{12} - 5 x^{11} + 3 x^{10} + 14 x^{9} - 11 x^{8} - 19 x^{7} + 3 x^{6} + 26 x^{5} + 9 x^{4} - 21 x^{3} - 7 x^{2} + 5 x + 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 7^{2}\cdot 43^{2}\cdot 179^{2}$ |
$4$ |
$13.7421575489$ |
$519.0327542650849$ |
|
|
? |
$S_6\times C_2$ (as 12T219) |
trivial |
$2$ |
$9$ |
$216.664760258$ |
12.8.47211387828125.1 |
$x^{12} - 6 x^{10} - 3 x^{9} + 11 x^{8} + 16 x^{7} - 6 x^{6} - 24 x^{5} - 4 x^{4} + 11 x^{3} + 5 x^{2} - x - 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 29^{3}\cdot 229\cdot 541$ |
$4$ |
$13.7880832604$ |
$4238.384715902982$ |
|
|
? |
$S_3\wr D_4$ (as 12T274) |
trivial |
$2$ |
$9$ |
$225.817592693$ |
12.8.47466656328125.1 |
$x^{12} - x^{11} - 7 x^{10} + 8 x^{9} + 17 x^{8} - 15 x^{7} - 32 x^{6} - 4 x^{5} + 49 x^{4} + 26 x^{3} - 30 x^{2} - 12 x - 1$ |
$12$ |
[8,2] |
$5^{7}\cdot 157^{4}$ |
$2$ |
$13.7942805134$ |
$41.89646002154997$ |
|
|
? |
$C_4\times S_4$ (as 12T53) |
trivial |
$2$ |
$9$ |
$249.254034357$ |
12.8.51942673828125.1 |
$x^{12} - 2 x^{11} - 6 x^{10} + 11 x^{9} + 15 x^{8} - 17 x^{7} - 27 x^{6} + 4 x^{5} + 29 x^{4} + 4 x^{3} - 12 x^{2} + 1$ |
$12$ |
[8,2] |
$3^{6}\cdot 5^{9}\cdot 191^{2}$ |
$3$ |
$13.8982576497$ |
$80.03958242980093$ |
|
|
? |
$S_3^2:C_4$ (as 12T79) |
trivial |
$2$ |
$9$ |
$245.622566038$ |
12.8.52649684000000.1 |
$x^{12} - 8 x^{10} - 3 x^{9} + 21 x^{8} + 14 x^{7} - 21 x^{6} - 18 x^{5} + 5 x^{4} + 3 x^{3} + x^{2} + 3 x + 1$ |
$12$ |
[8,2] |
$2^{8}\cdot 5^{6}\cdot 19^{4}\cdot 101$ |
$4$ |
$13.9139246589$ |
$254.00060640965427$ |
|
|
? |
$A_4^2:D_4$ (as 12T208) |
trivial |
$2$ |
$9$ |
$238.420109994$ |
12.8.53626953329261.1 |
$x^{12} - x^{11} - 2 x^{10} + 8 x^{9} - 10 x^{8} - 19 x^{7} + 26 x^{6} + 23 x^{5} - 22 x^{4} - 12 x^{3} + 8 x^{2} + 2 x - 1$ |
$12$ |
[8,2] |
$13^{10}\cdot 389$ |
$2$ |
$13.9352659137$ |
$167.20949205345389$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$9$ |
$240.048042471$ |
12.8.53894294828125.1 |
$x^{12} - 5 x^{11} + 5 x^{10} + 9 x^{9} - 17 x^{8} + x^{7} + 12 x^{6} - 4 x^{5} - 2 x^{4} - 5 x^{3} + x^{2} + 4 x + 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 229\cdot 3881^{2}$ |
$3$ |
$13.9410419109$ |
$2108.0192124361674$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$9$ |
$238.451434556$ |
12.8.54738442953125.1 |
$x^{12} - 6 x^{11} + 12 x^{10} - 5 x^{9} - 21 x^{8} + 48 x^{7} - 48 x^{6} + 21 x^{5} + 10 x^{4} - 22 x^{3} + 6 x^{2} + 4 x - 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 29^{3}\cdot 379^{2}$ |
$3$ |
$13.9591091556$ |
$234.42482803662244$ |
|
|
? |
$D_6\wr C_2$ (as 12T125) |
trivial |
$2$ |
$9$ |
$244.611008736$ |
12.8.55336169149373.1 |
$x^{12} - 3 x^{11} + 4 x^{9} + 2 x^{7} - 10 x^{6} + 3 x^{5} + 21 x^{4} - 4 x^{3} - 14 x^{2} - 2 x + 1$ |
$12$ |
[8,2] |
$7^{8}\cdot 181^{2}\cdot 293$ |
$3$ |
$13.9717484372$ |
$842.6976657804249$ |
|
|
? |
$D_4\wr C_3$ (as 12T222) |
trivial |
$2$ |
$9$ |
$242.797003084$ |
12.8.56034909078125.1 |
$x^{12} - x^{11} - 2 x^{10} - 2 x^{9} + 6 x^{8} + 5 x^{7} - 16 x^{6} + 8 x^{5} + 17 x^{4} - 14 x^{3} - 8 x^{2} + 4 x + 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 9649\cdot 371669$ |
$3$ |
$13.9863660154$ |
$133907.3220738881$ |
|
|
? |
$S_6\wr C_2$ (as 12T299) |
trivial |
$2$ |
$9$ |
$246.984429478$ |
12.8.56819956000000.1 |
$x^{12} - x^{11} - 5 x^{10} + x^{9} + 9 x^{8} + 12 x^{7} - 5 x^{6} - 32 x^{5} - 3 x^{4} + 27 x^{3} + 2 x^{2} - 6 x + 1$ |
$12$ |
[8,2] |
$2^{8}\cdot 5^{6}\cdot 19^{4}\cdot 109$ |
$4$ |
$14.0025911294$ |
$263.86835860861856$ |
|
|
✓ |
$A_4^2:D_4$ (as 12T208) |
trivial |
$2$ |
$9$ |
$248.524487865$ |
12.8.58003456000000.1 |
$x^{12} - 4 x^{11} + 2 x^{10} + 4 x^{9} + 12 x^{8} - 26 x^{7} - 22 x^{6} + 72 x^{5} - 32 x^{4} - 32 x^{3} + 27 x^{2} - 2 x - 1$ |
$12$ |
[8,2] |
$2^{18}\cdot 5^{6}\cdot 7^{2}\cdot 17^{2}$ |
$4$ |
$14.0266670802$ |
$68.99275324264136$ |
|
|
? |
$S_3^2:C_2^2$ (as 12T77) |
trivial |
$2$ |
$9$ |
$251.0296206$ |
12.8.58599345953125.1 |
$x^{12} - x^{11} - 7 x^{10} + 8 x^{9} + 12 x^{8} - 13 x^{7} - 14 x^{5} + 34 x^{3} - 13 x^{2} - 9 x + 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 61\cdot 7841^{2}$ |
$3$ |
$14.038619313531752$ |
$1546.4491585564654$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$9$ |
$265.6642429284124$ |