Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
18.10.684...177.1 | $x^{18} - 4 x^{17} - x^{16} + 12 x^{15} + 15 x^{14} - 21 x^{13} - 62 x^{12} - 3 x^{11} + 117 x^{10} + 86 x^{9} - 121 x^{8} - 128 x^{7} + 57 x^{6} + 70 x^{5} - 6 x^{4} - 9 x^{3} - x^{2} - 2 x + 1$ | $73\cdot 9685993193^{2}$ | $C_2^9.S_9$ (as 18T968) | trivial |
18.10.834...161.1 | $x^{18} - 9 x^{17} + 34 x^{16} - 68 x^{15} + 60 x^{14} + 56 x^{13} - 254 x^{12} + 354 x^{11} - 193 x^{10} - 135 x^{9} + 327 x^{8} - 218 x^{7} - 12 x^{6} + 114 x^{5} - 63 x^{4} - 6 x^{3} + 14 x^{2} - 2 x - 1$ | $89\cdot 9685993193^{2}$ | $C_2^9.S_9$ (as 18T968) | trivial |
18.10.106...197.1 | $x^{18} - 6 x^{17} + 7 x^{16} + 21 x^{15} - 49 x^{14} - 5 x^{13} + 87 x^{12} - 97 x^{11} + 63 x^{10} + 116 x^{9} - 329 x^{8} + 93 x^{7} + 293 x^{6} - 176 x^{5} - 84 x^{4} + 59 x^{3} + 12 x^{2} - 6 x - 1$ | $19^{16}\cdot 37$ | $C_2\wr C_9$ (as 18T460) | trivial |
18.10.113...129.1 | $x^{18} - 5 x^{17} + 7 x^{16} + 12 x^{15} - 49 x^{14} + 22 x^{13} + 97 x^{12} - 132 x^{11} - 48 x^{10} + 256 x^{9} - 151 x^{8} - 165 x^{7} + 222 x^{6} - 41 x^{5} - 73 x^{4} + 59 x^{3} - 7 x^{2} - 5 x + 1$ | $11^{2}\cdot 9685993193^{2}$ | $C_2^8.S_9$ (as 18T964) | trivial |
18.10.119...029.1 | $x^{18} - 9 x^{17} + 27 x^{16} - 12 x^{15} - 93 x^{14} + 147 x^{13} + 82 x^{12} - 297 x^{11} + 15 x^{10} + 288 x^{9} - 36 x^{8} - 171 x^{7} - 17 x^{6} + 66 x^{5} + 34 x^{4} - 14 x^{3} - 13 x^{2} + 2 x + 1$ | $109^{2}\cdot 541^{2}\cdot 12041^{2}\cdot 23669$ | $C_2^9.S_9$ (as 18T968) | trivial |
18.10.158...081.1 | $x^{18} - 5 x^{17} + 37 x^{15} - 50 x^{14} - 54 x^{13} + 130 x^{12} - 18 x^{11} - 35 x^{10} - 49 x^{9} - 4 x^{8} + 97 x^{7} - 76 x^{6} + 43 x^{5} - 15 x^{4} + 2 x^{3} + 2 x^{2} - 4 x - 1$ | $13^{2}\cdot 9685993193^{2}$ | $C_2^8.S_9$ (as 18T964) | trivial |
18.10.172...784.1 | $x^{18} + 2 x^{16} - 16 x^{14} - 26 x^{12} + 73 x^{10} + 57 x^{8} - 132 x^{6} + 33 x^{4} + 8 x^{2} - 1$ | $2^{6}\cdot 37^{4}\cdot 229^{6}$ | $A_4^3.S_4$ (as 18T711) | trivial |
18.10.196...456.1 | $x^{18} - 9 x^{16} - 8 x^{15} + 24 x^{14} + 41 x^{13} - 21 x^{12} - 91 x^{11} - 14 x^{10} + 151 x^{9} + 112 x^{8} - 119 x^{7} - 161 x^{6} + 5 x^{5} + 79 x^{4} + 27 x^{3} - 10 x^{2} - 7 x - 1$ | $2^{6}\cdot 7^{12}\cdot 53^{6}$ | $C_2^4:(A_4\times S_4)$ (as 18T463) | trivial |
18.10.297...113.1 | $x^{18} - 7 x^{17} + 16 x^{16} - 6 x^{15} - 41 x^{14} + 97 x^{13} - 93 x^{12} - 6 x^{11} + 141 x^{10} - 205 x^{9} + 141 x^{8} - 6 x^{7} - 93 x^{6} + 97 x^{5} - 41 x^{4} - 6 x^{3} + 16 x^{2} - 7 x + 1$ | $7^{12}\cdot 53^{6}\cdot 97$ | $C_2^5.(A_4\times S_4)$ (as 18T544) | trivial |
18.10.434...129.1 | $x^{18} - 3 x^{17} - 3 x^{16} + 14 x^{15} - 11 x^{14} + 25 x^{13} - 28 x^{12} - 75 x^{11} + 161 x^{10} - 138 x^{9} + 34 x^{8} + 178 x^{7} - 246 x^{6} + 16 x^{5} + 216 x^{4} - 196 x^{3} + 51 x^{2} + 6 x - 1$ | $23^{2}\cdot 5569^{3}\cdot 21817^{2}$ | $C_2^9.S_9$ (as 18T968) | trivial |
18.10.539...576.1 | $x^{18} + 3 x^{16} - 4 x^{14} - 11 x^{12} + 4 x^{10} - 4 x^{8} + 33 x^{6} - 32 x^{4} + 10 x^{2} - 1$ | $2^{18}\cdot 453771377^{2}$ | $C_2^8.S_9$ (as 18T964) | trivial |
18.10.544...984.1 | $x^{18} - 8 x^{16} + 22 x^{14} - 26 x^{12} + 20 x^{10} - 20 x^{8} + 6 x^{6} + 2 x^{4} + 5 x^{2} - 1$ | $2^{18}\cdot 109^{2}\cdot 4181741^{2}$ | $C_2^8.S_9$ (as 18T964) | trivial |
18.10.554...001.1 | $x^{18} - 6 x^{17} + 13 x^{16} - 12 x^{15} - 8 x^{14} + 56 x^{13} - 92 x^{12} + 64 x^{11} - 25 x^{10} + 24 x^{9} + 81 x^{8} - 221 x^{7} + 116 x^{6} - 31 x^{5} + 102 x^{4} - 54 x^{3} - 14 x^{2} + 6 x + 1$ | $7^{12}\cdot 13^{4}\cdot 41\cdot 43^{4}$ | $C_2\times A_4^3.A_4$ (as 18T696) | trivial |
18.10.573...376.1 | $x^{18} - 8 x^{16} + 19 x^{14} - 4 x^{12} - 27 x^{10} + x^{8} + 27 x^{6} - 9 x^{4} - 1$ | $2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2}$ | $S_4\wr C_3$ (as 18T703) | trivial |
18.10.573...376.2 | $x^{18} - 7 x^{16} + 21 x^{14} - 41 x^{12} + 49 x^{10} - 28 x^{8} + 12 x^{6} - 14 x^{4} + 7 x^{2} - 1$ | $2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2}$ | $S_4\wr C_3$ (as 18T703) | trivial |
18.10.638...904.1 | $x^{18} - 6 x^{17} + 9 x^{16} + 10 x^{15} - 44 x^{14} + 60 x^{13} - 44 x^{12} - 10 x^{11} + 78 x^{10} - 116 x^{9} + 78 x^{8} - 10 x^{7} - 44 x^{6} + 60 x^{5} - 44 x^{4} + 10 x^{3} + 9 x^{2} - 6 x + 1$ | $2^{18}\cdot 101^{6}\cdot 479^{2}$ | $S_4^3.S_4$ (as 18T883) | trivial |
18.10.669...569.1 | $x^{18} - 4 x^{17} + 8 x^{15} - 3 x^{14} + 6 x^{13} + 14 x^{12} - 18 x^{11} - 59 x^{10} - 26 x^{9} + 69 x^{8} + 92 x^{7} + 23 x^{6} - 67 x^{5} - 69 x^{4} - x^{3} + 23 x^{2} + 9 x + 1$ | $7^{12}\cdot 97^{2}\cdot 22679^{2}$ | $S_4\wr C_3$ (as 18T703) | trivial |
18.10.669...569.2 | $x^{18} - 6 x^{16} - 4 x^{15} - 12 x^{14} - 10 x^{13} + 111 x^{12} + 194 x^{11} - 28 x^{10} - 377 x^{9} - 412 x^{8} - 17 x^{7} + 333 x^{6} + 281 x^{5} + 54 x^{4} - 53 x^{3} - 28 x^{2} + x + 1$ | $7^{12}\cdot 97^{2}\cdot 22679^{2}$ | $S_4^3.A_4$ (as 18T838) | trivial |
18.10.669...569.3 | $x^{18} - 3 x^{17} + 3 x^{16} - 18 x^{14} + 37 x^{13} - 27 x^{12} - 12 x^{11} + 107 x^{10} - 158 x^{9} - 7 x^{8} + 207 x^{7} - 134 x^{6} - 64 x^{5} + 90 x^{4} - 10 x^{3} - 16 x^{2} + 2 x + 1$ | $7^{12}\cdot 97^{2}\cdot 22679^{2}$ | $S_4^3.A_4$ (as 18T838) | trivial |
18.10.855...992.1 | $x^{18} - 4 x^{17} + 3 x^{16} + 14 x^{15} - 46 x^{14} + 41 x^{13} + 72 x^{12} - 216 x^{11} + 76 x^{10} + 273 x^{9} - 151 x^{8} - 170 x^{7} + 53 x^{6} + 93 x^{5} - 79 x^{4} + 45 x^{3} - 7 x + 1$ | $2^{12}\cdot 37^{9}\cdot 401^{2}$ | $S_3\wr S_3$ (as 18T319) | trivial |
18.10.946...001.1 | $x^{18} - 3 x^{17} - 4 x^{16} + 32 x^{15} - 38 x^{14} - 92 x^{13} + 269 x^{12} - 37 x^{11} - 577 x^{10} + 459 x^{9} + 400 x^{8} - 596 x^{7} + 54 x^{6} + 295 x^{5} - 75 x^{4} - 92 x^{3} - 6 x^{2} + 10 x + 1$ | $83\cdot 1523\cdot 865377817^{2}$ | $C_2^9.S_9$ (as 18T968) | trivial |
18.10.100...536.1 | $x^{18} - 8 x^{16} - 3 x^{15} + 6 x^{14} - 14 x^{13} + 28 x^{12} + 68 x^{11} - 70 x^{10} - 101 x^{9} + 62 x^{8} + 66 x^{7} - 8 x^{6} - 2 x^{5} - 10 x^{4} - 19 x^{3} - 2 x^{2} + 4 x + 1$ | $2^{12}\cdot 101^{7}\cdot 479^{2}$ | $A_4^3.(C_2\times S_4)$ (as 18T773) | trivial |
18.10.140...525.1 | $x^{18} - x^{17} - 9 x^{16} + 15 x^{15} + 17 x^{14} - 71 x^{13} + 30 x^{12} + 89 x^{11} - 142 x^{10} + 61 x^{9} + 128 x^{8} - 265 x^{7} + 227 x^{6} - 66 x^{5} - 73 x^{4} + 95 x^{3} - 47 x^{2} + 11 x - 1$ | $5^{2}\cdot 257^{6}\cdot 269^{3}$ | $D_6\wr S_3$ (as 18T556) | trivial |
18.10.148...501.1 | $x^{18} - 9 x^{17} + 27 x^{16} - 12 x^{15} - 93 x^{14} + 147 x^{13} + 83 x^{12} - 303 x^{11} + 24 x^{10} + 298 x^{9} - 69 x^{8} - 165 x^{7} + 18 x^{6} + 48 x^{5} + 21 x^{4} - 4 x^{3} - 12 x^{2} + 1$ | $3^{24}\cdot 19\cdot 2053^{2}\cdot 6551$ | $C_2\times S_4^3.A_4$ (as 18T879) | trivial |
18.10.173...289.1 | $x^{18} - 4 x^{17} + x^{16} + x^{15} + 23 x^{14} + 6 x^{13} - 75 x^{12} - 10 x^{11} + 39 x^{10} + 124 x^{9} - 36 x^{8} - 145 x^{7} + 75 x^{6} + 12 x^{5} - 43 x^{4} + 15 x^{3} + 12 x^{2} - 2 x - 1$ | $7^{12}\cdot 3540067^{2}$ | $S_4\wr C_3$ (as 18T703) | trivial |
18.10.180...616.1 | $x^{18} + x^{16} - 15 x^{14} + 56 x^{10} - 23 x^{8} - 57 x^{6} + 45 x^{4} - 6 x^{2} - 1$ | $2^{18}\cdot 37^{6}\cdot 16361^{2}$ | $S_4^3.S_4$ (as 18T883) | trivial |
18.10.180...616.2 | $x^{18} - 6 x^{17} + 10 x^{16} + 16 x^{15} - 91 x^{14} + 116 x^{13} + 83 x^{12} - 398 x^{11} + 415 x^{10} + 52 x^{9} - 624 x^{8} + 604 x^{7} - 28 x^{6} - 292 x^{5} + 151 x^{4} + 14 x^{3} - 33 x^{2} + 10 x - 1$ | $2^{18}\cdot 37^{6}\cdot 16361^{2}$ | $S_4^3.S_4$ (as 18T883) | trivial |
18.10.180...616.3 | $x^{18} + 6 x^{16} - 13 x^{14} - 51 x^{12} + 47 x^{10} + 104 x^{8} - 64 x^{6} - 49 x^{4} + 19 x^{2} - 1$ | $2^{18}\cdot 37^{6}\cdot 16361^{2}$ | $A_4^3.(C_2\times S_4)$ (as 18T776) | trivial |
18.10.237...529.1 | $x^{18} - 2 x^{17} - 11 x^{16} + 9 x^{15} + 47 x^{14} + 14 x^{13} - 85 x^{12} - 98 x^{11} + 48 x^{10} + 147 x^{9} + 48 x^{8} - 98 x^{7} - 85 x^{6} + 14 x^{5} + 47 x^{4} + 9 x^{3} - 11 x^{2} - 2 x + 1$ | $7^{14}\cdot 769^{4}$ | $A_4\wr C_3$ (as 18T473) | trivial |
18.10.250...216.1 | $x^{18} - 8 x^{17} + 23 x^{16} - 36 x^{15} + 57 x^{14} - 80 x^{13} + 30 x^{12} + 44 x^{11} - 70 x^{10} + 136 x^{9} - 139 x^{8} + 18 x^{7} + 83 x^{6} - 106 x^{5} + 35 x^{4} + 24 x^{3} - 12 x^{2} - 2 x + 1$ | $2^{12}\cdot 37^{6}\cdot 89\cdot 16361^{2}$ | $C_2\times S_4^3.S_4$ (as 18T912) | trivial |
18.10.256...128.1 | $x^{18} - 17 x^{14} - 15 x^{12} + 71 x^{10} + 62 x^{8} - 120 x^{6} - 79 x^{4} + 135 x^{2} - 37$ | $2^{24}\cdot 37^{7}\cdot 401^{2}$ | $A_4^3.(C_2\times S_4)$ (as 18T773) | trivial |
18.10.266...517.1 | $x^{18} - 3 x^{17} - 2 x^{16} + 9 x^{15} - 10 x^{14} - 14 x^{13} + 20 x^{12} + 46 x^{11} + 21 x^{10} - 78 x^{9} - 32 x^{8} + 42 x^{7} - 33 x^{6} + 4 x^{5} + 53 x^{4} - 3 x^{3} - 19 x^{2} - 2 x + 1$ | $7^{12}\cdot 13^{4}\cdot 43^{4}\cdot 197$ | $C_2\times A_4^3.A_4$ (as 18T696) | trivial |
18.10.269...336.1 | $x^{18} - 7 x^{17} + 26 x^{16} - 66 x^{15} + 111 x^{14} - 111 x^{13} + 19 x^{12} + 138 x^{11} - 198 x^{10} + 159 x^{9} - 188 x^{8} + 15 x^{7} + 326 x^{6} - 200 x^{5} - 118 x^{4} + 78 x^{3} + 22 x^{2} - 5 x - 1$ | $2^{12}\cdot 7^{12}\cdot 41^{6}$ | $A_4^3:A_4$ (as 18T646) | trivial |
18.10.272...168.1 | $x^{18} - 3 x^{17} - 2 x^{16} + 10 x^{15} + 3 x^{14} - 35 x^{13} + 24 x^{12} + 147 x^{11} - 120 x^{10} - 425 x^{9} + 194 x^{8} + 737 x^{7} - 254 x^{6} - 625 x^{5} + 287 x^{4} + 154 x^{3} - 114 x^{2} + 21 x - 1$ | $2^{12}\cdot 37^{6}\cdot 97\cdot 16361^{2}$ | $C_2\times S_4^3.S_4$ (as 18T912) | trivial |
18.10.289...217.1 | $x^{18} - 3 x^{17} + 12 x^{15} - 15 x^{14} - 15 x^{13} + 21 x^{12} + 33 x^{11} - 18 x^{10} - 114 x^{9} + 90 x^{8} + 171 x^{7} - 109 x^{6} - 105 x^{5} + 15 x^{4} + 24 x^{3} + 15 x^{2} - 3 x - 1$ | $3^{24}\cdot 73^{2}\cdot 577^{3}$ | $C_2\times S_4^3.A_4$ (as 18T879) | trivial |
18.10.289...217.2 | $x^{18} - 6 x^{16} - 3 x^{15} + 9 x^{14} + 21 x^{13} - x^{12} - 21 x^{11} + 27 x^{10} - 60 x^{9} - 162 x^{8} - 3 x^{7} + 183 x^{6} + 162 x^{5} - 48 x^{4} - 92 x^{3} + 12 x^{2} + 9 x - 1$ | $3^{24}\cdot 73^{2}\cdot 577^{3}$ | $C_2\times S_4^3.A_4$ (as 18T879) | trivial |
18.10.289...217.3 | $x^{18} - 3 x^{17} - 9 x^{16} + 26 x^{15} + 18 x^{14} - 57 x^{13} + 9 x^{12} - 75 x^{10} + 123 x^{9} + 105 x^{8} - 129 x^{7} - 34 x^{6} + 51 x^{5} - 33 x^{4} - 20 x^{3} + 18 x^{2} + 9 x + 1$ | $3^{24}\cdot 73^{2}\cdot 577^{3}$ | $C_2\times S_4^3.A_4$ (as 18T879) | trivial |
18.10.289...217.4 | $x^{18} - 3 x^{17} + 20 x^{15} - 30 x^{14} - 66 x^{13} + 79 x^{12} + 147 x^{11} + 3 x^{10} - 107 x^{9} - 180 x^{8} - 210 x^{7} + 12 x^{6} + 273 x^{5} + 231 x^{4} + 48 x^{3} - 24 x^{2} - 12 x - 1$ | $3^{24}\cdot 73^{2}\cdot 577^{3}$ | $C_2\times S_4^3.A_4$ (as 18T879) | trivial |
18.10.306...096.1 | $x^{18} - 2 x^{17} - 7 x^{16} + 23 x^{15} - 19 x^{14} - 17 x^{13} + 101 x^{12} - 207 x^{11} + 139 x^{10} + 202 x^{9} - 406 x^{8} + 149 x^{7} + 137 x^{6} - 109 x^{5} - 9 x^{4} + 32 x^{3} - 7 x^{2} - 3 x + 1$ | $2^{12}\cdot 37^{6}\cdot 109\cdot 16361^{2}$ | $C_2\times S_4^3.S_4$ (as 18T912) | trivial |
18.10.334...808.1 | $x^{18} - 13 x^{16} - 10 x^{15} + 58 x^{14} + 89 x^{13} - 98 x^{12} - 286 x^{11} - 20 x^{10} + 429 x^{9} + 229 x^{8} - 282 x^{7} - 227 x^{6} + 53 x^{5} + 71 x^{4} + 5 x^{3} - 2 x^{2} + 3 x + 1$ | $2^{12}\cdot 13^{2}\cdot 37^{9}\cdot 61^{2}$ | $S_3\wr S_3$ (as 18T319) | trivial |
18.10.385...928.1 | $x^{18} - x^{17} - 13 x^{16} + 4 x^{15} + 70 x^{14} + 21 x^{13} - 184 x^{12} - 139 x^{11} + 233 x^{10} + 255 x^{9} - 148 x^{8} - 188 x^{7} + 84 x^{6} + 61 x^{5} - 48 x^{4} - 5 x^{3} + 4 x^{2} + 1$ | $2^{12}\cdot 37^{6}\cdot 137\cdot 16361^{2}$ | $C_2\times S_4^3.S_4$ (as 18T912) | trivial |
18.10.394...289.1 | $x^{18} - 7 x^{17} + 13 x^{16} + 14 x^{15} - 64 x^{14} + 25 x^{13} + 62 x^{12} - 6 x^{11} - 16 x^{10} - 110 x^{9} + 40 x^{8} + 67 x^{7} + 43 x^{6} - 53 x^{5} - 20 x^{4} + 14 x^{3} - 4 x^{2} - x + 1$ | $19^{16}\cdot 37^{2}$ | $C_2^8:C_9$ (as 18T368) | trivial |
18.10.394...289.2 | $x^{18} - 8 x^{17} + 21 x^{16} + 7 x^{15} - 171 x^{14} + 414 x^{13} - 353 x^{12} - 237 x^{11} + 757 x^{10} - 490 x^{9} - 127 x^{8} + 306 x^{7} - 159 x^{6} + 12 x^{5} + 57 x^{4} - 27 x^{3} - 9 x^{2} + 4 x + 1$ | $19^{16}\cdot 37^{2}$ | $C_2^8:C_9$ (as 18T368) | trivial |
18.10.402...125.1 | $x^{18} - x^{17} - 10 x^{16} + 9 x^{15} + 32 x^{14} - 12 x^{13} - 34 x^{12} - 81 x^{11} - 41 x^{10} + 173 x^{9} + 109 x^{8} - 111 x^{7} - 63 x^{6} + 22 x^{5} - 2 x^{4} + 9 x^{2} - 1$ | $5^{9}\cdot 453771377^{2}$ | $C_2\times S_9$ (as 18T913) | trivial |
18.10.425...000.1 | $x^{18} - 2 x^{17} - 7 x^{16} + 10 x^{15} + 18 x^{14} - 12 x^{13} - 10 x^{12} + 14 x^{11} - 52 x^{10} - 28 x^{9} + 52 x^{8} + 14 x^{7} + 10 x^{6} - 12 x^{5} - 18 x^{4} + 10 x^{3} + 7 x^{2} - 2 x - 1$ | $2^{20}\cdot 5^{5}\cdot 37^{9}$ | $C_6^3:S_4$ (as 18T485) | trivial |
18.10.427...125.1 | $x^{18} - 2 x^{17} - x^{16} + 10 x^{15} - 22 x^{14} - 16 x^{13} + 27 x^{12} - 47 x^{11} - 41 x^{10} + 83 x^{9} + 135 x^{8} + 65 x^{7} - 52 x^{6} - 66 x^{5} - 20 x^{4} + 7 x^{3} + 10 x^{2} + x - 1$ | $5^{9}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2}$ | $S_3^3:C_6$ (as 18T286) | trivial |
18.10.442...816.1 | $x^{18} - 9 x^{16} + 29 x^{14} - 36 x^{12} + 33 x^{8} - 17 x^{6} - 5 x^{4} + 6 x^{2} - 1$ | $2^{30}\cdot 37^{6}\cdot 401^{2}$ | $A_4^3.(C_2\times S_4)$ (as 18T776) | trivial |
18.10.442...816.2 | $x^{18} - 3 x^{16} + 5 x^{14} - 18 x^{12} + 54 x^{10} - 97 x^{8} + 103 x^{6} - 57 x^{4} + 14 x^{2} - 1$ | $2^{30}\cdot 37^{6}\cdot 401^{2}$ | $A_4^3.(C_2\times S_4)$ (as 18T776) | trivial |
18.10.655...000.1 | $x^{18} - 7 x^{17} + 12 x^{16} + 13 x^{15} - 22 x^{14} - 136 x^{13} + 316 x^{12} - 145 x^{11} - 39 x^{10} - 229 x^{9} + 332 x^{8} + 77 x^{7} - 618 x^{6} + 931 x^{5} - 367 x^{4} - 349 x^{3} + 245 x^{2} - 15 x - 1$ | $2^{12}\cdot 5^{3}\cdot 13^{3}\cdot 37^{6}\cdot 61^{3}$ | $D_6\wr S_3$ (as 18T556) | trivial |
18.10.770...157.1 | $x^{18} - 3 x^{17} - 6 x^{16} + 29 x^{15} - 45 x^{14} + 21 x^{13} + 110 x^{12} - 246 x^{11} + 186 x^{10} + 44 x^{9} - 144 x^{8} + 27 x^{7} - 62 x^{6} + 123 x^{5} - 243 x^{4} + 214 x^{3} - 84 x^{2} + 15 x - 1$ | $3^{24}\cdot 7^{12}\cdot 197$ | $C_2^9:C_3^2$ (as 18T459) | trivial |