A Database for Number Fields - Created by Jürgen Klüners & Gunter Malle
Missing polynomials
This is a list of groups with no polynomials in a special complex conjugation class.
The red cross means there is no polynomial for any conjugation class of this signature.
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Missing groups: 23 Missing polynomials: 69
| Missing polynomials of degree 20 | |||||||||||||||||
| G | |G| | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | Quotients | Products | Wreath product quotients | Blocks | Properties |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 20T272 | 3420 |  | - | - | - | - | - | - | - | - | - |  | - | - | - | - | not solvable, primitive, simple, irreducible, even |
| 20T362 | 6840 | | | - | - | - | - | - | - | - | - | | - | - | - | - | not solvable, primitive, irreducible |
| 20T935 | 518400 | | - | | - | - | - | | - | - | - | | - | - | - | (2T1, 10T31) | not solvable, irreducible, even |
| 20T936 | 518400 | | - | | - | - | - | | - | - | - | | - | - | - | (2T1, 10T30) | not solvable, irreducible, even |
| 20T938 | 518400 | | - | | - | - | - | | - | - | - | | - | - | - | (2T1, 10T30) | not solvable, irreducible |
| 20T939 | 518400 | - | - | | - | - | - | | - | - | - | | - | - | - | (2T1, 10T31) | not solvable, irreducible, even |
| 20T969 | 1036800 | | - | | - |  | - | | - | - | - | | - | - | - | (2T1, 10T35) | not solvable, irreducible |
| 20T970 | 1036800 | | - | | - | | - | | - | - | - | | - | - | - | (2T1, 10T35) | not solvable, irreducible |
| 20T971 | 1036800 | | | | - | - | | | - | - | - | | - | 10T30  2T1 | 10T30 2T1 | (2T1, 10T30) | not solvable, irreducible |
| 20T972 | 1036800 | | - | | - | - | - | | - | - | - | | - | - | - | (2T1, 10T35) | not solvable, irreducible, even |
| 20T974 | 1036800 | | - | | - | - | - | | - | - | - | | - | - | - | (2T1, 10T35) | not solvable, irreducible |
| 20T975 | 1036800 | | - | | - | - | - | | - | - | - | | - | 10T31 2T1 | 10T31 2T1 | (2T1, 10T31) | not solvable, irreducible, even |
| 20T976 | 1036800 | | - | | - | | - | | - | - | - | | - | - | - | (2T1, 10T35) | not solvable, irreducible |
| 20T977 | 1036800 | | - | | - | | - | | - | - | - | | - | - | - | (2T1, 10T35) | not solvable, irreducible, even |
| 20T978 | 1036800 | | - | | - | | - | | - | - | - | | - | - | - | (2T1, 10T35) | not solvable, irreducible, even |
| 20T997 | 2073600 | | - | | - | | - | | - | - | - | | - | - | - | (2T1, 10T35) | not solvable, irreducible, even |
| 20T998 | 2073600 | | | | - | | | | - | - | - | | - | - | - | (2T1, 10T35) | not solvable, irreducible |
| 20T999 | 2073600 | | | | - | | | | - | - | - | | - | - | - | (2T1, 10T35) | not solvable, irreducible |
| 20T1001 | 2073600 | | - | | - | | - | | - | - | - | | - | - | - | (2T1, 10T35) | not solvable, irreducible |
| 20T1112 | 6584094720000 | | - | | - | | - | | - | | - | | - | 10T44 2T1 | 10T44 2T1 | (2T1, 10T44) | not solvable, irreducible, even |
| 20T1113 | 13168189440000 | | - | | - | | - | | - | | - | | - | - | - | (2T1, 10T45) | not solvable, irreducible |
| 20T1114 | 13168189440000 | | - | | - | | - | | - | | - | | - | - | - | (2T1, 10T45) | not solvable, irreducible, even |
| 20T1116 | 1216451004088320000 | | - | | - | | - | | - | | - | | - | - | - | - | not solvable, primitive, simple, irreducible, even |
6 | 1,83 ms