Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1045$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,2)(3,11,8,15,20,4,12,7,16,19)(5,9,13,18,6,10,14,17), (1,4,9,19,17,12,5,15,2,3,10,20,18,11,6,16)(7,14,8,13), (1,6,13,2,5,14)(9,10)(11,20,12,19)(17,18) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $D_{4}$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 3 32: $C_2^2 \wr C_2$ 28800: $S_5^2 \wr C_2$ 57600: 20T655 115200: 20T781 7372800: 20T1022 14745600: 20T1038 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: None
Degree 10: $S_5^2 \wr C_2$
Low degree siblings
20T1045 x 7, 40T182661 x 4, 40T182662 x 8, 40T182663 x 8, 40T182675 x 4, 40T182686 x 4, 40T182721 x 8, 40T182740 x 4, 40T182741 x 4, 40T182756 x 8, 40T182757 x 8, 40T182758 x 8, 40T182759 x 8, 40T182760 x 8, 40T182761 x 8, 40T182762 x 8, 40T182763 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 702 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $29491200=2^{17} \cdot 3^{2} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |