Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $647$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,9,13,18)(2,5,10,14,17)(3,15,7,19,11,4,16,8,20,12), (1,15,18,12,13,8,9,3,6,20)(2,16,17,11,14,7,10,4,5,19) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 5: $C_5$ 8: $D_{4}$ 10: $D_{5}$, $C_{10}$ x 3 20: $D_{10}$, 20T3 40: 20T7, 20T12 50: $D_5\times C_5$ 100: 20T24 200: 20T53 12800: 20T455 25600: 20T538 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: None
Degree 10: $D_5\times C_5$
Low degree siblings
20T647 x 5, 40T18704 x 3, 40T18727 x 6, 40T18728 x 6, 40T18750 x 6, 40T18751 x 12, 40T18752 x 24, 40T18775 x 6, 40T18776 x 12, 40T18777 x 24Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 152 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $51200=2^{11} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |