Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $538$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,10,13,18,2,5,9,14,17)(3,11,19,8,16,4,12,20,7,15), (1,19,17,15,14,11,9,7,6,4)(2,20,18,16,13,12,10,8,5,3) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 5: $C_5$ 10: $D_{5}$, $C_{10}$ x 3 20: $D_{10}$, 20T3 50: $D_5\times C_5$ 100: 20T24 12800: 20T455 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
20T538 x 2, 40T14314 x 3, 40T14332 x 3, 40T14334 x 6, 40T14336 x 12Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 88 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $25600=2^{10} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |