Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $534$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,9,3,17,12,5,20,13,7,2,15,10,4,18,11,6,19,14,8), (1,9,17,6,13,2,10,18,5,14)(19,20) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 4: $C_4$ 5: $C_5$ 10: $D_{5}$, $C_{10}$ 20: 20T1, 20T2 50: $D_5\times C_5$ 100: 20T25 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
20T534 x 2, 40T14315 x 3, 40T14333 x 3, 40T14335 x 6, 40T14337 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. |