Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1105$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,10,14,12,19,5,3,17)(2,9,13,11,20,6,4,18), (1,2)(3,9,15)(4,10,16)(5,20,7,14)(6,19,8,13)(11,18,12,17) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3628800: $S_{10}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: None
Degree 10: $S_{10}$
Low degree siblings
20T1105, 40T252685Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 251 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1857945600=2^{17} \cdot 3^{4} \cdot 5^{2} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |