Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1106$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14,18,8,19,4,10,15)(2,13,17,7,20,3,9,16)(5,11,6,12), (1,11,20,10,17,5,15,2,12,19,9,18,6,16)(7,8) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 1814400: $A_{10}$ 3628800: 20T1006 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: None
Degree 10: $A_{10}$
Low degree siblings
20T1106, 40T252680Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 260 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. |