Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1110$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,9,8,16)(2,10,7,15)(3,19,17,14,5)(4,20,18,13,6), (1,17,3,2,18,4)(5,6)(7,12,19,9,13,16,8,11,20,10,14,15) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 3628800: $S_{10}$ 7257600: 20T1021 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: None
Degree 10: $S_{10}$
Low degree siblings
20T1110 x 3, 40T268331 x 2, 40T268347 x 2, 40T268348 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 481 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $3715891200=2^{18} \cdot 3^{4} \cdot 5^{2} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |