Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $638$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,20,3,17,5,16,8,13,9,12)(2,19,4,18,6,15,7,14,10,11), (1,14,7,17)(2,13,8,18)(3,11,6,19,4,12,5,20)(9,15,10,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ 200: $D_5^2 : C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: None
Degree 10: $D_5^2 : C_2$
Low degree siblings
20T637 x 3, 20T638 x 2, 20T641 x 3, 20T649 x 3, 32T1520136, 40T18719 x 3, 40T18720 x 3, 40T18723 x 3, 40T18724 x 3, 40T18741 x 3, 40T18742 x 3, 40T18778 x 3, 40T18779 x 6, 40T18780 x 6, 40T18781 x 6, 40T18782, 40T18783 x 3, 40T18784 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 65 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $51200=2^{11} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |