Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $845$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (3,9,14,20)(4,10,13,19)(5,18,15,7,6,17,16,8)(11,12), (1,17)(2,18)(3,15,14,6,4,16,13,5)(7,11,8,12)(19,20) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 10: $D_{5}$ 20: $D_{10}$ 160: $(C_2^4 : C_5) : C_2$ x 5 320: $C_2\times (C_2^4 : D_5)$ x 5 2560: 20T240 5120: 20T307 10240: 10240T? 81920: 81920T? Resolvents shown for degrees $\leq 23$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $D_{5}$
Degree 10: $C_2\times (C_2^4 : D_5)$
Low degree siblings
20T845 x 31Siblings are shown with degree $\leq 23$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 280 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $163840=2^{15} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |