Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $846$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,10,3,18)(2,15,9,4,17)(5,20,14,7,12)(6,19,13,8,11), (1,7,3,9,15,11,17,14,20,6,2,8,4,10,16,12,18,13,19,5), (1,16,19,14,18,11,6,9,3,7)(2,15,20,13,17,12,5,10,4,8) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 5: $C_5$ 10: $C_{10}$ x 3 20: 20T3 80: $C_2^4 : C_5$ x 17 160: $C_2 \times (C_2^4 : C_5)$ x 51 320: 20T72 x 17 1280: 20T190 2560: 20T263 x 3 5120: 20T341 10240: 10240T? 81920: 81920T? Resolvents shown for degrees $\leq 23$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $C_5$
Degree 10: $C_2 \times (C_2^4 : C_5)$
Low degree siblings
20T846 x 511Siblings are shown with degree $\leq 23$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 649 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. |