Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $946$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18,16,10,2,17,15,9)(3,4)(5,19,12,7,6,20,11,8), (1,7,16,9,2,8,15,10)(3,4)(5,19,11,17)(6,20,12,18), (1,19,8,15,14,12,10,17,6,4)(2,20,7,16,13,11,9,18,5,3) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_4$ x 4, $C_2^2$ x 7 8: $C_4\times C_2$ x 6, $C_2^3$ 16: $C_4\times C_2^2$ 20: $F_5$ 40: $F_{5}\times C_2$ x 3 80: 20T16 320: $(C_2^4 : C_5):C_4$ x 3 640: $((C_2^4 : C_5):C_4)\times C_2$ x 9 1280: 20T196 x 3 5120: 20T306 10240: 20T406 x 3 20480: 20T528 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $F_5$
Degree 10: $((C_2^4 : C_5):C_4)\times C_2$
Low degree siblings
20T946 x 15, 40T141739 x 4, 40T141741 x 8, 40T141922 x 4, 40T141925 x 8, 40T142012 x 4, 40T142013 x 4, 40T142014 x 4, 40T142015 x 4, 40T142016 x 8, 40T142017 x 4, 40T142018 x 4, 40T142019 x 8, 40T142498 x 4, 40T142510 x 4, 40T142514 x 4, 40T142526 x 4, 40T142543 x 8, 40T142545 x 8, 40T142547 x 8, 40T142549 x 8, 40T144726 x 4, 40T144740 x 4, 40T144750 x 8, 40T144752 x 8, 40T145486 x 4, 40T145487 x 4, 40T145490 x 8, 40T145491 x 8, 40T146519 x 4, 40T146540 x 4, 40T146564 x 4, 40T146597 x 8, 40T146598 x 8, 40T146605 x 8, 40T146608 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 331 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $655360=2^{17} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |