Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $347$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,9,14,18,2,5,10,13,17)(3,7,12,16,19,4,8,11,15,20), (3,4)(5,6)(9,10)(13,14)(15,16)(17,18), (1,15)(2,16)(3,13)(4,14)(5,11,6,12)(7,10,8,9)(17,19)(18,20) | |
| $|\Aut(F/K)|$: | $2$ |
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 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: $D_{5}$
Degree 10: $D_5$
Low degree siblings
20T307 x 90, 20T322 x 180, 20T347 x 17, 20T348 x 180, 40T3062 x 18, 40T3456 x 360, 40T3496 x 45, 40T3500 x 30, 40T4350 x 360, 40T4352 x 360, 40T4376 x 90, 40T4380 x 90, 40T4382 x 90, 40T4547 x 45, 40T4556 x 90, 40T4730 x 180, 40T4756 x 180, 40T4771 x 60, 40T4826 x 360, 40T4866 x 90, 40T4867 x 180, 40T4870 x 180, 40T4871 x 360, 40T4872 x 360, 40T4931 x 180, 40T4943 x 180, 40T4944 x 180, 40T4987 x 180, 40T4996 x 180, 40T5004 x 360, 40T5020 x 180, 40T5025 x 720, 40T5039 x 18, 40T5041 x 36, 40T5043 x 72, 40T5045 x 90, 40T5047 x 180, 40T5051 x 180, 40T5052 x 180, 40T5054 x 360, 40T5055 x 180Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 104 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $5120=2^{10} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |