Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $303$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11,8,19,13,3,10,5,18,16,2,12,7,20,14,4,9,6,17,15), (1,17,12,16,7,2,18,11,15,8)(3,19,10,14,5,4,20,9,13,6) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 5: $C_5$ 10: $C_{10}$ 80: $C_2^4 : C_5$ 160: $C_2 \times (C_2^4 : C_5)$ 2560: 20T251 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $C_5$
Degree 10: $C_2 \times (C_2^4 : C_5)$
Low degree siblings
20T303 x 15, 40T3647 x 4, 40T3896 x 4, 40T3965 x 8, 40T3975 x 8, 40T3982 x 8, 40T3983 x 8, 40T4011 x 8, 40T4017 x 8, 40T4024 x 8, 40T4029 x 8, 40T4073 x 2, 40T4086 x 2, 40T4216 x 4, 40T4283 x 4, 40T4298 x 8, 40T4305 x 8, 40T4316 x 8, 40T4334 x 8, 40T4416 x 4, 40T4522 x 8, 40T4706 x 8, 40T4709 x 8, 40T5033 x 16, 40T5034 x 16, 40T5035 x 16, 40T5036 x 16, 40T5037 x 32, 40T5038 x 32Siblings are shown with degree $\leq 47$
A number field with this Galois group has exactly one arithmetically equivalent field.
Conjugacy Classes
There are 50 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. |