Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $335$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,12,6,18,14,3,10,8,20,15,2,11,5,17,13,4,9,7,19,16), (1,7,16,12,20)(2,8,15,11,19)(3,6,14,10,17)(4,5,13,9,18) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 4: $C_4$ 5: $C_5$ 10: $C_{10}$ 20: 20T1 80: $C_2^4 : C_5$ 160: $C_2 \times (C_2^4 : C_5)$ 320: 20T75 1280: 20T193 2560: 20T250 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
20T335 x 47, 40T4014 x 96, 40T4039 x 96, 40T4308 x 96, 40T4506 x 24, 40T4697 x 48Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 224 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. |