Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $331$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,20,12,16,5,4,17,9,13,7)(2,19,11,15,6,3,18,10,14,8), (1,9,5,17,13,4,12,8,19,15)(2,10,6,18,14,3,11,7,20,16), (1,14,18,5,9)(2,13,17,6,10)(3,15,19,8,11)(4,16,20,7,12) | |
| $|\Aut(F/K)|$: | $2$ |
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: $C_2^4 : C_5$ 160: $C_2 \times (C_2^4 : C_5)$ x 3 320: 20T72 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
20T331 x 7, 20T336 x 8, 40T3242 x 8, 40T3247 x 8, 40T3265 x 2, 40T3268 x 2, 40T3319 x 4, 40T3320 x 4, 40T3376 x 2, 40T3379 x 2, 40T3407 x 4, 40T3531 x 32, 40T3532 x 32, 40T3882 x 4, 40T3969 x 8, 40T3976 x 8, 40T3988 x 8, 40T4005 x 8, 40T4019 x 8, 40T4031 x 8, 40T4062 x 16, 40T4063 x 16, 40T4068 x 2, 40T4072 x 2, 40T4076 x 2, 40T4084 x 2, 40T4209 x 4, 40T4292 x 4, 40T4293 x 4, 40T4306 x 8, 40T4323 x 8, 40T4396 x 16, 40T4509 x 4, 40T4513 x 4, 40T4580 x 16, 40T4694 x 4, 40T4719 x 8, 40T4741 x 16, 40T4806 x 16, 40T4807 x 16, 40T4809 x 32, 40T4810 x 32, 40T4956 x 16Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 56 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. |