Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $263$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,12,17,15,4,7,9,20,13)(2,5,11,18,16,3,8,10,19,14), (1,8,12,19,13,4,5,9,18,15)(2,7,11,20,14,3,6,10,17,16), (1,15,20,9,8)(2,16,19,10,7)(3,14,18,11,6)(4,13,17,12,5) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 5: $C_5$ 10: $C_{10}$ 80: $C_2^4 : C_5$ x 17 160: $C_2 \times (C_2^4 : C_5)$ x 17 1280: 20T190 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $C_5$
Degree 10: $C_2^4 : C_5$, $C_2 \times (C_2^4 : C_5)$ x 2
Low degree siblings
20T263 x 6119, 40T1955 x 6120, 40T2037 x 1020, 40T2135 x 24480, 40T2175 x 12240, 40T2214 x 2040, 40T2246 x 6120, 40T2274 x 12240, 40T2275 x 24480, 40T2276 x 48960Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 112 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2560=2^{9} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |