Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $350$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16)(2,15)(3,13,4,14)(5,11,6,12)(7,9)(8,10)(17,19,18,20), (1,13,5,18,9)(2,14,6,17,10)(3,16,8,20,12)(4,15,7,19,11) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 4: $C_4$ 10: $D_{5}$ 20: 20T2 160: $(C_2^4 : C_5) : C_2$ x 5 320: 20T82 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
20T334 x 90, 20T350 x 17, 40T3054 x 18, 40T4349 x 360, 40T4351 x 360, 40T4372 x 90, 40T4375 x 90, 40T4379 x 90, 40T4551 x 90, 40T4886 x 360, 40T4910 x 90, 40T4911 x 180, 40T4912 x 180, 40T4913 x 360, 40T4914 x 360, 40T5040 x 18, 40T5042 x 36, 40T5044 x 72, 40T5046 x 90, 40T5048 x 180, 40T5049 x 180, 40T5050 x 180, 40T5053 x 360, 40T5056 x 360Siblings 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. |