Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $326$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,11,19,15,2,5,12,20,16)(3,7,10,17,14)(4,8,9,18,13), (3,4)(7,8)(9,11)(10,12)(13,14)(17,20)(18,19) | |
| $|\Aut(F/K)|$: | $2$ |
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: 20T257 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $C_5$
Degree 10: $C_2^4 : C_5$
Low degree siblings
20T304 x 24, 20T326 x 23, 40T3244 x 48, 40T3321 x 24, 40T3406 x 12, 40T3530 x 192, 40T3967 x 48, 40T4015 x 48, 40T4016 x 48, 40T4061 x 96, 40T4290 x 24, 40T4325 x 48, 40T4395 x 48, 40T4534 x 24, 40T4579 x 48, 40T4693 x 12, 40T4699 x 24, 40T4740 x 48, 40T4805 x 96, 40T4808 x 192, 40T4955 x 48Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 80 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. |