Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $432$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,20,8,16,10)(2,19,7,15,9)(3,18,5,14,12,4,17,6,13,11), (1,3)(2,4)(5,8)(6,7)(9,10)(13,16)(14,15)(17,20)(18,19), (1,6,10,20,14,3,7,12,18,16)(2,5,9,19,13,4,8,11,17,15) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 5: $C_5$ 8: $D_{4}$ 10: $C_{10}$ x 3 20: 20T3 40: 20T12 80: $C_2^4 : C_5$ 160: $C_2 \times (C_2^4 : C_5)$ x 3 320: 20T72 640: 20T130 2560: 20T257 5120: 20T304 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
20T432 x 95, 40T6397 x 192, 40T6659 x 192, 40T7171 x 192, 40T7498 x 48, 40T7740 x 96, 40T8082 x 96, 40T9177 x 192, 40T9188 x 192, 40T9221 x 192, 40T9907 x 48, 40T9941 x 48Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 136 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $10240=2^{11} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |