Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $426$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,15,10,3,17,11,5,19,14,7,2,16,9,4,18,12,6,20,13,8), (1,5)(2,6)(7,19,8,20)(9,18,10,17)(11,15,12,16)(13,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_4$ x 2, $C_2^2$ 8: $C_4\times C_2$ 10: $D_{5}$ 20: $D_{10}$ 40: 20T6 160: $(C_2^4 : C_5) : C_2$ 320: $C_2\times (C_2^4 : D_5)$ 640: 20T144 5120: 20T328 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: $D_{5}$
Degree 10: $D_{10}$
Low degree siblings
20T404 x 12, 20T426 x 11, 40T5890 x 6, 40T5894 x 6, 40T5897 x 6, 40T5915 x 12, 40T5916 x 12, 40T7861 x 6, 40T7882 x 6, 40T7886 x 6, 40T7895 x 12, 40T8128 x 6, 40T8145 x 6, 40T8193 x 12, 40T8196 x 12, 40T9314 x 6, 40T9332 x 12, 40T9432 x 6, 40T9451 x 6, 40T9462 x 6, 40T9612 x 6, 40T9638 x 12, 40T10153 x 12, 40T10154 x 12, 40T10155 x 24, 40T10156 x 24, 40T10229 x 12, 40T10230 x 12, 40T10234 x 12, 40T10236 x 12, 40T10242 x 12, 40T10244 x 12, 40T10247 x 24, 40T10335 x 12, 40T10338 x 12, 40T10343 x 12, 40T10348 x 12, 40T10352 x 12, 40T10354 x 12, 40T10357 x 24Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 100 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. |