Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $418$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,11,18,13,4,8,9,20,16,2,5,12,17,14,3,7,10,19,15), (1,14,3,16,2,13,4,15)(5,20,8,18,6,19,7,17) | |
| $|\Aut(F/K)|$: | $4$ |
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 2560: 20T244 5120: 20T313 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $D_{5}$
Degree 10: $C_2\times (C_2^4 : D_5)$
Low degree siblings
20T418 x 23, 40T7828 x 6, 40T7874 x 12, 40T8130 x 6, 40T8172 x 12, 40T9305 x 12, 40T9327 x 24, 40T9430 x 6, 40T9442 x 12, 40T9458 x 12, 40T9582 x 12, 40T9630 x 24Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 208 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. |