Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $436$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18,5,16,9,3,19,7,14,12,2,17,6,15,10,4,20,8,13,11), (1,6,4,8)(2,5,3,7)(9,13)(10,14)(11,16,12,15)(17,18)(19,20) | |
| $|\Aut(F/K)|$: | $2$ |
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: 40T3412 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
20T436 x 7, 40T7862 x 2, 40T7896 x 4, 40T8154 x 2, 40T8188 x 4, 40T9301 x 2, 40T9328 x 4, 40T9335 x 4, 40T9446 x 4, 40T9447 x 2, 40T9454 x 2, 40T9470 x 4, 40T9575 x 2, 40T9599 x 2, 40T9635 x 4, 40T9642 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 76 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. |