Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $412$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7)(2,8)(3,6)(4,5)(9,14,11,15)(10,13,12,16)(17,18)(19,20), (1,6,4,8)(2,5,3,7)(9,14,11,15)(10,13,12,16)(17,18)(19,20), (5,13,7,16)(6,14,8,15)(9,17,11,20)(10,18,12,19) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $C_2^3$ 10: $D_{5}$ 20: $D_{10}$ x 3 40: 20T8 160: $(C_2^4 : C_5) : C_2$ x 5 320: $C_2\times (C_2^4 : D_5)$ x 15 640: 20T141 x 5 2560: 20T240 5120: 20T307 x 3 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $D_{5}$
Degree 10: $C_2\times (C_2^4 : D_5)$ x 3
Low degree siblings
20T412 x 719, 40T5903 x 54, 40T7903 x 1080, 40T8176 x 540, 40T8199 x 1080, 40T9339 x 1080, 40T9420 x 1080, 40T9423 x 2160, 40T9457 x 270, 40T9459 x 540, 40T9473 x 180, 40T9619 x 540, 40T9644 x 1080, 40T9972 x 2160, 40T10151 x 1440, 40T10152 x 1440, 40T10205 x 2160, 40T10361 x 36, 40T10365 x 216, 40T10368 x 540, 40T10373 x 360, 40T10376 x 1080Siblings 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. |