Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $803$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,2)(3,19)(4,20)(5,17)(6,18)(7,16,8,15)(9,14,10,13), (1,7,14,16,2,8,13,15)(3,5,12,18,4,6,11,17)(9,20,10,19) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ 120: $S_5$ 240: $S_5\times C_2$ 480: 20T116 1920: $(C_2^4:A_5) : C_2$ 3840: $C_2 \wr S_5$ 7680: 20T366 30720: 20T564 61440: 20T663 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: $S_5$
Degree 10: $S_5$
Low degree siblings
20T795 x 2, 20T803, 40T45661 x 2, 40T45662 x 2, 40T45729, 40T45739 x 2, 40T45740 x 2, 40T45811, 40T45857 x 2, 40T45909, 40T45994, 40T46017 x 2, 40T46024 x 2, 40T46035 x 2, 40T46036 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 126 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $122880=2^{13} \cdot 3 \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |