Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $797$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,14,19)(2,8,13,20)(3,9,12,17,4,10,11,18)(5,15)(6,16), (1,19,5,4,18,11,9,15,14,7)(2,20,6,3,17,12,10,16,13,8) | |
| $|\Aut(F/K)|$: | $2$ |
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 61440: 20T667 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: $S_5$
Degree 10: $S_5\times C_2$
Low degree siblings
20T792 x 2, 20T797, 40T45698 x 2, 40T45699 x 2, 40T45737, 40T45745 x 2, 40T45746 x 2, 40T45787 x 2, 40T45790 x 2, 40T45803, 40T45912, 40T46006, 40T46011 x 2, 40T46047 x 2, 40T46048 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 108 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. |