Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $792$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,9,7,20,3,12,6,17)(2,10,8,19,4,11,5,18)(15,16), (1,6,19,14,9,2,5,20,13,10)(3,8,17,16,11)(4,7,18,15,12), (1,15,2,16)(3,13,4,14)(5,12)(6,11)(7,10)(8,9)(19,20) | |
| $|\Aut(F/K)|$: | $2$ |
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: None
Degree 4: None
Degree 5: $S_5$
Degree 10: $(C_2^4:A_5) : C_2$
Low degree siblings
20T792, 20T797 x 2, 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. |