Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $808$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,8,9,4,2,7,10,3)(5,16,6,15)(11,18,20,14,12,17,19,13), (1,15,9,2,16,10)(3,13,18,7,19,11,4,14,17,8,20,12) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 120: $S_5$ 240: $S_5\times C_2$ 1920: $(C_2^4:A_5) : C_2$ 3840: $C_2 \wr S_5$, 20T276 7680: 20T365 61440: 30T1280 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: None
Degree 10: $S_5$
Low degree siblings
20T808 x 7, 40T45633 x 4, 40T45637 x 4, 40T45658 x 4, 40T45666 x 4, 40T45690 x 4, 40T45691 x 4, 40T45712 x 8, 40T45776 x 8, 40T45783 x 4, 40T45784 x 8, 40T45786 x 8, 40T45792 x 8, 40T45861 x 4, 40T45884 x 4, 40T45950 x 8, 40T45952 x 8, 40T46028 x 8, 40T46029 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 136 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. |