Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $802$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,17,6,10,2,18,5,9)(7,15,19,11)(8,16,20,12)(13,14), (1,15,9,11,6,20,2,16,10,12,5,19)(3,18)(4,17)(7,14)(8,13) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_4$ x 2, $C_2^2$ 8: $C_4\times C_2$ 120: $S_5$ 240: $S_5\times C_2$ 480: 20T123 1920: $(C_2^4:A_5) : C_2$ 3840: $C_2 \wr S_5$ 7680: 20T369 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
20T790 x 2, 20T802, 40T45693 x 2, 40T45696 x 2, 40T45735, 40T45759 x 2, 40T45760 x 2, 40T45854, 40T45917 x 2, 40T45997, 40T45998, 40T46015 x 2, 40T46022 x 2, 40T46045 x 2, 40T46046 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 138 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. |