Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $790$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,5,16,20)(2,6,15,19)(3,7,14,17)(4,8,13,18)(9,12,10,11), (1,9,18)(2,10,17)(3,12,20,4,11,19)(7,8)(13,16,14,15) | |
| $|\Aut(F/K)|$: | $2$ |
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: None
Degree 4: None
Degree 5: $S_5$
Degree 10: $C_2 \wr S_5$
Low degree siblings
20T790, 20T802 x 2, 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. |