Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $968$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,9,6,4,8)(2,10,5,3,7)(11,19,15,13,18,12,20,16,14,17), (1,5,14,2,6,13)(3,11,15,4,12,16)(7,8)(9,10)(19,20) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 60: $A_5$ 120: $A_5\times C_2$ 960: $C_2^4 : A_5$ x 3 1920: $C_2 \wr A_5$ x 3 15360: 20T468 30720: 20T561, 32T1123291 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $A_5$
Degree 10: $C_2^4 : A_5$
Low degree siblings
20T963 x 2, 20T968, 40T147583, 40T147587, 40T147677, 40T147781, 40T147783 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 188 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $983040=2^{16} \cdot 3 \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |