Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $966$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,9,4,7,2,5,10,3,8)(11,15,20,13,17,12,16,19,14,18), (1,5,19,4,12,16,10,14,2,6,20,3,11,15,9,13)(7,8)(17,18) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 120: $S_5$ 1920: $(C_2^4:A_5) : C_2$ x 3 30720: 20T555 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
20T966 x 3, 40T147542 x 2, 40T147713 x 2, 40T147718 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 149 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. |