Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $964$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,9,4,12,20,14,2,10,3,11,19,13)(5,17,16,8,6,18,15,7), (3,15,13,6,4,16,14,5)(7,19,18,10)(8,20,17,9)(11,12) | |
| $|\Aut(F/K)|$: | $2$ |
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 61440: 32T1520177 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
20T964 x 3, 40T147546 x 2, 40T147716 x 2, 40T147838 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 155 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. |