Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $965$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,17,15)(2,18,16)(3,20)(4,19)(5,11,8)(6,12,7)(9,13,10,14), (1,3,12,14)(2,4,11,13)(5,9,7,15,20,18,6,10,8,16,19,17) | |
| $|\Aut(F/K)|$: | $2$ |
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
20T962 x 2, 20T965, 40T147541, 40T147545, 40T147714, 40T147719 x 2, 40T147837Siblings 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. |