Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $990$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,5,11,15,2,6,12,16)(3,4)(7,8)(13,14)(17,18), (1,8,13,16)(2,7,14,15)(3,6,11,18,4,5,12,17)(9,10), (1,8)(2,7)(3,10,13,20,4,9,14,19)(5,15,6,16)(11,18)(12,17) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 120: $S_5$ 240: $S_5\times C_2$ 1920: $(C_2^4:A_5) : C_2$ x 3 3840: $C_2 \wr S_5$ x 3 30720: 20T555 61440: 20T664 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
20T990 x 7, 40T153180 x 4, 40T153267 x 4, 40T153391 x 4, 40T153700 x 4, 40T153707 x 4, 40T153802 x 4, 40T153814 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 280 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1966080=2^{17} \cdot 3 \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |