Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $992$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,17,16,11,8,6)(2,18,15,12,7,5)(3,10,13,19)(4,9,14,20), (1,3,17,2,4,18)(7,11,13)(8,12,14)(15,16)(19,20) | |
| $|\Aut(F/K)|$: | $2$ |
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, 32T1520177 x 2 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
20T992 x 3, 20T994 x 4, 40T153084 x 2, 40T153178 x 2, 40T153250 x 2, 40T153252 x 2, 40T153266 x 2, 40T153390 x 2, 40T153544 x 2, 40T153629 x 2, 40T153699 x 2, 40T153703 x 2, 40T153800 x 2, 40T153812 x 2, 40T153815 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. |