Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $673$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,4,2,3)(5,7,6,8)(9,13,17,10,14,18)(11,16,19,12,15,20), (1,9,3,11,2,10,4,12)(5,6)(7,8)(17,19,18,20), (1,7,9,3,5,11,2,8,10,4,6,12)(13,14)(15,16)(17,20,18,19) | |
| $|\Aut(F/K)|$: | $4$ |
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: $(C_2^4:A_5) : C_2$ 3840: $C_2 \wr S_5$ 30720: 20T568 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
20T673, 40T19078 x 2, 40T19081 x 2, 40T19083 x 2, 40T19113 x 2, 40T19136, 40T19185 x 2, 40T19186 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 126 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $61440=2^{12} \cdot 3 \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |