Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $691$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,3,2,4)(5,9,16,19,7,11,14,17,6,10,15,20,8,12,13,18), (1,9,4,12,2,10,3,11)(5,19,14,7,18,15)(6,20,13,8,17,16) | |
| $|\Aut(F/K)|$: | $2$ |
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: $(C_2^4:A_5) : C_2$ 3840: $C_2 \wr S_5$ 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
20T682, 20T684, 20T687, 40T19061, 40T19062, 40T19065, 40T19066, 40T19069, 40T19070, 40T19073, 40T19074, 40T19142, 40T19176, 40T19189, 40T19191, 40T19193, 40T19205, 40T19206, 40T19207, 40T19208, 40T19215, 40T19218, 40T19219, 40T19220, 40T19221Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 69 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. |