Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $685$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14,8,19,12,3,16,5,18,9)(2,13,7,20,11,4,15,6,17,10), (1,9,8,2,10,7)(3,11,5,4,12,6)(13,16,14,15)(17,19,18,20) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 60: $A_5$ 120: $A_5\times C_2$ x 3 240: 20T64 960: $C_2^4 : A_5$ 1920: $C_2 \wr A_5$ x 3 3840: 20T277 30720: 20T556 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $A_5$
Degree 10: $C_2 \wr A_5$
Low degree siblings
20T680, 40T19023, 40T19025, 40T19028 x 2, 40T19122 x 2, 40T19125, 40T19128, 40T19167, 40T19170 x 2, 40T19181 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 90 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. |