Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $693$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (3,15)(4,16)(5,12)(6,11)(7,14)(8,13)(9,19)(10,20)(17,18), (1,18,8,20,12)(2,17,7,19,11)(3,6,14,16,10,4,5,13,15,9) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 60: $A_5$ 120: $A_5\times C_2$ 960: $C_2^4 : A_5$ 1920: $C_2 \wr A_5$, 20T220 3840: 12T255 30720: 30T1085 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: None
Degree 10: $A_{5}$
Low degree siblings
20T693 x 3, 40T18923 x 2, 40T18928 x 2, 40T18944 x 2, 40T18964 x 2, 40T19021 x 2, 40T19022 x 4, 40T19042 x 4, 40T19092 x 2, 40T19119 x 4, 40T19132 x 4, 40T19155 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 104 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. |