Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $676$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14,5,17,10,2,13,6,18,9)(3,15,7,19,12,4,16,8,20,11), (1,8,13,2,7,14)(3,12,20,9,5,16)(4,11,19,10,6,15)(17,18) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 120: $S_5$ 1920: $(C_2^4:A_5) : C_2$, 16T1329 3840: 12T257 30720: 30T1084 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: None
Degree 10: $S_5$
Low degree siblings
20T674 x 2, 20T676, 40T18929 x 2, 40T18932 x 2, 40T18947, 40T18948, 40T18954 x 2, 40T19049 x 2, 40T19054 x 2, 40T19055 x 2, 40T19088 x 2, 40T19089 x 2, 40T19090 x 2, 40T19100 x 2, 40T19109 x 2, 40T19110 x 2, 40T19115 x 2, 40T19116 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 74 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. |