Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $671$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18,3,20,2,17,4,19)(5,15,12,6,16,11)(7,13,9,8,14,10), (1,14,12,6,4,15,9,8,2,13,11,5,3,16,10,7) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 4: $C_4$ 120: $S_5$ 240: 12T124 1920: $(C_2^4:A_5) : C_2$ 3840: 20T283 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
20T671, 40T19101 x 2, 40T19106 x 2, 40T19137Siblings 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. |