Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $568$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18,7,4,19,5,2,17,8,3,20,6)(9,12,10,11), (5,20,16,9)(6,19,15,10)(7,17,13,12)(8,18,14,11) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 120: $S_5$ 1920: $(C_2^4:A_5) : C_2$ 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
20T573, 40T14573, 40T14574, 40T14575, 40T14576, 40T14581, 40T14586, 40T14598, 40T14599, 40T14604Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 63 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $30720=2^{11} \cdot 3 \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |