Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $561$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,17,2,18)(3,20,4,19)(5,15,6,16)(7,13,8,14), (1,16,17,8,9)(2,15,18,7,10)(3,14,20,6,12)(4,13,19,5,11), (1,17,2,18)(3,20,4,19)(5,6)(7,8)(9,14,11,15)(10,13,12,16) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 60: $A_5$ 120: $A_5\times C_2$ 960: $C_2^4 : A_5$ x 3 1920: $C_2 \wr A_5$ x 3 15360: 20T468 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $A_5$
Degree 10: $C_2^4 : A_5$, $C_2 \wr A_5$ x 2
Low degree siblings
20T561 x 2, 40T14430 x 3, 40T14530 x 3, 40T14532 x 3, 40T14533 x 3, 40T14559 x 6, 40T14615Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 84 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. |