Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $555$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,17)(2,18)(3,19)(4,20)(9,13)(10,14)(11,16)(12,15), (1,10,20)(2,9,19)(3,12,18)(4,11,17)(5,15,6,16)(7,13,8,14) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 120: $S_5$ 1920: $(C_2^4:A_5) : C_2$ x 3 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $S_5$
Degree 10: $(C_2^4:A_5) : C_2$, $(C_2^4:A_5) : C_2$ x 2
Low degree siblings
20T555 x 2, 20T567, 40T14436 x 3, 40T14437 x 3, 40T14571 x 3, 40T14572 x 6, 40T14584 x 3, 40T14585 x 3, 40T14589, 40T14590 x 3, 40T14591 x 3, 40T14607Siblings 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. |