Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1010$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,9,6,2,10,5)(7,15)(8,16)(11,19,12,20)(13,14)(17,18), (1,16,9,19,6,4)(2,15,10,20,5,3)(7,18)(8,17)(11,14,12,13) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 4: $C_4$ 7200: $A_5 \wr C_2$ 14400: 20T460 1843200: 20T985 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: None
Degree 10: $A_5 \wr C_2$
Low degree siblings
40T161997, 40T162000, 40T162008Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 180 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $3686400=2^{14} \cdot 3^{2} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |