Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1013$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,17,10,11,8,15,5,14,3,19)(2,18,9,12,7,16,6,13,4,20), (1,4,7,2,3,8)(5,10,6,9)(11,12)(13,17,19,15,14,18,20,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 14400: $(A_5^2 : C_2):C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: None
Degree 10: $(A_5^2 : C_2):C_2$
Low degree siblings
20T1009, 32T2660825, 40T162001, 40T162004, 40T162005, 40T162006, 40T162007Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 114 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. |