Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1028$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,9,6,13,18,2,10,5,14,17)(3,19,11,8,15,4,20,12,7,16), (1,9,2,10)(3,7,19,16)(4,8,20,15)(13,14), (1,15,17,20,13,3,9,12,5,7)(2,16,18,19,14,4,10,11,6,8) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $C_2^3$ 14400: $(A_5^2 : C_2):C_2$ 28800: 20T548 3686400: 20T1009 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
20T1028, 40T171494, 40T171507 x 2, 40T171508 x 2, 40T171541 x 2, 40T171542 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 228 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $7372800=2^{15} \cdot 3^{2} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |