Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1025$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,9,14,5,17,2,10,13,6,18)(3,19,16,11,7,4,20,15,12,8), (1,11,13,16,18,19,10,4)(2,12,14,15,17,20,9,3)(5,8)(6,7) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_4$ x 2, $C_2^2$ 8: $C_4\times C_2$ 14400: $A_5^2 : C_4$ 28800: 20T541 3686400: 20T1011 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: None
Degree 10: $A_5^2 : C_4$
Low degree siblings
20T1027, 40T171498, 40T171513, 40T171514, 40T171515, 40T171516, 40T171527, 40T171528, 40T171535, 40T171536Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 216 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. |