Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1037$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,8,2,7)(3,10,4,9)(5,12,13,20)(6,11,14,19)(15,17)(16,18), (5,18,9,14,6,17,10,13)(7,15,12,19)(8,16,11,20) | |
| $|\Aut(F/K)|$: | $2$ |
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: $D_{4}$ x 2, $C_4\times C_2$ 16: $C_2^2:C_4$ 14400: $A_5^2 : C_4$ 28800: 20T541 57600: 20T659 3686400: 20T1011 7372800: 20T1025 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
20T1037 x 3, 40T178060 x 2, 40T178071 x 4, 40T178072 x 4, 40T178089 x 2, 40T178112 x 2, 40T178155 x 4, 40T178156 x 4, 40T178157 x 4, 40T178158 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 384 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $14745600=2^{16} \cdot 3^{2} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |