Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $756$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,12,14,20,2,11,13,19)(3,5,8,10,4,6,7,9)(15,18,16,17), (1,9)(2,10)(3,19,4,20)(7,15)(8,16)(11,12)(13,18)(14,17), (1,5,9,13,18)(2,6,10,14,17)(3,8,4,7)(11,20,12,19)(15,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $D_{4}$ x 2, $C_2^3$ 16: $D_4\times C_2$ 200: $D_5^2 : C_2$ 400: 20T92 51200: 20T637 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: None
Degree 10: $D_5^2 : C_2$
Low degree siblings
20T756 x 5, 20T760 x 6, 40T45249 x 6, 40T45259 x 3, 40T45260 x 3, 40T45307 x 6, 40T45334 x 6, 40T45335 x 6, 40T45336 x 6, 40T45337 x 6, 40T45362 x 6, 40T45363 x 6, 40T45364 x 6, 40T45365 x 6, 40T45422 x 12, 40T45423 x 12, 40T45426 x 6, 40T45428 x 6, 40T45433 x 12, 40T45456 x 6, 40T45458 x 6Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 130 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $102400=2^{12} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |