Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $755$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,6,11,10,8,14,4,18,19,2,15,5,12,9,7,13,3,17,20), (1,8,14,19,2,7,13,20)(3,17,4,18)(5,11,9,16,6,12,10,15) | |
| $|\Aut(F/K)|$: | $2$ |
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: $C_2^2:C_4$ 200: $D_5^2 : C_2$ 400: 20T93 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
20T755 x 5, 20T771 x 6, 40T45248 x 6, 40T45258 x 3, 40T45261 x 3, 40T45306 x 6, 40T45338 x 6, 40T45339 x 6, 40T45340 x 6, 40T45341 x 6, 40T45342 x 6, 40T45343 x 6, 40T45344 x 6, 40T45345 x 6, 40T45421 x 12, 40T45424 x 12, 40T45425 x 6, 40T45427 x 6, 40T45432 x 12, 40T45455 x 6, 40T45457 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. |