Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $872$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,2,5)(3,4)(7,8)(9,17)(10,18)(11,12)(15,16)(19,20), (1,17,6,10,2,18,5,9)(7,16,20,12)(8,15,19,11)(13,14), (7,20)(8,19)(9,10)(11,15)(12,16)(17,18), (1,17,14,9,5)(2,18,13,10,6)(7,8)(11,12), (1,12)(2,11)(3,14)(4,13)(5,16,6,15)(7,17)(8,18)(9,19,10,20) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 15 4: $C_2^2$ x 35 8: $C_2^3$ x 15 16: $Q_8:C_2$ x 2, $C_2^4$ 32: $C_2 \times (C_4\times C_2):C_2$ 400: $(D_5 \wr C_2):C_2$ 800: 20T154 102400: 20T763 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: None
Degree 10: $(D_5 \wr C_2):C_2$
Low degree siblings
20T872 x 3, 40T105867 x 2, 40T105897 x 2, 40T105903 x 2, 40T105918 x 2, 40T105931 x 2, 40T105952 x 2, 40T106088 x 4, 40T106089 x 4, 40T106090 x 4, 40T106091 x 4, 40T106205 x 2, 40T106215 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 116 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $204800=2^{13} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |