Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $925$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (19,20), (1,12,2,11)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,20,10,19), (1,14,18,6)(2,13,17,5)(3,7,15,11)(4,8,16,12)(9,10)(19,20), (1,2)(5,6)(7,19,8,20)(11,15)(12,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 15 4: $C_2^2$ x 35 8: $D_{4}$ x 4, $C_2^3$ x 15 16: $D_4\times C_2$ x 6, $Q_8:C_2$ x 4, $C_2^4$ 32: $C_2 \times (C_4\times C_2):C_2$ x 2, $C_2^2 \times D_4$ 64: 16T117 400: $(D_5 \wr C_2):C_2$ 800: 20T154 1600: 20T214 102400: 20T763 204800: 20T872 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
20T925 x 7, 40T138455 x 4, 40T138495 x 4, 40T138496 x 4, 40T138503 x 4, 40T138506 x 4, 40T138514 x 4, 40T138659 x 4, 40T138660 x 4, 40T138662 x 4, 40T138663 x 4, 40T138811 x 8, 40T138812 x 8, 40T138813 x 8, 40T138814 x 8, 40T138815 x 8, 40T138816 x 8, 40T138817 x 8, 40T138818 x 8, 40T138835 x 4, 40T138838 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 190 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $409600=2^{14} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |