Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $633$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,12,2,11)(3,18,19,5)(4,17,20,6)(7,10,16,14)(8,9,15,13), (1,18,10,14)(2,17,9,13)(3,12,7,19,4,11,8,20)(5,6), (1,19,2,20)(3,17,4,18)(5,16)(6,15)(7,13)(8,14)(9,12)(10,11) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_4$ x 4, $C_2^2$ x 7 8: $D_{4}$ x 2, $C_4\times C_2$ x 6, $C_2^3$ 16: $D_4\times C_2$, $Q_8:C_2$, $C_4\times C_2^2$ 20: $F_5$ 32: $C_4 \times D_4$ 40: $F_{5}\times C_2$ x 3 80: 20T16 160: 20T42 320: $(C_2^4 : C_5):C_4$ 640: $((C_2^4 : C_5):C_4)\times C_2$ x 3 1280: 20T196 2560: 20T261 10240: 20T416 20480: 20T511 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: $F_5$
Degree 10: $F_{5}\times C_2$
Low degree siblings
20T632 x 4, 20T633 x 3, 40T15736 x 2, 40T15737 x 2, 40T15738 x 2, 40T15739 x 2, 40T15740 x 2, 40T15741 x 2, 40T15742, 40T15743, 40T15751, 40T15753, 40T15762 x 2, 40T15763 x 2, 40T15936 x 4, 40T15937 x 4, 40T15938 x 4, 40T15939 x 4, 40T16225, 40T16227 x 2, 40T16232, 40T16235 x 2, 40T16279 x 2, 40T16280 x 2, 40T16283 x 2, 40T16284 x 2, 40T16392, 40T16399 x 2, 40T16400, 40T16406 x 2, 40T16448 x 2, 40T16451, 40T16453, 40T16454 x 2, 40T18242 x 2, 40T18248, 40T18270, 40T18282 x 2, 40T18286 x 2, 40T18290 x 2, 40T18294 x 2, 40T18297 x 4, 40T18434 x 4, 40T18435 x 4, 40T18436 x 4, 40T18437 x 4, 40T18499 x 2, 40T18500 x 2, 40T18501 x 2, 40T18502 x 2, 40T18546 x 2, 40T18548 x 2, 40T18550 x 2, 40T18551 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 124 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $40960=2^{13} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |