Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $423$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,20)(2,19)(3,17,4,18)(5,15,6,16)(7,13)(8,14)(9,11)(10,12), (1,4,2,3)(5,19)(6,20)(7,18,8,17)(9,16)(10,15)(11,14,12,13) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ 10: $D_{5}$ 20: $D_{10}$ 40: 20T7 160: $(C_2^4 : C_5) : C_2$ x 5 320: $C_2\times (C_2^4 : D_5)$ x 5 640: 20T136 x 5 2560: 20T240 5120: 20T307 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: $D_{5}$
Degree 10: $D_5$
Low degree siblings
20T408 x 180, 20T423 x 35, 40T5905 x 18, 40T5939 x 36, 40T5940 x 36, 40T7326 x 720, 40T7327 x 720, 40T7345 x 90, 40T7346 x 90, 40T7347 x 180, 40T7881 x 90, 40T7884 x 90, 40T8169 x 90, 40T8182 x 90, 40T9330 x 180, 40T9424 x 720, 40T9425 x 720, 40T9460 x 90, 40T9467 x 180, 40T9472 x 180, 40T9631 x 180, 40T10084 x 720, 40T10087 x 720, 40T10105 x 360, 40T10106 x 360, 40T10107 x 720, 40T10108 x 720, 40T10109 x 720, 40T10110 x 720, 40T10111 x 180, 40T10112 x 180, 40T10113 x 360, 40T10114 x 360, 40T10157 x 36, 40T10158 x 72, 40T10159 x 144, 40T10160 x 180, 40T10161 x 360, 40T10162 x 360, 40T10163 x 360, 40T10164 x 720, 40T10218 x 720, 40T10363 x 36, 40T10366 x 72, 40T10370 x 144, 40T10372 x 180, 40T10377 x 360, 40T10379 x 360, 40T10380 x 360, 40T10381 x 720, 40T10382 x 720Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 160 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $10240=2^{11} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |