Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $369$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,2)(3,4)(5,11)(6,12)(7,10)(8,9)(13,14)(15,16)(17,18)(19,20), (1,9,19,3,11,18,2,10,20,4,12,17)(5,7,6,8)(13,15,14,16), (1,3,2,4)(5,15,19,7,13,18,6,16,20,8,14,17)(9,11,10,12) | |
| $|\Aut(F/K)|$: | $4$ |
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: $C_4\times C_2$ 120: $S_5$ 240: $S_5\times C_2$ 480: 20T123 1920: $(C_2^4:A_5) : C_2$ 3840: $C_2 \wr S_5$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: $S_5$
Degree 10: $S_5\times C_2$
Low degree siblings
20T369, 40T5472 x 2, 40T5475 x 2, 40T5504, 40T5535 x 2, 40T5536 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 72 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $7680=2^{9} \cdot 3 \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |