Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $368$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20), (1,3,9)(2,4,10)(5,7,15,17)(6,8,16,18)(11,13,19)(12,14,20), (1,11)(2,12)(3,6)(4,5)(7,8)(9,19)(10,20)(13,15)(14,16)(17,18) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $C_2^3$ 120: $S_5$ 240: $S_5\times C_2$ x 3 480: 20T117 1920: $(C_2^4:A_5) : C_2$ 3840: $C_2 \wr S_5$ x 3 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: $S_5$
Degree 10: $S_5\times C_2$, $C_2 \wr S_5$ x 2
Low degree siblings
20T368 x 11, 40T5478 x 12, 40T5479 x 12, 40T5491 x 24, 40T5507 x 3, 40T5512 x 4, 40T5513 x 4Siblings 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. |