Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $466$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,20,7,10,14,4,17,5,11,15)(2,19,8,9,13,3,18,6,12,16), (1,16)(2,15)(3,13)(4,14)(5,18,10,8,19,12,6,17,9,7,20,11), (1,8,17,2,7,18)(3,6,19)(4,5,20)(9,10)(15,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $D_{4}$ x 2, $C_2^3$ 16: $D_4\times C_2$ 120: $S_5$ 240: $S_5\times C_2$ x 3 480: 20T117 960: 20T174 1920: $(C_2^4:A_5) : C_2$ 3840: $C_2 \wr S_5$ x 3 7680: 20T368 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
20T466 x 3, 40T10563 x 4, 40T10564 x 4, 40T10584 x 2, 40T10598 x 2, 40T10599 x 2, 40T10639 x 4, 40T10640 x 4, 40T10641 x 4, 40T10642 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 90 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $15360=2^{10} \cdot 3 \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |