Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $886$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6)(2,5)(3,8)(4,7)(9,18,10,17)(11,19,12,20)(15,16), (1,12,5,4,10,7,2,11,6,3,9,8)(13,20,15,17)(14,19,16,18), (1,7,20,15,12,3,6,18,13,10)(2,8,19,16,11,4,5,17,14,9) | |
| $|\Aut(F/K)|$: | $2$ |
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 15360: 20T466 61440: 20T667 122880: 20T794 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $S_5$
Degree 10: $C_2 \wr S_5$
Low degree siblings
20T886 x 3, 20T887 x 4, 40T106464 x 4, 40T106465 x 4, 40T106491 x 2, 40T106516 x 2, 40T106517 x 2, 40T106549 x 4, 40T106550 x 4, 40T106551 x 4, 40T106552 x 4, 40T106571 x 2, 40T106600 x 2, 40T106608 x 2, 40T106662 x 2, 40T106669 x 2, 40T106672 x 4, 40T106674 x 4, 40T106757 x 2, 40T106759 x 2, 40T106762 x 2, 40T106766 x 2, 40T106771 x 4, 40T106826 x 4, 40T106827 x 4, 40T106828 x 4, 40T106829 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 201 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $245760=2^{14} \cdot 3 \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |