Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $794$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,8,13,20,2,7,14,19)(3,10,12,18,4,9,11,17)(5,15)(6,16), (1,11,2,12)(3,18,20,6)(4,17,19,5)(7,10,16,14,8,9,15,13), (1,3,5,7,10,11,13,16,18,19)(2,4,6,8,9,12,14,15,17,20) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $C_2^3$ 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 7680: 20T368 61440: 20T667 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
20T794, 20T804 x 2, 40T45694 x 2, 40T45695 x 2, 40T45713 x 4, 40T45736, 40T45742 x 2, 40T45743 x 2, 40T45777 x 2, 40T45780 x 2, 40T45781 x 4, 40T45808, 40T45903, 40T45916 x 2, 40T45920 x 4, 40T45921 x 4, 40T46000, 40T46041 x 2, 40T46042 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 138 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $122880=2^{13} \cdot 3 \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |