Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $796$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,4,2,3)(5,7,10,16,17,19)(6,8,9,15,18,20)(11,14,12,13), (1,17,6,2,18,5)(3,19)(4,20)(7,15,12)(8,16,11)(9,13)(10,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ 120: $S_5$ 240: $S_5\times C_2$ 480: 20T120 1920: $(C_2^4:A_5) : C_2$ 3840: $C_2 \wr S_5$ 7680: 20T375 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
20T796, 20T800 x 2, 40T45697 x 2, 40T45700 x 2, 40T45734, 40T45751 x 2, 40T45752 x 2, 40T45855, 40T45910, 40T45914, 40T46009 x 2, 40T46019 x 2, 40T46026 x 2, 40T46071 x 2, 40T46072 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 108 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. |