Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $807$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14,19)(2,13,20)(3,16,17,4,15,18)(5,8)(6,7)(9,12)(10,11), (1,8,16,4,6,13)(2,7,15,3,5,14)(9,11)(10,12)(19,20), (1,14,10,17,2,13,9,18)(3,16,12,19,4,15,11,20)(5,6) | |
| $|\Aut(F/K)|$: | $2$ |
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: 20T682 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $S_5$
Degree 10: $(C_2^4:A_5) : C_2$
Low degree siblings
20T807, 20T810 x 2, 40T45778 x 2, 40T45779 x 2, 40T45782 x 4, 40T45807, 40T45850, 40T45905, 40T45915 x 2, 40T45919 x 4, 40T45922 x 4, 40T45947 x 4, 40T45995, 40T46014 x 2, 40T46021 x 2, 40T46043 x 4, 40T46044 x 4Siblings 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. |