Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $791$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,4,2,3)(5,9,16,17,8,12,13,19,6,10,15,18,7,11,14,20), (1,10,5,3,12,7,2,9,6,4,11,8)(13,19)(14,20)(15,18)(16,17) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_4$ x 2, $C_2^2$ 8: $C_4\times C_2$ 120: $S_5$ 240: $S_5\times C_2$ 480: 20T123 1920: $(C_2^4:A_5) : C_2$ 3840: $C_2 \wr S_5$ 7680: 20T369 30720: 20T568 61440: 20T673 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
20T791 x 3, 40T45853 x 2, 40T45900 x 2, 40T46003 x 2, 40T46013 x 4, 40T46020 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 252 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. |