Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $1021$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,4,5,13,7,17,15,9,11,2,3,6,14,8,18,16,10,12)(19,20), (1,17,3,2,18,4)(5,16,14,20,7,12)(6,15,13,19,8,11)(9,10) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 3628800: $S_{10}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 5: None
Degree 10: $S_{10}$
Low degree siblings
20T1021, 40T171487Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 84 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $7257600=2^{9} \cdot 3^{4} \cdot 5^{2} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |