Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $148$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,19,5,14,12,8,16,3,21,4,13,10,7,17,2,20,6,15,11,9,18), (1,14,17,12,20,9,4,3,13,16,11,19,8,5,2,15,18,10,21,7,6) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2520: $A_7$ 161280: 14T53 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $A_7$
Low degree siblings
42T4491Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 150 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $352719360=2^{9} \cdot 3^{9} \cdot 5 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |