Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $143$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,13,20)(2,10,16)(3,14,19,7,9,15)(4,11,21)(5,8,17,6,12,18), (1,18,10,4,17,8,2,20,14)(3,16,9,5,21,13,6,19,11)(7,15,12) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 3: $C_3$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 7: None
Low degree siblings
21T143, 24T24055, 42T2782 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has exactly one arithmetically equivalent field.
Conjugacy Classes
There are 88 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $14224896=2^{9} \cdot 3^{4} \cdot 7^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |