Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $39$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,13,6,16,7,21,10)(2,14,4,17,8,20,11)(3,15,5,18,9,19,12), (1,15,4,16,8,19,12)(2,13,5,17,9,21,10)(3,14,6,18,7,20,11) | |
| $|\Aut(F/K)|$: | $3$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 7: $C_7$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $C_7$
Low degree siblings
21T39 x 51Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 111 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $5103=3^{6} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [5103, 4034] |
| Character table: Data not available. |