Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $61$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,8,15,19,5,10,17,3,7,13,20,4,11,18,2,9,14,21,6,12,16), (1,21,17,14,10,9,4,3,19,18,15,11,8,6,2,20,16,13,12,7,5) | |
| $|\Aut(F/K)|$: | $3$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 3: $C_3$ 7: $C_7$ 21: $C_{21}$ 5103: 21T39 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $C_7$
Low degree siblings
21T61 x 103Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 333 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $15309=3^{7} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |