Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $30$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,15,5,19,2,16,6,20,3,17,7,21,4,18)(8,14)(9,13)(10,12), (1,12,2,13,3,14,4,8,5,9,6,10,7,11)(15,21)(16,20)(17,19) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 6: $S_3$ 14: $D_{7}$ 42: $D_{21}$ 294: 14T15 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 7: None
Low degree siblings
21T30 x 5, 42T267 x 6, 42T280 x 3, 42T283 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 77 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2058=2 \cdot 3 \cdot 7^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |