Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $32$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18,12,3,16,10,5,21,8,7,19,13,2,17,11,4,15,9,6,20,14), (1,7,6,5,4,3,2)(8,19,13,17,11,15,9,20,14,18,12,16,10,21) | |
| $|\Aut(F/K)|$: | $7$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 6: $S_3$ 7: $C_7$ 14: $C_{14}$ 42: 21T6 294: 14T15 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 7: None
Low degree siblings
21T32 x 5, 42T269 x 6, 42T281 x 3, 42T282 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 140 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. |