Group action invariants
| Degree $n$: | $21$ | |
| Transitive number $t$: | $32$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $7$ | |
| 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) |
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: | not available |
| Character table: not available. |