Group action invariants
| Degree $n$: | $21$ | |
| Transitive number $t$: | $28$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $7$ | |
| Generators: | (1,20,8,3,16,14,5,19,13,7,15,12,2,18,11,4,21,10,6,17,9), (1,7,6,5,4,3,2)(8,10,12,14,9,11,13)(15,18,21,17,20,16,19) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $7$: $C_7$ $21$: $C_7:C_3$ x 2, $C_{21}$ $147$: 21T12, 21T13 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 7: None
Low degree siblings
21T28 x 11Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 133 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1029=3 \cdot 7^{3}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [1029, 15] |
| Character table: not available. |