Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $52$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,3,5,2,4)(7,19,8,21,9,20)(10,18,12,17,11,16)(13,14,15), (1,16,10,4,19,13,9)(2,17,11,5,21,14,7)(3,18,12,6,20,15,8) | |
| $|\Aut(F/K)|$: | $3$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 14: $D_{7}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $D_{7}$
Low degree siblings
21T51 x 13, 21T52 x 12, 42T555 x 13, 42T556 x 13, 42T557 x 13Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 96 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $10206=2 \cdot 3^{6} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |