Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $51$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14,6,16,9,20,10)(2,15,4,17,7,19,11)(3,13,5,18,8,21,12), (1,13,2,15,3,14)(4,12,6,10,5,11)(7,8)(16,19)(17,20)(18,21) | |
| $|\Aut(F/K)|$: | $1$ |
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 12, 21T52 x 13, 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. |