Group action invariants
| Degree $n$ : | $14$ | |
| Transitive number $t$ : | $55$ | |
| CHM label : | $[2^{6}]S(7)$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (3,13,5)(6,12,10), (2,9)(7,14), (3,5)(10,12), (1,3,5,7,9,11,13)(2,4,6,8,10,12,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 5040: $S_7$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 7: $S_7$
Low degree siblings
14T54, 28T945, 42T1589, 42T1590, 42T1591, 42T1592Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 55 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $322560=2^{10} \cdot 3^{2} \cdot 5 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |