Group action invariants
| Degree $n$: | $14$ | |
| Transitive number $t$: | $57$ | |
| CHM label: | $[2^{7}]S(7)$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (3,13,5)(6,12,10), (3,5)(10,12), (7,14), (1,3,5,7,9,11,13)(2,4,6,8,10,12,14) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $5040$: $S_7$ $10080$: $S_7\times C_2$ $322560$: 14T54 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 7: $S_7$
Low degree siblings
14T57, 28T1097 x 2, 28T1098, 28T1099 x 2, 42T1778 x 2, 42T1779 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 110 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $645120=2^{11} \cdot 3^{2} \cdot 5 \cdot 7$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | no | |
| GAP id: | not available |
| Character table: not available. |