Group action invariants
| Degree $n$ : | $14$ | |
| Transitive number $t$ : | $56$ | |
| CHM label : | $[2^{7}]A(7)=2wrA(7)$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (3,13,5)(6,12,10), (7,14), (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: $C_2$ 2520: $A_7$ 5040: $A_7\times C_2$ 161280: 14T53 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 7: $A_7$
Low degree siblings
28T946, 42T1587, 42T1588Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 64 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. |