Group action invariants
| Degree $n$ : | $14$ | |
| Transitive number $t$ : | $61$ | |
| CHM label : | $[S(7)^{2}]2=S(7)wr2$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (2,4,6,8,10,12,14), (10,12), (1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 7: None
Low degree siblings
28T1634, 28T1635, 28T1636, 42T3347Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 135 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $50803200=2^{9} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |