Group action invariants
| Degree $n$: | $28$ | |
| Transitive number $t$: | $47$ | |
| Group: | $C_7\times D_{14}:C_2$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $14$ | |
| Generators: | (1,25,5,16,9,20,13,23,3,28,8,18,12,21,2,26,6,15,10,19,14,24,4,27,7,17,11,22), (1,21)(2,22)(3,24)(4,23)(5,26)(6,25)(7,28)(8,27)(9,15)(10,16)(11,18)(12,17)(13,19)(14,20) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $7$: $C_7$ $8$: $D_{4}$ $14$: $D_{7}$, $C_{14}$ x 3 $28$: $D_{14}$, 28T2 $56$: 28T5, 28T6 $98$: $C_7 \wr C_2$ $196$: 28T34 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 7: None
Degree 14: $C_7 \wr C_2$
Low degree siblings
28T47 x 5Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 119 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $392=2^{3} \cdot 7^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [392, 27] |
| Character table: not available. |