Group action invariants
| Degree $n$: | $28$ | |
| Transitive number $t$: | $34$ | |
| Group: | $C_{14}\times D_7$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $14$ | |
| Generators: | (1,26,22,18,13,10,6,2,25,21,17,14,9,5)(3,8,12,16,20,23,28,4,7,11,15,19,24,27), (1,11,25,8,22,4,17,27,13,23,9,19,6,16)(2,12,26,7,21,3,18,28,14,24,10,20,5,15) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $7$: $C_7$ $14$: $D_{7}$, $C_{14}$ x 3 $28$: $D_{14}$, 28T2 $98$: $C_7 \wr C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 7: None
Degree 14: $C_7 \wr C_2$
Low degree siblings
28T34 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 70 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $196=2^{2} \cdot 7^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [196, 10] |
| Character table: not available. |