Group action invariants
| Degree $n$ : | $28$ | |
| Transitive number $t$ : | $33$ | |
| Group : | $C_7\times C_7:C_4$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,2)(3,23,15,8,28,19,12,4,24,16,7,27,20,11)(5,6)(9,10)(13,14)(17,18)(21,22)(25,26), (1,27,5,3,9,8,14,12,17,16,21,20,25,23,2,28,6,4,10,7,13,11,18,15,22,19,26,24) | |
| $|\Aut(F/K)|$: | $14$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 4: $C_4$ 7: $C_7$ 14: $D_{7}$, $C_{14}$ 28: $C_{28}$, 28T3 98: $C_7 \wr C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $C_4$
Degree 7: None
Degree 14: $C_7 \wr C_2$
Low degree siblings
28T33 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, 5] |
| Character table: Data not available. |