Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $131$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14)(2,13)(3,15)(4,12,5,10)(6,11)(7,8,9)(16,20)(17,21,18,19), (1,6,9,10,13,18,20,3,5,7,11,15,16,19)(2,4,8,12,14,17,21) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 14: $D_{7}$ 28: $D_{14}$ 896: 14T27 1792: 14T38 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $D_{7}$
Low degree siblings
42T2321, 42T2322 x 3, 42T2323 x 3, 42T2324 x 3, 42T2325 x 3, 42T2326, 42T2327, 42T2328, 42T2329 x 3, 42T2330 x 3, 42T2331 x 3, 42T2332 x 3, 42T2333, 42T2334, 42T2335, 42T2336 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 288 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $3919104=2^{8} \cdot 3^{7} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |