Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $112$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,19,16,6,13,11,7,2,20,18,4,14,12,9)(3,21,17,5,15,10,8), (1,21,18,5,13,10,7,2,19,16,6,15,12,8)(3,20,17,4,14,11,9) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 7: $C_7$ 14: $C_{14}$ 56: $C_2^3:C_7$ 112: 14T9 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $C_7$
Low degree siblings
24T19235, 42T1505 x 3, 42T1506, 42T1507 x 3, 42T1508, 42T1509 x 3, 42T1510 x 3, 42T1511, 42T1512 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 72 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $244944=2^{4} \cdot 3^{7} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |