Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $127$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,15,16)(2,14,18)(3,13,17)(4,21,7)(5,20,8,6,19,9)(11,12), (1,20,17,14,10,7,4,3,21,18,13,11,9,5,2,19,16,15,12,8,6) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 3: $C_3$ 21: $C_7:C_3$ 168: $C_2^3:(C_7: C_3)$ x 2 1344: 14T35 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $C_7:C_3$
Low degree siblings
42T2239 x 2, 42T2240, 42T2244Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 99 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2939328=2^{6} \cdot 3^{8} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |