Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $126$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,17,10,8,2,18,12,7)(3,16,11,9)(4,20)(5,21)(6,19)(13,15), (1,5,12,13,19,9,18,2,4,10,14,20,8,17,3,6,11,15,21,7,16) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 168: $\GL(3,2)$ 1344: 14T33 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $\GL(3,2)$
Low degree siblings
42T2236, 42T2237, 42T2238, 42T2242Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 60 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2939328=2^{6} \cdot 3^{8} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |