Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $125$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,21,4,16,15,12,7,2,20,5,17,14,10,8,3,19,6,18,13,11,9), (1,10,15,3,11,14,2,12,13)(4,17,8,6,16,7)(5,18,9)(20,21) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 168: $\GL(3,2)$ 1344: $C_2^3:\GL(3,2)$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $\GL(3,2)$
Low degree siblings
24T22757, 42T2233, 42T2234, 42T2235, 42T2243Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 120 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. |