Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $147$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,12,6)(2,11,4)(3,10,5)(7,8,9)(13,20,18,15,19,17,14,21,16), (1,12,19,8,18,6,13,3,10,20,7,17,4,15)(2,11,21,9,16,5,14) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 168: $\GL(3,2)$ 336: 14T17 1344: $C_2^3:\GL(3,2)$ 2688: 14T43 10752: 14T50 21504: 14T51 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $\GL(3,2)$
Low degree siblings
42T3339, 42T3340, 42T3341, 42T3342, 42T3343, 42T3344, 42T3345, 42T3346Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 228 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $47029248=2^{10} \cdot 3^{8} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |