Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $136$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,16,3,9,17)(2,8,18)(4,14,21,6,15,19,5,13,20)(10,11,12), (1,2)(4,14,16,6,15,18)(5,13,17)(7,20,12,9,21,10,8,19,11) | |
| $|\Aut(F/K)|$: | $1$ |
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 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $\GL(3,2)$
Low degree siblings
24T23418, 42T2487, 42T2488, 42T2489, 42T2490, 42T2491, 42T2492, 42T2493, 42T2509Siblings 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: | $5878656=2^{7} \cdot 3^{8} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |