Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $135$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,21,13)(2,19,14)(3,20,15)(4,18,11,6,16,12,5,17,10)(7,8,9), (1,16,5,21,14,9,11,2,18,4,20,13,8,10)(3,17,6,19,15,7,12) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 168: $\GL(3,2)$ 336: 14T17 1344: 14T33 2688: 14T42 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $\GL(3,2)$
Low degree siblings
42T2480, 42T2481, 42T2482, 42T2483, 42T2484, 42T2485, 42T2486, 42T2508Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 84 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. |