Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $119$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,6,7)(2,17,5,9)(3,18,4,8)(11,12)(13,19)(14,21,15,20), (1,20,14,4,3,19,15,6,2,21,13,5)(7,12,9,10)(8,11) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 168: $\GL(3,2)$ 336: 14T17 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $\GL(3,2)$
Low degree siblings
21T119, 24T20695, 42T1834 x 2, 42T1835 x 2, 42T1836 x 2, 42T1847 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 72 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $734832=2^{4} \cdot 3^{8} \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |