Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $117$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,2,3)(4,7,12,5,9,11,6,8,10)(13,21,16,15,19,17)(14,20,18), (1,18,15,9,20,4,10)(2,16,13,7,21,5,12)(3,17,14,8,19,6,11) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 21: $C_7:C_3$ 42: $(C_7:C_3) \times C_2$ 168: $C_2^3:(C_7: C_3)$ 336: 14T18 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $C_7:C_3$
Low degree siblings
24T20694, 42T1828, 42T1829, 42T1830, 42T1844Siblings 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: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |