Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $964$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,12,18,8,5,9,2,15,11,17,7,6,10)(3,13,4,14), (1,11,15,2,12,16)(3,7)(4,8)(5,9,17,6,10,18) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 362880: $S_9$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 6: None
Degree 9: $S_9$
Low degree siblings
18T965Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 150 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $92897280=2^{15} \cdot 3^{4} \cdot 5 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |