Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $966$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,5,7,4,2,6,8,3)(9,18)(10,17)(11,14,15)(12,13,16), (1,18,8,11,9,2,17,7,12,10)(3,4)(5,13,16)(6,14,15) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 181440: $A_9$ 362880: 18T888 46448640: 18T963 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 6: None
Degree 9: $A_9$
Low degree siblings
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 168 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. |