Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $968$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,17,4,11,13,5,9,16,2,18,3,12,14,6,10,15), (1,8,17,10,5,14,12,4,16,2,7,18,9,6,13,11,3,15) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 362880: $S_9$ 725760: 18T913 92897280: 18T964 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 6: None
Degree 9: $S_9$
Low degree siblings
18T968Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 300 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $185794560=2^{16} \cdot 3^{4} \cdot 5 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |