Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $962$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,4)(2,18,5)(3,17,6)(7,15)(8,13,9,14), (1,3)(4,13,12,8)(5,15,11,9,6,14,10,7)(16,18,17) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 720: $S_6$ 1440: $S_6\times C_2$ 23040: 30T937 46080: 12T293 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 6: $S_6$
Degree 9: None
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 221 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $33592320=2^{10} \cdot 3^{8} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |