Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $552$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11,18,2,12,17)(3,8,14,4,7,13)(5,10,16,6,9,15), (1,12,16,6,9,13,4,8,17,2,11,15,5,10,14,3,7,18) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ x 4 6: $C_6$ x 4 9: $C_3^2$ 18: $C_6 \times C_3$ 27: $C_3^2:C_3$ 54: 18T15 81: $C_3 \wr C_3 $ 162: 18T75 5184: 12T265 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 6: None
Degree 9: $C_3 \wr C_3 $
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 64 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $10368=2^{7} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |