Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $586$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,5,8,3,11,14,9,18)(2,15,6,7,4,12,13,10,17), (1,17,3,14,11,16,8,5,10,2,18,4,13,12,15,7,6,9) | |
| $|\Aut(F/K)|$: | $2$ |
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: $C_3^2$ 12: $A_4$ 18: $C_6 \times C_3$ 24: $A_4\times C_2$ 27: $C_9:C_3$ 36: $C_3\times A_4$ 54: 18T14 72: 18T25 108: 18T47 216: 18T92 1728: 12T228 3456: 18T429 6912: 18T515 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 6: None
Degree 9: $C_9:C_3$
Low degree siblings
18T586 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 80 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $13824=2^{9} \cdot 3^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |