Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $630$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,2)(3,9)(4,10)(5,6)(7,13)(8,14)(11,18,12,17)(15,16), (1,13,10,15)(2,14,9,16)(3,6,8,18,4,5,7,17)(11,12) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ 72: $C_3^2:D_4$ 1152: $S_4\wr C_2$ x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 6: None
Degree 9: $S_3^2:C_2$
Low degree siblings
18T626, 18T627 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 54 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $18432=2^{11} \cdot 3^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |