Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $691$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,11,3,9,14)(2,5,12,4,10,13)(7,16,18,8,15,17), (1,4,13,11)(2,3,14,12)(5,16,9,18,6,15,10,17)(7,8), (1,6,11,7)(2,5,12,8)(3,14,16,17)(4,13,15,18)(9,10) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $D_{4}$ x 2, $C_2^3$ 16: $D_4\times C_2$ 72: $C_3^2:D_4$ 144: 12T77 1152: $S_4\wr C_2$ x 2 2304: 12T235 x 2 18432: 18T626 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
18T691 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 108 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $36864=2^{12} \cdot 3^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |