Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $773$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,13,2,14)(3,16,5,18,4,15,6,17)(7,10,8,9), (1,11,6,8,2,12,5,7)(3,9,4,10)(13,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 24: $S_4$ 48: $S_4\times C_2$ 1296: $S_3\wr S_3$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: None
Degree 9: $S_3\wr S_3$
Low degree siblings
12T294, 18T770, 18T776, 18T777, 18T779, 18T780, 18T783, 18T785Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 65 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $82944=2^{10} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |