Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $775$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,8,14)(2,7,13)(3,5,15,18,9,11,4,6,16,17,10,12), (1,18,3,2,17,4)(5,11)(6,12)(7,14)(8,13)(9,15,10,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ x 2 12: $D_{6}$ x 2 24: $S_4$ 36: $S_3^2$ 48: $S_4\times C_2$ 108: $C_3^2 : D_{6} $ 144: 12T83 324: $((C_3^3:C_3):C_2):C_2$ 432: 18T152 1296: 18T299 20736: 12T283 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: None
Degree 9: $((C_3^3:C_3):C_2):C_2$
Low degree siblings
18T771, 18T774, 18T778Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 84 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. |