Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $767$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14,10,2,13,9)(3,18,7,4,17,8)(5,16,11,6,15,12), (1,5,2,6)(7,10,11)(8,9,12)(15,17)(16,18), (1,11,18,2,12,17)(3,8,16,5,9,13,4,7,15,6,10,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 3: $C_3$ 4: $C_2^2$ 6: $C_6$ x 3 12: $A_4$, $C_6\times C_2$ 24: $A_4\times C_2$ x 3 48: $C_2^2 \times A_4$ 648: $S_3 \wr C_3 $ 1296: 18T283 41472: 12T292 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 6: None
Degree 9: $S_3 \wr C_3 $
Low degree siblings
18T765 x 2, 18T767 x 3, 18T768 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 110 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. |