Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $838$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,3)(2,4)(5,6)(7,10,8,9)(11,14,15,12,13,16)(17,18), (1,14,8,4,15,9,2,13,7,3,16,10)(5,18,11,6,17,12), (1,11,9)(2,12,10)(3,15,6,4,16,5)(7,17,13,8,18,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 12: $A_4$ x 5 24: $A_4\times C_2$ x 5 48: $C_2^4:C_3$ 96: 12T56 648: $S_3 \wr C_3 $ 2592: 18T399 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
18T838 x 11, 18T840 x 12Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 180 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $165888=2^{11} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |