Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $837$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (9,10)(11,12)(15,16)(17,18), (1,3)(2,4)(7,8)(13,14), (1,2)(7,8)(13,14), (1,15,9,3,18,11,6,14,7)(2,16,10,4,17,12,5,13,8), (1,11,2,12)(3,7,4,8)(5,9)(6,10)(13,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 6: $S_3$ 8: $C_2^3$ 12: $D_{6}$ x 3 24: $S_4$, $S_3 \times C_2^2$ 48: $S_4\times C_2$ x 3 96: 12T48 1296: $S_3\wr S_3$ 2592: 18T394 82944: 12T294 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
18T836 x 4, 18T837 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 130 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. |