Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $459$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (7,8)(11,12)(13,14)(15,16)(17,18), (1,3,17)(2,4,18)(5,8,9,6,7,10)(11,13,15,12,14,16), (1,14,8)(2,13,7)(3,15,10)(4,16,9)(5,17,11,6,18,12) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ x 4 6: $C_6$ x 4 9: $C_3^2$ 12: $A_4$ x 4 18: $C_6 \times C_3$ 24: $A_4\times C_2$ x 4 36: $C_3\times A_4$ x 4 72: 18T25 x 4 144: 12T85 x 6 288: 18T109 x 6 576: 12T164 x 4 1152: 18T263 x 4 2304: 18T369 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$ x 4
Degree 6: None
Degree 9: $C_3^2$
Low degree siblings
18T459 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 96 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $4608=2^{9} \cdot 3^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |