Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $657$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,16)(2,5,15)(3,10,11,18,7,13)(4,9,12,17,8,14), (1,8,13,2,7,14)(3,5,16,18,9,12)(4,6,15,17,10,11) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 3: $C_3$ 4: $C_2^2$ 6: $S_3$, $C_6$ x 3 12: $A_4$, $D_{6}$, $C_6\times C_2$ 18: $S_3\times C_3$ 24: $A_4\times C_2$ x 3 36: $C_6\times S_3$ 48: $C_2^2 \times A_4$ 54: $C_3^2 : C_6$ 72: 12T43 108: 18T41 144: 18T60 216: 18T100 432: 18T148 3456: 12T251 6912: 18T513 13824: 18T589 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 6: None
Degree 9: $C_3^2 : S_3 $
Low degree siblings
18T657 x 5Siblings 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: | $27648=2^{10} \cdot 3^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |