Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $548$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,3,2,4)(5,17,6,18)(7,15,8,16)(9,13,10,14), (1,4,5,8,10,12,14,15,17,2,3,6,7,9,11,13,16,18) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 18: $D_{9}$ 24: $S_4$ 36: $D_{18}$ 48: $S_4\times C_2$ 72: 18T38 144: 18T67 1152: 12T207 2304: 18T375 4608: 18T465 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: None
Degree 9: $D_{9}$
Low degree siblings
18T548 x 13Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 88 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $9216=2^{10} \cdot 3^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |