Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $460$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18,15,13,12,10,7,6,3,2,17,16,14,11,9,8,5,4), (1,18,16,14,11,9,7,5,3)(2,17,15,13,12,10,8,6,4) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 9: $C_9$ 12: $A_4$ 18: $C_{18}$ 24: $A_4\times C_2$ 36: $C_2^2 : C_9$ 72: 18T26 576: 12T166 1152: 18T264 2304: 18T368 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 6: None
Degree 9: $C_9$
Low degree siblings
18T460 x 20Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 80 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. |