Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $705$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,4,2,3)(7,12)(8,11)(9,10)(13,17,16)(14,18,15), (1,12,18,6,7,13,3,10,15,2,11,17,5,8,14,4,9,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 12: $A_4$ 24: $A_4\times C_2$ 324: $((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ 648: 18T199 20736: 12T284 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 6: None
Low degree siblings
18T699 x 2, 18T700Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 64 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $41472=2^{9} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |