Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $930$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6)(2,4,3,5)(7,9,8)(10,13,11,15)(12,14)(16,17), (1,15,9)(2,13,7,3,14,8)(4,16,12,5,17,10,6,18,11), (1,5,11,13,3,6,12,14)(2,4,10,15)(7,16,8,17)(9,18) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 24: $S_4$ x 3 48: $S_4\times C_2$ x 3 96: $V_4^2:S_3$ 192: $C_2^3:S_4$ x 2, 12T100 384: 16T747 768: 16T1063 1536: 12T226 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: $S_4$
Degree 9: None
Low degree siblings
18T932Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 174 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1119744=2^{9} \cdot 3^{7}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |