Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $485$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,4)(2,3)(7,15,9,14,12,18,8,16,10,13,11,17), (1,15,12,5,14,8,4,18,10,2,16,11,6,13,7,3,17,9) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 24: $S_4$ x 3 48: $S_4\times C_2$ x 3 96: $V_4^2:S_3$ 192: 12T100 648: $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ 1296: 18T301 2592: 18T402 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: $S_4\times C_2$
Degree 9: $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$
Low degree siblings
18T485 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 58 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $5184=2^{6} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |