Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $544$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,12,7,17,14,5,2,11,8,18,13,6)(3,15,10)(4,16,9), (1,14,8)(2,13,7)(3,12,10,17,16,5)(4,11,9,18,15,6) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 3: $C_3$ 4: $C_2^2$ 6: $S_3$, $C_6$ x 3 12: $A_4$, $D_{6}$, $C_6\times C_2$ 18: $S_3\times C_3$ 24: $S_4$, $A_4\times C_2$ x 3 36: $C_6\times S_3$ 48: $S_4\times C_2$, $C_2^2 \times A_4$ 72: 12T43, 12T45 144: 18T60, 18T61 288: $A_4\wr C_2$, 16T709 576: 12T158, 18T176 1152: 12T205, 12T206 2304: 18T366, 18T367 4608: 18T462 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 6: None
Degree 9: $S_3\times C_3$
Low degree siblings
18T544 x 5Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 96 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. |