Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $766$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,17,4)(2,18,3)(9,10)(11,13,16)(12,14,15), (3,17,4,18)(5,8,6,7)(11,16)(12,15)(13,14), (1,5,12,18,8,16,2,6,11,17,7,15)(3,9,14)(4,10,13) | |
| $|\Aut(F/K)|$: | $2$ |
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: $A_4\times C_2$ x 3 36: $C_6\times S_3$ 48: $C_2^2 \times A_4$ 54: $C_3^2 : C_6$ 72: 12T43 108: 18T41 144: 18T60 162: $(C_3^2:C_3):C_2$ 216: 18T100 324: 18T125 432: 18T148 648: 18T200 1296: 18T282 10368: 12T273 20736: 18T631 41472: 18T701 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 6: None
Degree 9: $(C_3^2:C_3):C_2$
Low degree siblings
18T766 x 5Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 144 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $82944=2^{10} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |