Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $662$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,13)(2,8,14)(3,10,16,4,9,15)(5,12,18,6,11,17), (1,2)(5,8,10,6,7,9)(11,15,13)(12,16,14)(17,18), (17,18), (5,12,6,11)(7,13)(8,14)(9,15)(10,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ x 4 12: $D_{6}$ x 4 18: $C_3^2:C_2$ 24: $S_4$ 36: 18T12 48: $S_4\times C_2$ 54: $(C_3^2:C_3):C_2$ 72: 12T44 108: 18T52 144: 18T66 216: 18T107 432: 18T156 3456: 12T252 6912: 18T521 13824: 18T594 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: None
Degree 9: $(C_3^2:C_3):C_2$
Low degree siblings
18T662Siblings 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: | $27648=2^{10} \cdot 3^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |