Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $782$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,15,5,18,2,16,6,17)(3,13,4,14)(7,8)(9,11,10,12), (3,4)(5,6)(7,12,8,11)(9,10)(13,16,14,15)(17,18), (1,15,10,2,16,9)(3,18,12,4,17,11)(5,14,8,6,13,7) | |
| $|\Aut(F/K)|$: | $2$ |
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: $S_4$ 48: $S_4\times C_2$ 648: $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ 1296: 18T305 41472: 12T290 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: None
Degree 9: $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$
Low degree siblings
18T769 x 2, 18T782Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 80 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. |