Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $764$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,18,5,3,9,2,8,17,6,4,10)(11,16,13,12,15,14), (1,11,18,16,3,13,2,12,17,15,4,14)(5,9,7)(6,10,8) | |
| $|\Aut(F/K)|$: | $2$ |
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: $D_{6}$, $C_6\times C_2$ 18: $S_3\times C_3$ 24: $S_4$ 36: $C_6\times S_3$ 48: $S_4\times C_2$ 54: $C_3^2 : C_6$ 72: 12T45 108: 18T41 144: 18T61 162: $C_3 \wr S_3 $ 216: 18T97 324: 18T119 432: 18T149 648: 18T203 1296: 18T284 10368: 12T275 20736: 18T632 41472: 18T704 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: None
Degree 9: $C_3 \wr S_3 $
Low degree siblings
18T764Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 192 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. |