Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $632$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,17,3,14,6,15)(2,18,4,13,5,16)(7,9,12,8,10,11), (1,5,3)(2,6,4)(7,17,12,15,10,13)(8,18,11,16,9,14) | |
| $|\Aut(F/K)|$: | $2$ |
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: $S_3\times C_3$ 36: $C_6\times S_3$ 54: $C_3^2 : C_6$ 108: 18T41 162: $C_3 \wr S_3 $ 324: 18T119 10368: 12T275 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
18T632Siblings 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: | $20736=2^{8} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |