Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $903$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11,3,12)(2,10)(4,13,5,14,6,15)(7,17,8,18)(9,16), (1,7,2,8,3,9)(10,18,12,17,11,16)(13,15,14), (4,18,6,17)(5,16)(7,14,9,15)(8,13)(10,11) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 6: $S_3$ 8: $D_{4}$ x 2, $C_2^3$ 12: $D_{6}$ x 3 16: $D_4\times C_2$ 24: $S_4$, $S_3 \times C_2^2$ 48: $S_4\times C_2$ x 3, 12T28 96: 12T48 192: $V_4^2:(S_3\times C_2)$, 12T86 384: 12T136 768: 12T186 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 3: $S_3$
Degree 6: $D_{6}$
Degree 9: None
Low degree siblings
18T901Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 174 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $559872=2^{8} \cdot 3^{7}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |