Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $884$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,3,17)(2,4,18)(5,12,7,13,6,11,8,14)(9,15)(10,16), (1,16,3,12)(2,15,4,11)(5,6)(7,9)(8,10)(13,17)(14,18), (1,18,3,2,17,4)(5,16)(6,15)(7,13)(8,14)(9,12)(10,11) | |
| $|\Aut(F/K)|$: | $2$ |
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: $S_4$ x 3 48: $S_4\times C_2$ x 3 96: $V_4^2:S_3$ 192: 12T100 1296: $S_3\wr S_3$ 5184: 18T483 82944: 12T294 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: None
Degree 9: $S_3\wr S_3$
Low degree siblings
18T880 x 2, 18T883 x 2, 18T884, 18T885 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 165 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $331776=2^{12} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |