Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $734$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,17,14,3,11,2,15,18,13,4,12)(5,7,9)(6,8,10), (3,17)(4,18)(5,13,9,15,8,12,6,14,10,16,7,11), (1,9,16,17,6,14,2,10,15,18,5,13)(3,8,12)(4,7,11) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 6: $S_3$ x 2 8: $C_2^3$ 12: $D_{6}$ x 6 24: $S_4$, $S_3 \times C_2^2$ x 2 36: $S_3^2$ 48: $S_4\times C_2$ x 3 72: 12T37 96: 12T48 108: $C_3^2 : D_{6} $ 144: 12T83 216: 18T94 288: 18T111 432: 18T152 864: 18T228 6912: 12T268 13824: 18T587 27648: 18T659 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: None
Degree 9: $C_3^2 : D_{6} $
Low degree siblings
18T734 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 120 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $55296=2^{11} \cdot 3^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |