Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $461$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,13,4,16,5,17)(2,14,3,15,6,18)(7,11,10,8,12,9), (1,12)(2,11)(3,9)(4,10)(5,7)(6,8)(15,17)(16,18), (1,14,11)(2,13,12)(3,15,7,4,16,8)(5,18,10)(6,17,9) | |
| $|\Aut(F/K)|$: | $2$ |
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 144: 12T83 288: 18T111 576: $(A_4\wr C_2):C_2$ 1152: 12T195 2304: 12T239 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$ x 2
Degree 6: None
Degree 9: $S_3^2$
Low degree siblings
18T461 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 60 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $4608=2^{9} \cdot 3^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |