Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $857$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,13,12,8,4,3,17,14,11,9,5,2,18,15,10,7,6), (1,7,15)(2,9,14,3,8,13)(4,11,17)(5,10,18)(6,12,16) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 3: $C_3$ 4: $C_2^2$ 6: $C_6$ x 3 8: $D_{4}$ 12: $A_4$, $C_6\times C_2$ 24: $A_4\times C_2$ x 3, $D_4 \times C_3$ 48: $C_2^2 \times A_4$ 96: $C_2^4:C_6$, 12T51 192: 12T87 384: 12T134 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 3: $C_3$
Degree 6: $C_6$
Degree 9: None
Low degree siblings
18T858Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 159 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $279936=2^{7} \cdot 3^{7}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |