Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $874$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14,7)(2,13,8)(3,15,9)(4,16,12,5,17,10)(6,18,11), (1,10,2,11,3,12)(4,7,5,9,6,8)(13,18,14,17)(15,16), (1,8,13,3,7,14,2,9,15)(4,10,16,6,11,18,5,12,17) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 8: $D_{4}$ 12: $D_{6}$ 24: $S_4$ x 3, $(C_6\times C_2):C_2$ 48: $S_4\times C_2$ x 3 96: $V_4^2:S_3$, 12T49 x 3 192: 12T100 384: 12T135 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 3: $S_3$
Degree 6: $S_3$
Degree 9: None
Low degree siblings
18T871 x 3Siblings 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: | $279936=2^{7} \cdot 3^{7}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |