Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $556$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,10,2,9)(3,12,6,7)(4,11,5,8), (1,2)(3,6)(4,5)(13,14)(15,16)(17,18), (1,2)(3,4)(5,6), (13,15,18)(14,16,17), (1,14,10)(2,13,9)(3,18,8)(4,17,7)(5,15,12)(6,16,11) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 6: $S_3$ 8: $C_2^3$ 12: $D_{6}$ x 3 24: $S_4$ x 3, $S_3 \times C_2^2$ 48: $S_4\times C_2$ x 9 96: $V_4^2:S_3$, 12T48 x 3 192: 12T100 x 3 384: 12T139 1296: $S_3\wr S_3$ 2592: 18T394 5184: 18T483 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: $S_4\times C_2$
Degree 9: $S_3\wr S_3$
Low degree siblings
18T556 x 7Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 98 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $10368=2^{7} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |