Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $912$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,5,16)(2,6,15)(3,8,14)(4,7,13)(9,11,17,10,12,18), (7,8)(9,10)(11,15)(12,16), (1,6,17,9,2,5,18,10)(3,8,4,7)(11,14)(12,13) | |
| $|\Aut(F/K)|$: | $2$ |
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 10368: 18T556 82944: 12T294 165888: 18T836 331776: 18T880 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: None
Degree 9: $S_3\wr S_3$
Low degree siblings
18T912 x 7Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 330 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $663552=2^{13} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |