Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $472$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (3,5)(4,6)(7,11,10)(8,12,9)(13,14)(15,17)(16,18), (1,5)(2,6)(7,12,10,8,11,9)(13,14)(15,17)(16,18), (1,9,13)(2,10,14)(3,12,15,5,8,18)(4,11,16,6,7,17) | |
| $|\Aut(F/K)|$: | $2$ |
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 12: $A_4$ x 5, $C_6\times C_2$ 24: $A_4\times C_2$ x 15 48: $C_2^2 \times A_4$ x 5, $C_2^4:C_3$ 96: 12T56 x 3 192: 12T90 648: $S_3 \wr C_3 $ 1296: 18T283 2592: 18T399 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 6: $A_4\times C_2$
Degree 9: $S_3 \wr C_3 $
Low degree siblings
18T472 x 23Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 88 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $5184=2^{6} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |