Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $396$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6)(2,5)(7,11)(8,12)(13,15)(14,16), (1,2)(3,4)(5,6), (1,11)(2,12)(3,9)(4,10)(5,8)(6,7)(13,16)(14,15)(17,18), (13,15,18)(14,16,17), (1,16,12,6,14,9,4,17,8)(2,15,11,5,13,10,3,18,7) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 6: $S_3$ x 2 8: $C_2^3$ 12: $D_{6}$ x 6 24: $S_4$, $S_3 \times C_2^2$ x 2 36: $S_3^2$ 48: $S_4\times C_2$ x 3 72: 12T37 96: 12T48 108: $C_3^2 : D_{6} $ 144: 12T83 216: 18T94 288: 18T111 324: $((C_3^3:C_3):C_2):C_2$ 432: 18T152 648: 18T194 864: 18T228 1296: 18T299 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: $S_4\times C_2$
Degree 9: $((C_3^3:C_3):C_2):C_2$
Low degree siblings
18T396 x 11Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 70 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2592=2^{5} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |