Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $696$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,12,10,4,14,6,17,16,7,2,11,9,3,13,5,18,15,8), (1,18,3,2,17,4)(5,10,8)(6,9,7)(11,16,14)(12,15,13), (1,3,18)(2,4,17)(5,7,10)(6,8,9)(11,16,13,12,15,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ x 4 6: $C_6$ x 4 9: $C_3^2$ 12: $A_4$ 18: $C_6 \times C_3$ 24: $A_4\times C_2$ 27: $C_3^2:C_3$ 36: $C_3\times A_4$ 54: 18T15 72: 18T25 81: $C_3 \wr C_3 $ 108: 18T48 162: 18T75 216: 18T91 324: 18T127 648: 18T188 5184: 12T265 10368: 18T552 20736: 18T633 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 6: None
Degree 9: $C_3 \wr C_3 $
Low degree siblings
18T696 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 192 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $41472=2^{9} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |