Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $188$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,12,14,4,7,15,5,10,17,2,11,13,3,8,16,6,9,18), (1,13,11,3,15,7,5,18,9)(2,14,12,4,16,8,6,17,10) | |
| $|\Aut(F/K)|$: | $6$ |
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 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 6: $A_4\times C_2$
Degree 9: $C_3 \wr C_3 $
Low degree siblings
18T188 x 8Siblings 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: | $648=2^{3} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [648, 320] |
| Character table: Data not available. |