Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $284$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,13,10,2,14,9)(3,15,11,4,16,12)(5,18,7,6,17,8), (1,12,4,8,6,9,2,11,3,7,5,10)(13,15,17)(14,16,18) | |
| $|\Aut(F/K)|$: | $6$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 3: $C_3$ 4: $C_2^2$ 6: $S_3$, $C_6$ x 3 12: $D_{6}$, $C_6\times C_2$ 18: $S_3\times C_3$ 24: $S_4$ 36: $C_6\times S_3$ 48: $S_4\times C_2$ 54: $C_3^2 : C_6$ 72: 12T45 108: 18T41 144: 18T61 162: $C_3 \wr S_3 $ 216: 18T97 324: 18T119 432: 18T149 648: 18T203 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 \wr S_3 $
Low degree siblings
18T284 x 5Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 98 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1296=2^{4} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [1296, 1827] |
| Character table: Data not available. |