Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $772$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,8,18,10,3,6)(2,7,17,9,4,5)(11,16,12,15), (1,12,7)(2,11,8)(3,13,10)(4,14,9)(5,17,15)(6,18,16), (1,15,6,18,13,10,4,12,8,2,16,5,17,14,9,3,11,7) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ x 4 12: $D_{6}$ x 4 18: $C_3^2:C_2$ 24: $S_4$ 36: 18T12 48: $S_4\times C_2$ 54: $(C_3^2:C_3):C_2$ 72: 12T44 108: 18T52 144: 18T66 162: $(C_3^3:C_3):C_2$ 216: 18T107 324: 18T134 432: 18T156 648: 18T225 1296: 18T308 10368: 12T276 20736: 18T644 41472: 18T717 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: None
Degree 9: $(C_3^3:C_3):C_2$
Low degree siblings
18T772Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 144 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $82944=2^{10} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |