Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $982$ | |
| Group : | $A_{18}$ | |
| Parity: | $1$ | |
| Primitive: | Yes | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18), (1,2,3) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
NoneResolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 6: None
Degree 9: None
Low degree siblings
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 200 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $3201186852864000=2^{15} \cdot 3^{8} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |