Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $400$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,8,13,6,11,17,4,10,16,2,7,14,5,12,18,3,9,15), (1,8,17)(2,7,18)(3,9,16)(4,10,15)(5,12,14)(6,11,13), (1,10,14,2,9,13)(3,11,18,4,12,17)(5,8,15,6,7,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 12: $A_4$ x 5 24: $A_4\times C_2$ x 5 48: $C_2^4:C_3$ 96: 12T56 324: $((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ 648: 18T199 1296: 18T322 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 6: $A_4\times C_2$
Low degree siblings
18T400 x 11Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 56 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2592=2^{5} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |