Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $945$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,15)(2,14)(3,13)(4,12)(5,11,6,10)(7,18,9,17,8,16), (1,6,9,11,14,18,3,5,7,12,15,16,2,4,8,10,13,17), (1,15,10,5)(2,13,12,4,3,14,11,6)(7,8) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 6: $S_3$ 8: $C_2^3$ 12: $D_{6}$ x 3 24: $S_4$ x 3, $S_3 \times C_2^2$ 48: $S_4\times C_2$ x 9 96: $V_4^2:S_3$, 12T48 x 3 192: 12T100 x 3 384: 12T139 768: 16T1055 1536: 24T3386 3072: 12T250 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: $S_4\times C_2$
Degree 9: None
Low degree siblings
18T945Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 255 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2239488=2^{10} \cdot 3^{7}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |