Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $555$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,15,6,10)(2,16,8,18)(3,12,4,13)(5,14)(7,11,9,17), (1,12,6,11,8,18,4,17,3,15,2,14)(5,16,7,10,9,13), (1,16,4,13,2,11,5,17,9,12,3,18)(6,15,8,14,7,10) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $D_{4}$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 3 32: $C_2^2 \wr C_2$ 64: $(((C_4 \times C_2): C_2):C_2):C_2$ 128: $C_2 \wr C_2\wr C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 3: None
Degree 6: None
Degree 9: None
Low degree siblings
12T274 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 54 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $10368=2^{7} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |