Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $623$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,3,2,4)(5,6)(7,9,8,10)(13,15)(14,16)(17,18), (1,7,13)(2,8,14)(3,10,16,4,9,15)(5,12,18,6,11,17), (1,4,18,2,3,17)(5,8,10,6,7,9)(11,13,15)(12,14,16), (17,18), (5,12,6,11)(7,13)(8,14)(9,15)(10,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 6: $S_3$ x 2 8: $C_2^3$ 12: $D_{6}$ x 6 24: $S_4$ x 2, $S_3 \times C_2^2$ x 2 36: $S_3^2$ 48: $S_4\times C_2$ x 6 72: 12T37 96: 12T48 x 2 144: 12T83 x 2 288: 18T111 x 2 576: $(A_4\wr C_2):C_2$, 16T1033 1152: 12T195, 18T266 2304: 12T239 x 2 4608: 18T461 x 2 9216: 18T545 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$ x 2
Degree 6: None
Degree 9: $S_3^2$
Low degree siblings
18T623 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 120 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $18432=2^{11} \cdot 3^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |