Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $915$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11,13,5,9,17,3,10,15,4,7,16,2,12,14,6,8,18), (1,6,14,18,8,12)(2,5,13,17,9,10,3,4,15,16,7,11) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 3: $C_3$ 4: $C_2^2$ 6: $S_3$, $C_6$ x 3 8: $D_{4}$ 12: $D_{6}$, $C_6\times C_2$ 18: $S_3\times C_3$ 24: $(C_6\times C_2):C_2$, $D_4 \times C_3$ 36: $C_6\times S_3$ 72: 12T42 288: $A_4\wr C_2$ 576: 12T158 1152: 12T208 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 3: None
Degree 6: $S_3\times C_3$
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 170 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $839808=2^{7} \cdot 3^{8}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |