Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $702$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,5,3)(2,6,4)(9,12)(10,11)(13,18,16,14,17,15), (1,7,14,4,11,16,2,8,13,3,12,15)(5,9,17)(6,10,18) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 12: $A_4$ 24: $A_4\times C_2$ 648: $S_3 \wr C_3 $ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 6: None
Degree 9: $S_3 \wr C_3 $
Low degree siblings
12T292, 18T702, 18T703, 18T706 x 2, 18T707, 18T708, 18T709Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 55 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $41472=2^{9} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |