Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $882$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,16,17,6,14,4,9,11,2,8,15,18,5,13,3,10,12), (1,10,4,8)(2,9,3,7)(5,17,6,18)(11,14,12,13)(15,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 24: $S_4$ x 3 48: $S_4\times C_2$ x 3 96: $V_4^2:S_3$ 192: 12T100 648: $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ 1296: 18T305 2592: 18T403 5184: 18T487 41472: 12T290 82944: 18T769 165888: 18T841 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 6: None
Degree 9: $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$
Low degree siblings
18T882 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 192 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $331776=2^{12} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |