Group action invariants
| Degree $n$ : | $33$ | |
| Transitive number $t$ : | $38$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,2,12)(3,19,11,20)(4,15,10,13)(5,22,9,17)(6,18,8,21)(7,14)(24,33)(25,32)(26,31)(27,30)(28,29), (1,23)(2,29,11,28)(3,24,10,33)(4,30,9,27)(5,25,8,32)(6,31,7,26)(13,22)(14,21)(15,20)(16,19)(17,18) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 6: $S_3$ 24: $S_4$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: None
Low degree siblings
44T231Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 175 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $31944=2^{3} \cdot 3 \cdot 11^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |