Group action invariants
| Degree $n$ : | $33$ | |
| Transitive number $t$ : | $46$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11,10,9,8,7,6,5,4,3,2)(12,31,22,24)(13,27,21,28)(14,23,20,32)(15,30,19,25)(16,26,18,29)(17,33), (1,23,6,31)(2,29,5,25)(3,24,4,30)(7,26,11,28)(8,32,10,33)(9,27)(12,20)(13,19)(14,18)(15,17)(21,22) | |
| $|\Aut(F/K)|$: | $1$ |
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: $S_4$ 48: $S_4\times C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: None
Low degree siblings
44T293Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 140 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $63888=2^{4} \cdot 3 \cdot 11^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |