Properties

Label 33T46
Order \(63888\)
n \(33\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

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

44T293

Siblings 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.