Properties

Label 33T29
Order \(8019\)
n \(33\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

Degree $n$ :  $33$
Transitive number $t$ :  $29$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,33,29,26,23,20,17,13,11,8,5,2,31,30,27,24,21,18,14,12,9,6,3,32,28,25,22,19,16,15,10,7,4), (1,22,11,31,20,9,28,16,6,25,15,2,23,12,32,21,7,29,17,4,26,13,3,24,10,33,19,8,30,18,5,27,14)
$|\Aut(F/K)|$:  $3$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$
11:  $C_{11}$
33:  $C_{33}$
2673:  33T18

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 11: $C_{11}$

Low degree siblings

33T29 x 21

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 99 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $8019=3^{6} \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [8019, 505]
Character table: Data not available.