Properties

Label 33T44
Order \(40095\)
n \(33\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

Degree $n$ :  $33$
Transitive number $t$ :  $44$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,4,18,33,26,2,5,16,31,27,3,6,17,32,25)(7,29,15,20,12,8,30,13,21,10,9,28,14,19,11)(22,24,23), (1,22,30,26,11,3,24,29,25,10,2,23,28,27,12)(7,20,14,16,31)(8,21,15,17,32)(9,19,13,18,33)
$|\Aut(F/K)|$:  $3$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$
5:  $C_5$
15:  $C_{15}$
55:  $C_{11}:C_5$
165:  33T6
13365:  33T30

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 11: $C_{11}:C_5$

Low degree siblings

33T44

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 63 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $40095=3^{6} \cdot 5 \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.