Properties

Label 33T34
Order \(19965\)
n \(33\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

Degree $n$ :  $33$
Transitive number $t$ :  $34$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,20,23,7,17,30,6,12,27,8,22,33,4,13,32)(2,14,26,5,18,24,10,21,28,11,15,31,9,16,25)(3,19,29), (1,17,25,8,16,33,7,13,24,4,15,30,6,21,26)(2,20,23,11,14,27,5,18,28,9,19,31,10,22,29)(3,12,32)
$|\Aut(F/K)|$:  $1$

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
1815:  33T16

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: None

Low degree siblings

33T34 x 39

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 109 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $19965=3 \cdot 5 \cdot 11^{3}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.