Properties

Label 33T33
Order \(16038\)
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 $t$ :  $33$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,4,7,12,15,17,20,22,27,30,33)(2,6,8,11,13,16,21,24,25,29,31,3,5,9,10,14,18,19,23,26,28,32), (1,33,28,26,22,21,16,13,11,9,5,2,31,29,27,23,19,17,14,12,7,6,3,32,30,25,24,20,18,15,10,8,4)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
6:  $S_3$
11:  $C_{11}$
22:  22T1
66:  33T2
5346:  33T24

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 11: $C_{11}$

Low degree siblings

33T33 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 66 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $16038=2 \cdot 3^{6} \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.