Properties

Label 33T34
Degree $33$
Order $19965$
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)
$|\Aut(F/K)|$:  $1$
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)

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:  not available
Character table: not available.