Properties

Label 33T29
Degree $33$
Order $8019$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $33$
Transitive number $t$:  $29$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $3$
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)

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: not available.