Properties

Label 33T33
Degree $33$
Order $16038$
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)
$|\Aut(F/K)|$:  $1$
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)

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:  not available
Character table: not available.