Properties

Label 33T32
Degree $33$
Order $15972$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$6$:  $S_3$
$12$:  $D_{6}$
$22$:  $D_{11}$
$44$:  $D_{22}$
$132$:  33T5
$1452$:  33T15

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

33T32 x 9

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 221 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $15972=2^{2} \cdot 3 \cdot 11^{3}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.