Properties

Label 33T23
Degree $33$
Order $3993$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$3$:  $C_3$
$11$:  $C_{11}$
$33$:  $C_{33}$
$363$:  33T10

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: None

Low degree siblings

33T23 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 473 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $3993=3 \cdot 11^{3}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.