Properties

Label 33T31
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 $t$:  $31$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,31,21,10,32,13,8,33,16,6,23,19,4,24,22,2,25,14,11,26,17,9,27,20,7,28,12,5,29,15,3,30,18), (1,26,16,6,23,18,11,31,20,5,28,22,10,25,13,4,33,15,9,30,17,3,27,19,8,24,21,2,32,12,7,29,14)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$3$:  $C_3$
$12$:  $A_4$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: None

Low degree siblings

44T142

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 149 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.