Properties

Label 33T44
Degree $33$
Order $40095$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $33$
Transitive number $t$:  $44$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $3$
Generators:  (1,4,18,33,26,2,5,16,31,27,3,6,17,32,25)(7,29,15,20,12,8,30,13,21,10,9,28,14,19,11)(22,24,23), (1,22,30,26,11,3,24,29,25,10,2,23,28,27,12)(7,20,14,16,31)(8,21,15,17,32)(9,19,13,18,33)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$3$:  $C_3$
$5$:  $C_5$
$15$:  $C_{15}$
$55$:  $C_{11}:C_5$
$165$:  33T6
$13365$:  33T30

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 11: $C_{11}:C_5$

Low degree siblings

33T44

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 63 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $40095=3^{6} \cdot 5 \cdot 11$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.