Properties

Label 33T27
Degree $33$
Order $7986$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$6$:  $S_3$
$11$:  $C_{11}$
$22$:  22T1
$66$:  33T2
$726$:  33T13

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

33T27 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 418 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $7986=2 \cdot 3 \cdot 11^{3}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.