Properties

Label 33T28
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 $t$:  $28$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,17,6,19,11,21,5,12,10,14,4,16,9,18,3,20,8,22,2,13,7,15)(23,24)(25,33)(26,32)(27,31)(28,30), (1,28,21,8,30,16,4,32,22,11,23,17,7,25,12,3,27,18,10,29,13,6,31,19,2,33,14,9,24,20,5,26,15)

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

33T28 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 253 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.