Properties

Label 33T26
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 $t$:  $26$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,18,32,10,15,33)(2,14,26,9,19,28)(3,21,31,8,12,23)(4,17,25,7,16,29)(5,13,30,6,20,24)(11,22,27), (1,15,31,2,19,25,3,12,30,4,16,24,5,20,29,6,13,23,7,17,28,8,21,33,9,14,27,10,18,32,11,22,26)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $C_6$
$22$:  $D_{11}$
$66$:  33T4
$726$:  33T12

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: None

Low degree siblings

33T26 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 241 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.