Properties

Label 33T39
Degree $33$
Order $31944$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

Learn more about

Group action invariants

Degree $n$:  $33$
Transitive number $t$:  $39$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,19,25,3,22,24,5,14,23,7,17,33,9,20,32,11,12,31,2,15,30,4,18,29,6,21,28,8,13,27,10,16,26), (1,30,11,24)(2,25,10,29)(3,31,9,23)(4,26,8,28)(5,32,7,33)(6,27)(12,17,22,16,21,15,20,14,19,13,18)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$6$:  $S_3$
$24$:  $S_4$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

44T230

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 100 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $31944=2^{3} \cdot 3 \cdot 11^{3}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.