Properties

Label 33T46
Degree $33$
Order $63888$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $33$
Transitive number $t$:  $46$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,11,10,9,8,7,6,5,4,3,2)(12,31,22,24)(13,27,21,28)(14,23,20,32)(15,30,19,25)(16,26,18,29)(17,33), (1,23,6,31)(2,29,5,25)(3,24,4,30)(7,26,11,28)(8,32,10,33)(9,27)(12,20)(13,19)(14,18)(15,17)(21,22)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$6$:  $S_3$
$12$:  $D_{6}$
$24$:  $S_4$
$48$:  $S_4\times C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

44T293

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 140 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $63888=2^{4} \cdot 3 \cdot 11^{3}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.