Properties

Label 46T24
Degree $46$
Order $512072$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $46$
Transitive number $t$:  $24$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,9,8,11,2,6,17,7,14,16,10,5,20,21,18,4,23,12,22,15,13,19)(24,32,41,31,37,38,42,35,30,33,45)(25,36,34,26,40,27,44,43,39,46,28), (1,40,11,25,5,34,4,24,23,30,7,31,12,35,9,28,20,46,18,26,10,38)(2,27,15,42,21,33,22,43,3,37,19,36,14,32,17,39,6,44,8,41,16,29)(13,45)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$8$:  $D_{4}$
$11$:  $C_{11}$
$22$:  $D_{11}$, 22T1 x 3
$44$:  $D_{22}$, 44T2
$88$:  44T5, 44T6
$242$:  22T7
$484$:  44T27
$968$:  44T33

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: None

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

There are 299 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $512072=2^{3} \cdot 11^{2} \cdot 23^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.