Properties

Label 46T19
Degree $46$
Order $47104$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$23$:  $C_{23}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $C_{23}$

Low degree siblings

46T19 x 88

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 112 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $47104=2^{11} \cdot 23$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.