Properties

Label 46T15
Degree $46$
Order $23276$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$11$:  $C_{11}$
$22$:  22T1 x 3
$44$:  44T2
$506$:  $F_{23}$ x 2
$1012$:  46T6 x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: None

Low degree siblings

46T15 x 10

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 59 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $23276=2^{2} \cdot 11 \cdot 23^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.