Galois group: 46T15

• Label: 46T15
• Degree: $46$
• Order: $23276$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• pp-group: no
• Group: $D_{23}:F_{23}$

Group invariants

Abstract group:		$D_{23}:F_{23}$
Order:		$23276=2^{2} \cdot 11 \cdot 23^{2}$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$46$
Transitive number $t$:		$15$
Parity:		$-1$
Primitive:		no
$\card{\Aut(F/K)}$:		$1$
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

$\card{(G/N)}$	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

Conjugacy classes not computed

Character table

59 x 59 character table

Regular extensions

Data not computed