Galois group: 23T2

• Label: 23T2
• Degree: $23$
• Order: $46$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: yes
• $p$-group: no
• Group: $D_{23}$

Group action invariants

Degree $n$:		$23$
Transitive number $t$:		$2$
Group:		$D_{23}$
Parity:		$-1$
Primitive:		yes
$\card{\Aut(F/K)}$:		$1$
Generators:		(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23), (2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)

Low degree resolvents

|G/N|	Galois groups for stem field(s)
$2$:	$C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

Low degree siblings

46T2

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

Label	Cycle Type	Size	Order	Representative
	$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$1$	$1$	$()$
	$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 $	$23$	$2$	$( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13)$
	$ 23 $	$2$	$23$	$( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)$
	$ 23 $	$2$	$23$	$( 1, 3, 5, 7, 9,11,13,15,17,19,21,23, 2, 4, 6, 8,10,12,14,16,18,20,22)$
	$ 23 $	$2$	$23$	$( 1, 4, 7,10,13,16,19,22, 2, 5, 8,11,14,17,20,23, 3, 6, 9,12,15,18,21)$
	$ 23 $	$2$	$23$	$( 1, 5, 9,13,17,21, 2, 6,10,14,18,22, 3, 7,11,15,19,23, 4, 8,12,16,20)$
	$ 23 $	$2$	$23$	$( 1, 6,11,16,21, 3, 8,13,18,23, 5,10,15,20, 2, 7,12,17,22, 4, 9,14,19)$
	$ 23 $	$2$	$23$	$( 1, 7,13,19, 2, 8,14,20, 3, 9,15,21, 4,10,16,22, 5,11,17,23, 6,12,18)$
	$ 23 $	$2$	$23$	$( 1, 8,15,22, 6,13,20, 4,11,18, 2, 9,16,23, 7,14,21, 5,12,19, 3,10,17)$
	$ 23 $	$2$	$23$	$( 1, 9,17, 2,10,18, 3,11,19, 4,12,20, 5,13,21, 6,14,22, 7,15,23, 8,16)$
	$ 23 $	$2$	$23$	$( 1,10,19, 5,14,23, 9,18, 4,13,22, 8,17, 3,12,21, 7,16, 2,11,20, 6,15)$
	$ 23 $	$2$	$23$	$( 1,11,21, 8,18, 5,15, 2,12,22, 9,19, 6,16, 3,13,23,10,20, 7,17, 4,14)$
	$ 23 $	$2$	$23$	$( 1,12,23,11,22,10,21, 9,20, 8,19, 7,18, 6,17, 5,16, 4,15, 3,14, 2,13)$

Group invariants

Order:		$46=2 \cdot 23$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent
Label:		46.1
Character table:

1A

2A

23A1

23A2

23A3

23A4

23A5

23A6

23A7

23A8

23A9

23A10

23A11

Size

1

23

2

2

2

2

2

2

2

2

2

2

2

2 P

1A

1A

23A7

23A2

23A9

23A10

23A1

23A11

23A3

23A5

23A8

23A6

23A4

23 P

1A

2A

23A4

23A11

23A8

23A9

23A6

23A3

23A5

23A7

23A2

23A10

23A1

Type

46.1.1a

R

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

46.1.1b

R

$1$

$-1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

46.1.2a1

R

$2$

$0$

${\zeta }_{23}^{-11}+{\zeta }_{23}^{11}$

${\zeta }_{23}^{-1}+{\zeta }_{23}$

${\zeta }_{23}^{-10}+{\zeta }_{23}^{10}$

${\zeta }_{23}^{-2}+{\zeta }_{23}^2$

${\zeta }_{23}^{-9}+{\zeta }_{23}^9$

${\zeta }_{23}^{-3}+{\zeta }_{23}^3$

${\zeta }_{23}^{-8}+{\zeta }_{23}^8$

${\zeta }_{23}^{-4}+{\zeta }_{23}^4$

${\zeta }_{23}^{-7}+{\zeta }_{23}^7$

${\zeta }_{23}^{-5}+{\zeta }_{23}^5$

${\zeta }_{23}^{-6}+{\zeta }_{23}^6$

46.1.2a2

R

$2$

$0$

${\zeta }_{23}^{-10}+{\zeta }_{23}^{10}$

${\zeta }_{23}^{-3}+{\zeta }_{23}^3$

${\zeta }_{23}^{-7}+{\zeta }_{23}^7$

${\zeta }_{23}^{-6}+{\zeta }_{23}^6$

${\zeta }_{23}^{-4}+{\zeta }_{23}^4$

${\zeta }_{23}^{-9}+{\zeta }_{23}^9$

${\zeta }_{23}^{-1}+{\zeta }_{23}$

${\zeta }_{23}^{-11}+{\zeta }_{23}^{11}$

${\zeta }_{23}^{-2}+{\zeta }_{23}^2$

${\zeta }_{23}^{-8}+{\zeta }_{23}^8$

${\zeta }_{23}^{-5}+{\zeta }_{23}^5$

46.1.2a3

R

$2$

$0$

${\zeta }_{23}^{-9}+{\zeta }_{23}^9$

${\zeta }_{23}^{-5}+{\zeta }_{23}^5$

${\zeta }_{23}^{-4}+{\zeta }_{23}^4$

${\zeta }_{23}^{-10}+{\zeta }_{23}^{10}$

${\zeta }_{23}^{-1}+{\zeta }_{23}$

${\zeta }_{23}^{-8}+{\zeta }_{23}^8$

${\zeta }_{23}^{-6}+{\zeta }_{23}^6$

${\zeta }_{23}^{-3}+{\zeta }_{23}^3$

${\zeta }_{23}^{-11}+{\zeta }_{23}^{11}$

${\zeta }_{23}^{-2}+{\zeta }_{23}^2$

${\zeta }_{23}^{-7}+{\zeta }_{23}^7$

46.1.2a4

R

$2$

$0$

${\zeta }_{23}^{-8}+{\zeta }_{23}^8$

${\zeta }_{23}^{-7}+{\zeta }_{23}^7$

${\zeta }_{23}^{-1}+{\zeta }_{23}$

${\zeta }_{23}^{-9}+{\zeta }_{23}^9$

${\zeta }_{23}^{-6}+{\zeta }_{23}^6$

${\zeta }_{23}^{-2}+{\zeta }_{23}^2$

${\zeta }_{23}^{-10}+{\zeta }_{23}^{10}$

${\zeta }_{23}^{-5}+{\zeta }_{23}^5$

${\zeta }_{23}^{-3}+{\zeta }_{23}^3$

${\zeta }_{23}^{-11}+{\zeta }_{23}^{11}$

${\zeta }_{23}^{-4}+{\zeta }_{23}^4$

46.1.2a5

R

$2$

$0$

${\zeta }_{23}^{-7}+{\zeta }_{23}^7$

${\zeta }_{23}^{-9}+{\zeta }_{23}^9$

${\zeta }_{23}^{-2}+{\zeta }_{23}^2$

${\zeta }_{23}^{-5}+{\zeta }_{23}^5$

${\zeta }_{23}^{-11}+{\zeta }_{23}^{11}$

${\zeta }_{23}^{-4}+{\zeta }_{23}^4$

${\zeta }_{23}^{-3}+{\zeta }_{23}^3$

${\zeta }_{23}^{-10}+{\zeta }_{23}^{10}$

${\zeta }_{23}^{-6}+{\zeta }_{23}^6$

${\zeta }_{23}^{-1}+{\zeta }_{23}$

${\zeta }_{23}^{-8}+{\zeta }_{23}^8$

46.1.2a6

R

$2$

$0$

${\zeta }_{23}^{-6}+{\zeta }_{23}^6$

${\zeta }_{23}^{-11}+{\zeta }_{23}^{11}$

${\zeta }_{23}^{-5}+{\zeta }_{23}^5$

${\zeta }_{23}^{-1}+{\zeta }_{23}$

${\zeta }_{23}^{-7}+{\zeta }_{23}^7$

${\zeta }_{23}^{-10}+{\zeta }_{23}^{10}$

${\zeta }_{23}^{-4}+{\zeta }_{23}^4$

${\zeta }_{23}^{-2}+{\zeta }_{23}^2$

${\zeta }_{23}^{-8}+{\zeta }_{23}^8$

${\zeta }_{23}^{-9}+{\zeta }_{23}^9$

${\zeta }_{23}^{-3}+{\zeta }_{23}^3$

46.1.2a7

R

$2$

$0$

${\zeta }_{23}^{-5}+{\zeta }_{23}^5$

${\zeta }_{23}^{-10}+{\zeta }_{23}^{10}$

${\zeta }_{23}^{-8}+{\zeta }_{23}^8$

${\zeta }_{23}^{-3}+{\zeta }_{23}^3$

${\zeta }_{23}^{-2}+{\zeta }_{23}^2$

${\zeta }_{23}^{-7}+{\zeta }_{23}^7$

${\zeta }_{23}^{-11}+{\zeta }_{23}^{11}$

${\zeta }_{23}^{-6}+{\zeta }_{23}^6$

${\zeta }_{23}^{-1}+{\zeta }_{23}$

${\zeta }_{23}^{-4}+{\zeta }_{23}^4$

${\zeta }_{23}^{-9}+{\zeta }_{23}^9$

46.1.2a8

R

$2$

$0$

${\zeta }_{23}^{-4}+{\zeta }_{23}^4$

${\zeta }_{23}^{-8}+{\zeta }_{23}^8$

${\zeta }_{23}^{-11}+{\zeta }_{23}^{11}$

${\zeta }_{23}^{-7}+{\zeta }_{23}^7$

${\zeta }_{23}^{-3}+{\zeta }_{23}^3$

${\zeta }_{23}^{-1}+{\zeta }_{23}$

${\zeta }_{23}^{-5}+{\zeta }_{23}^5$

${\zeta }_{23}^{-9}+{\zeta }_{23}^9$

${\zeta }_{23}^{-10}+{\zeta }_{23}^{10}$

${\zeta }_{23}^{-6}+{\zeta }_{23}^6$

${\zeta }_{23}^{-2}+{\zeta }_{23}^2$

46.1.2a9

R

$2$

$0$

${\zeta }_{23}^{-3}+{\zeta }_{23}^3$

${\zeta }_{23}^{-6}+{\zeta }_{23}^6$

${\zeta }_{23}^{-9}+{\zeta }_{23}^9$

${\zeta }_{23}^{-11}+{\zeta }_{23}^{11}$

${\zeta }_{23}^{-8}+{\zeta }_{23}^8$

${\zeta }_{23}^{-5}+{\zeta }_{23}^5$

${\zeta }_{23}^{-2}+{\zeta }_{23}^2$

${\zeta }_{23}^{-1}+{\zeta }_{23}$

${\zeta }_{23}^{-4}+{\zeta }_{23}^4$

${\zeta }_{23}^{-7}+{\zeta }_{23}^7$

${\zeta }_{23}^{-10}+{\zeta }_{23}^{10}$

46.1.2a10

R

$2$

$0$

${\zeta }_{23}^{-2}+{\zeta }_{23}^2$

${\zeta }_{23}^{-4}+{\zeta }_{23}^4$

${\zeta }_{23}^{-6}+{\zeta }_{23}^6$

${\zeta }_{23}^{-8}+{\zeta }_{23}^8$

${\zeta }_{23}^{-10}+{\zeta }_{23}^{10}$

${\zeta }_{23}^{-11}+{\zeta }_{23}^{11}$

${\zeta }_{23}^{-9}+{\zeta }_{23}^9$

${\zeta }_{23}^{-7}+{\zeta }_{23}^7$

${\zeta }_{23}^{-5}+{\zeta }_{23}^5$

${\zeta }_{23}^{-3}+{\zeta }_{23}^3$

${\zeta }_{23}^{-1}+{\zeta }_{23}$

46.1.2a11

R

$2$

$0$

${\zeta }_{23}^{-1}+{\zeta }_{23}$

${\zeta }_{23}^{-2}+{\zeta }_{23}^2$

${\zeta }_{23}^{-3}+{\zeta }_{23}^3$

${\zeta }_{23}^{-4}+{\zeta }_{23}^4$

${\zeta }_{23}^{-5}+{\zeta }_{23}^5$

${\zeta }_{23}^{-6}+{\zeta }_{23}^6$

${\zeta }_{23}^{-7}+{\zeta }_{23}^7$

${\zeta }_{23}^{-8}+{\zeta }_{23}^8$

${\zeta }_{23}^{-9}+{\zeta }_{23}^9$

${\zeta }_{23}^{-10}+{\zeta }_{23}^{10}$

${\zeta }_{23}^{-11}+{\zeta }_{23}^{11}$