Galois group: 11T1

• Label: 11T1
• Degree: $11$
• Order: $11$
• Cyclic: yes
• Abelian: yes
• Solvable: yes
• Primitive: yes
• $p$-group: yes
• Group: $C_{11}$

Group action invariants

Degree $n$:		$11$
Transitive number $t$:		$1$
Group:		$C_{11}$
CHM label:		$C(11)=11$
Parity:		$1$
Primitive:		yes
$\card{\Aut(F/K)}$:		$11$
Generators:		(1,2,3,4,5,6,7,8,9,10,11)

Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - 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

Label	Cycle Type	Size	Order	Representative
	$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$1$	$1$	$()$
	$ 11 $	$1$	$11$	$( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)$
	$ 11 $	$1$	$11$	$( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)$
	$ 11 $	$1$	$11$	$( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)$
	$ 11 $	$1$	$11$	$( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)$
	$ 11 $	$1$	$11$	$( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)$
	$ 11 $	$1$	$11$	$( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)$
	$ 11 $	$1$	$11$	$( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)$
	$ 11 $	$1$	$11$	$( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)$
	$ 11 $	$1$	$11$	$( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)$
	$ 11 $	$1$	$11$	$( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)$

Group invariants

Order:		$11$ (is prime)
Cyclic:		yes
Abelian:		yes
Solvable:		yes
Nilpotency class:		$1$
Label:		11.1
Character table:

1A

11A1

11A-1

11A2

11A-2

11A3

11A-3

11A4

11A-4

11A5

11A-5

Size

1

1

1

1

1

1

1

1

1

1

1

11 P

1A

11A3

11A1

11A4

11A-1

11A-4

11A2

11A-5

11A-2

11A5

11A-3

Type

11.1.1a

R

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

11.1.1b1

C

$1$

${\zeta }_{11}^{-5}$

${\zeta }_{11}^5$

${\zeta }_{11}$

${\zeta }_{11}^{-1}$

${\zeta }_{11}^{-4}$

${\zeta }_{11}^4$

${\zeta }_{11}^2$

${\zeta }_{11}^{-2}$

${\zeta }_{11}^{-3}$

${\zeta }_{11}^3$

11.1.1b2

C

$1$

${\zeta }_{11}^5$

${\zeta }_{11}^{-5}$

${\zeta }_{11}^{-1}$

${\zeta }_{11}$

${\zeta }_{11}^4$

${\zeta }_{11}^{-4}$

${\zeta }_{11}^{-2}$

${\zeta }_{11}^2$

${\zeta }_{11}^3$

${\zeta }_{11}^{-3}$

11.1.1b3

C

$1$

${\zeta }_{11}^{-4}$

${\zeta }_{11}^4$

${\zeta }_{11}^3$

${\zeta }_{11}^{-3}$

${\zeta }_{11}^{-1}$

${\zeta }_{11}$

${\zeta }_{11}^{-5}$

${\zeta }_{11}^5$

${\zeta }_{11}^2$

${\zeta }_{11}^{-2}$

11.1.1b4

C

$1$

${\zeta }_{11}^4$

${\zeta }_{11}^{-4}$

${\zeta }_{11}^{-3}$

${\zeta }_{11}^3$

${\zeta }_{11}$

${\zeta }_{11}^{-1}$

${\zeta }_{11}^5$

${\zeta }_{11}^{-5}$

${\zeta }_{11}^{-2}$

${\zeta }_{11}^2$

11.1.1b5

C

$1$

${\zeta }_{11}^{-3}$

${\zeta }_{11}^3$

${\zeta }_{11}^5$

${\zeta }_{11}^{-5}$

${\zeta }_{11}^2$

${\zeta }_{11}^{-2}$

${\zeta }_{11}^{-1}$

${\zeta }_{11}$

${\zeta }_{11}^{-4}$

${\zeta }_{11}^4$

11.1.1b6

C

$1$

${\zeta }_{11}^3$

${\zeta }_{11}^{-3}$

${\zeta }_{11}^{-5}$

${\zeta }_{11}^5$

${\zeta }_{11}^{-2}$

${\zeta }_{11}^2$

${\zeta }_{11}$

${\zeta }_{11}^{-1}$

${\zeta }_{11}^4$

${\zeta }_{11}^{-4}$

11.1.1b7

C

$1$

${\zeta }_{11}^{-2}$

${\zeta }_{11}^2$

${\zeta }_{11}^{-4}$

${\zeta }_{11}^4$

${\zeta }_{11}^5$

${\zeta }_{11}^{-5}$

${\zeta }_{11}^3$

${\zeta }_{11}^{-3}$

${\zeta }_{11}$

${\zeta }_{11}^{-1}$

11.1.1b8

C

$1$

${\zeta }_{11}^2$

${\zeta }_{11}^{-2}$

${\zeta }_{11}^4$

${\zeta }_{11}^{-4}$

${\zeta }_{11}^{-5}$

${\zeta }_{11}^5$

${\zeta }_{11}^{-3}$

${\zeta }_{11}^3$

${\zeta }_{11}^{-1}$

${\zeta }_{11}$

11.1.1b9

C

$1$

${\zeta }_{11}^{-1}$

${\zeta }_{11}$

${\zeta }_{11}^{-2}$

${\zeta }_{11}^2$

${\zeta }_{11}^{-3}$

${\zeta }_{11}^3$

${\zeta }_{11}^{-4}$

${\zeta }_{11}^4$

${\zeta }_{11}^{-5}$

${\zeta }_{11}^5$

11.1.1b10

C

$1$

${\zeta }_{11}$

${\zeta }_{11}^{-1}$

${\zeta }_{11}^2$

${\zeta }_{11}^{-2}$

${\zeta }_{11}^3$

${\zeta }_{11}^{-3}$

${\zeta }_{11}^4$

${\zeta }_{11}^{-4}$

${\zeta }_{11}^5$

${\zeta }_{11}^{-5}$