# Properties

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

# Related objects

## Group action invariants

 Degree $n$: $11$ Transitive number $t$: $1$ Group: $C_{11}$ CHM label: $C(11)=11$ Parity: $1$ Primitive: yes Nilpotency class: $1$ $\card{\Aut(F/K)}$: $11$ 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

 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 Label: 11.1
 Character table:  11 1 1 1 1 1 1 1 1 1 1 1 1a 11a 11b 11c 11d 11e 11f 11g 11h 11i 11j X.1 1 1 1 1 1 1 1 1 1 1 1 X.2 1 A B C D E /E /D /C /B /A X.3 1 B D /E /C /A A C E /D /B X.4 1 C /E /B A D /D /A B E /C X.5 1 D /C A E /B B /E /A C /D X.6 1 E /A D /B C /C B /D A /E X.7 1 /E A /D B /C C /B D /A E X.8 1 /D C /A /E B /B E A /C D X.9 1 /C E B /A /D D A /B /E C X.10 1 /B /D E C A /A /C /E D B X.11 1 /A /B /C /D /E E D C B A A = E(11) B = E(11)^2 C = E(11)^3 D = E(11)^4 E = E(11)^5