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Properties

Label 14T1
Order \(14\)
n \(14\)
Cyclic Yes
Abelian Yes
Solvable Yes
Primitive No
$p$-group No
Group: $C_{14}$

Related objects

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Group action invariants

Degree $n$ :  $14$
Transitive number $t$ :  $1$
Group :  $C_{14}$
CHM label :  $C(14)=7[x]2$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $1$
Generators:  (1,2,3,4,5,6,7,8,9,10,11,12,13,14)
$|\Aut(F/K)|$:  $14$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
7:  $C_7$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 7: $C_7$

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 TypeSizeOrderRepresentative
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 14 $ $1$ $14$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14)$
$ 7, 7 $ $1$ $7$ $( 1, 3, 5, 7, 9,11,13)( 2, 4, 6, 8,10,12,14)$
$ 14 $ $1$ $14$ $( 1, 4, 7,10,13, 2, 5, 8,11,14, 3, 6, 9,12)$
$ 7, 7 $ $1$ $7$ $( 1, 5, 9,13, 3, 7,11)( 2, 6,10,14, 4, 8,12)$
$ 14 $ $1$ $14$ $( 1, 6,11, 2, 7,12, 3, 8,13, 4, 9,14, 5,10)$
$ 7, 7 $ $1$ $7$ $( 1, 7,13, 5,11, 3, 9)( 2, 8,14, 6,12, 4,10)$
$ 2, 2, 2, 2, 2, 2, 2 $ $1$ $2$ $( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)$
$ 7, 7 $ $1$ $7$ $( 1, 9, 3,11, 5,13, 7)( 2,10, 4,12, 6,14, 8)$
$ 14 $ $1$ $14$ $( 1,10, 5,14, 9, 4,13, 8, 3,12, 7, 2,11, 6)$
$ 7, 7 $ $1$ $7$ $( 1,11, 7, 3,13, 9, 5)( 2,12, 8, 4,14,10, 6)$
$ 14 $ $1$ $14$ $( 1,12, 9, 6, 3,14,11, 8, 5, 2,13,10, 7, 4)$
$ 7, 7 $ $1$ $7$ $( 1,13,11, 9, 7, 5, 3)( 2,14,12,10, 8, 6, 4)$
$ 14 $ $1$ $14$ $( 1,14,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)$

Group invariants

Order:  $14=2 \cdot 7$
Cyclic:  Yes
Abelian:  Yes
Solvable:  Yes
GAP id:  [14, 2]
Character table:    
      2  1   1  1   1  1   1  1  1  1   1  1   1  1   1
      7  1   1  1   1  1   1  1  1  1   1  1   1  1   1

        1a 14a 7a 14b 7b 14c 7c 2a 7d 14d 7e 14e 7f 14f

X.1      1   1  1   1  1   1  1  1  1   1  1   1  1   1
X.2      1  -1  1  -1  1  -1  1 -1  1  -1  1  -1  1  -1
X.3      1   A  B   C /C  /B /A  1  A   B  C  /C /B  /A
X.4      1  -A  B  -C /C -/B /A -1  A  -B  C -/C /B -/A
X.5      1   B /C  /A  A   C /B  1  B  /C /A   A  C  /B
X.6      1  -B /C -/A  A  -C /B -1  B -/C /A  -A  C -/B
X.7      1   C /A   B /B   A /C  1  C  /A  B  /B  A  /C
X.8      1  -C /A  -B /B  -A /C -1  C -/A  B -/B  A -/C
X.9      1  /C  A  /B  B  /A  C  1 /C   A /B   B /A   C
X.10     1 -/C  A -/B  B -/A  C -1 /C  -A /B  -B /A  -C
X.11     1  /B  C   A /A  /C  B  1 /B   C  A  /A /C   B
X.12     1 -/B  C  -A /A -/C  B -1 /B  -C  A -/A /C  -B
X.13     1  /A /B  /C  C   B  A  1 /A  /B /C   C  B   A
X.14     1 -/A /B -/C  C  -B  A -1 /A -/B /C  -C  B  -A

A = E(7)^4
B = E(7)
C = E(7)^5