# Properties

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

# Related objects

## 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 Type Size Order Representative $1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1$ $1$ $()$ $14$ $1$ $14$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14)$ $7, 7$ $1$ $7$ $( 1, 3, 5, 7, 9,11,13)( 2, 4, 6, 8,10,12,14)$ $14$ $1$ $14$ $( 1, 4, 7,10,13, 2, 5, 8,11,14, 3, 6, 9,12)$ $7, 7$ $1$ $7$ $( 1, 5, 9,13, 3, 7,11)( 2, 6,10,14, 4, 8,12)$ $14$ $1$ $14$ $( 1, 6,11, 2, 7,12, 3, 8,13, 4, 9,14, 5,10)$ $7, 7$ $1$ $7$ $( 1, 7,13, 5,11, 3, 9)( 2, 8,14, 6,12, 4,10)$ $2, 2, 2, 2, 2, 2, 2$ $1$ $2$ $( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)$ $7, 7$ $1$ $7$ $( 1, 9, 3,11, 5,13, 7)( 2,10, 4,12, 6,14, 8)$ $14$ $1$ $14$ $( 1,10, 5,14, 9, 4,13, 8, 3,12, 7, 2,11, 6)$ $7, 7$ $1$ $7$ $( 1,11, 7, 3,13, 9, 5)( 2,12, 8, 4,14,10, 6)$ $14$ $1$ $14$ $( 1,12, 9, 6, 3,14,11, 8, 5, 2,13,10, 7, 4)$ $7, 7$ $1$ $7$ $( 1,13,11, 9, 7, 5, 3)( 2,14,12,10, 8, 6, 4)$ $14$ $1$ $14$ $( 1,14,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)$

## 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