# Properties

 Label 14T2 Order $$14$$ n $$14$$ Cyclic No Abelian No Solvable Yes Primitive No $p$-group No Group: $D_{7}$

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## Group action invariants

 Degree $n$ : $14$ Transitive number $t$ : $2$ Group : $D_{7}$ CHM label : $D_{14}(14)=[7]2$ Parity: $-1$ Primitive: No Nilpotency class: $-1$ (not nilpotent) Generators: (1,12)(2,11)(3,10)(4,9)(5,8)(6,7)(13,14), (1,3,5,7,9,11,13)(2,4,6,8,10,12,14) $|\Aut(F/K)|$: $14$

## Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

## Subfields

Degree 2: $C_2$

Degree 7: $D_{7}$

## Low degree siblings

7T2

Siblings are shown with degree $\leq 47$

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

## Conjugacy Classes

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

## Group invariants

 Order: $14=2 \cdot 7$ Cyclic: No Abelian: No Solvable: Yes GAP id: [14, 1]
 Character table:  2 1 1 . . . 7 1 . 1 1 1 1a 2a 7a 7b 7c 2P 1a 1a 7b 7c 7a 3P 1a 2a 7c 7a 7b 5P 1a 2a 7b 7c 7a 7P 1a 2a 1a 1a 1a X.1 1 1 1 1 1 X.2 1 -1 1 1 1 X.3 2 . A B C X.4 2 . B C A X.5 2 . C A B A = E(7)+E(7)^6 B = E(7)^2+E(7)^5 C = E(7)^3+E(7)^4