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Properties

Label 14T29
Order \(896\)
n \(14\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_2 \wr C_7$

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Group action invariants

Degree $n$ :  $14$
Transitive number $t$ :  $29$
Group :  $C_2 \wr C_7$
CHM label :  $[2^{7}]7=2wr7$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (7,14), (1,3,5,7,9,11,13)(2,4,6,8,10,12,14)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
7:  $C_7$
14:  $C_{14}$
56:  $C_2^3:C_7$ x 2
112:  14T9 x 2
448:  14T21

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 7: $C_7$

Low degree siblings

14T29 x 6, 28T104 x 7, 28T110 x 21, 28T111 x 42, 28T112 x 42, 28T113 x 21, 28T114 x 42, 28T115 x 42, 28T116 x 14, 28T117 x 42, 28T118 x 7

Siblings are shown 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 $ $1$ $1$ $()$
$ 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $7$ $2$ $( 7,14)$
$ 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $7$ $2$ $( 2, 9)( 7,14)$
$ 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $7$ $2$ $( 4,11)( 7,14)$
$ 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $7$ $2$ $( 2, 9)( 4,11)( 7,14)$
$ 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $7$ $2$ $( 6,13)( 7,14)$
$ 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $7$ $2$ $( 2, 9)( 6,13)( 7,14)$
$ 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $7$ $2$ $( 4,11)( 6,13)( 7,14)$
$ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $7$ $2$ $( 2, 9)( 4,11)( 6,13)( 7,14)$
$ 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $7$ $2$ $( 1, 8)( 2, 9)( 7,14)$
$ 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ $7$ $2$ $( 1, 8)( 4,11)( 7,14)$
$ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $7$ $2$ $( 1, 8)( 2, 9)( 4,11)( 7,14)$
$ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $7$ $2$ $( 1, 8)( 2, 9)( 6,13)( 7,14)$
$ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $7$ $2$ $( 1, 8)( 4,11)( 6,13)( 7,14)$
$ 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $7$ $2$ $( 1, 8)( 2, 9)( 4,11)( 6,13)( 7,14)$
$ 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ $7$ $2$ $( 2, 9)( 3,10)( 6,13)( 7,14)$
$ 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $7$ $2$ $( 2, 9)( 3,10)( 4,11)( 6,13)( 7,14)$
$ 2, 2, 2, 2, 2, 1, 1, 1, 1 $ $7$ $2$ $( 1, 8)( 2, 9)( 3,10)( 4,11)( 7,14)$
$ 2, 2, 2, 2, 2, 2, 1, 1 $ $7$ $2$ $( 1, 8)( 2, 9)( 3,10)( 4,11)( 6,13)( 7,14)$
$ 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 $ $64$ $7$ $( 1, 3, 5, 7, 9,11,13)( 2, 4, 6, 8,10,12,14)$
$ 14 $ $64$ $14$ $( 1, 3, 5,14, 2, 4, 6, 8,10,12, 7, 9,11,13)$
$ 7, 7 $ $64$ $7$ $( 1, 7,13, 5,11, 3, 9)( 2, 8,14, 6,12, 4,10)$
$ 14 $ $64$ $14$ $( 1,14, 6,12, 4,10, 2, 8, 7,13, 5,11, 3, 9)$
$ 7, 7 $ $64$ $7$ $( 1, 5, 9,13, 3, 7,11)( 2, 6,10,14, 4, 8,12)$
$ 14 $ $64$ $14$ $( 1, 5, 9,13, 3,14, 4, 8,12, 2, 6,10, 7,11)$
$ 7, 7 $ $64$ $7$ $( 1,13,11, 9, 7, 5, 3)( 2,14,12,10, 8, 6, 4)$
$ 14 $ $64$ $14$ $( 1,13,11, 9,14,12,10, 8, 6, 4, 2, 7, 5, 3)$
$ 7, 7 $ $64$ $7$ $( 1, 9, 3,11, 5,13, 7)( 2,10, 4,12, 6,14, 8)$
$ 14 $ $64$ $14$ $( 1, 9, 3,11, 5,13,14, 8, 2,10, 4,12, 6, 7)$
$ 7, 7 $ $64$ $7$ $( 1,11, 7, 3,13, 9, 5)( 2,12, 8, 4,14,10, 6)$
$ 14 $ $64$ $14$ $( 1,11,14,10, 6, 2,12, 8, 4, 7, 3,13, 9, 5)$

Group invariants

Order:  $896=2^{7} \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [896, 19347]
Character table: Data not available.