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Properties

Label 14T29
Degree $14$
Order $896$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2 \wr C_7$

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Show commands: Magma

magma: G := TransitiveGroup(14, 29);
 

Group action invariants

Degree $n$:  $14$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $29$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $C_2 \wr C_7$
CHM label:   $[2^{7}]7=2wr7$
Parity:  $-1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $2$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (7,14), (1,3,5,7,9,11,13)(2,4,6,8,10,12,14)
magma: Generators(G);
 

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

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

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $896=2^{7} \cdot 7$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  896.19347
magma: IdentifyGroup(G);
 
Character table:    32 x 32 character table

magma: CharacterTable(G);