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Properties

Label 14T8
Order \(98\)
n \(14\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_7 \wr C_2$

Related objects

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Group action invariants

Degree $n$ :  $14$
Transitive number $t$ :  $8$
Group :  $C_7 \wr C_2$
CHM label :  $[7^{2}]2=7wr2$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (2,4,6,8,10,12,14), (1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14)
$|\Aut(F/K)|$:  $7$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
7:  $C_7$
14:  $D_{7}$, $C_{14}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 7: None

Low degree siblings

14T8 x 2

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

Group invariants

Order:  $98=2 \cdot 7^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [98, 3]
Character table: Data not available.