Properties

Label 14T13
Order \(196\)
n \(14\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $D_7^2$

Related objects

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Group action invariants

Degree $n$ :  $14$
Transitive number $t$ :  $13$
Group :  $D_7^2$
CHM label :  $[1/2.D(7)^{2}]2$
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), (1,13)(2,12)(3,11)(4,10)(5,9)(6,8)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
14:  $D_{7}$ x 2
28:  $D_{14}$ x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 7: None

Low degree siblings

14T13 x 2, 28T36 x 3

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, 2, 2, 2, 2, 2, 1, 1 $ $49$ $2$ $( 3,13)( 4,14)( 5,11)( 6,12)( 7, 9)( 8,10)$
$ 7, 1, 1, 1, 1, 1, 1, 1 $ $4$ $7$ $( 2, 4, 6, 8,10,12,14)$
$ 7, 1, 1, 1, 1, 1, 1, 1 $ $4$ $7$ $( 2, 6,10,14, 4, 8,12)$
$ 7, 1, 1, 1, 1, 1, 1, 1 $ $4$ $7$ $( 2, 8,14, 6,12, 4,10)$
$ 2, 2, 2, 2, 2, 2, 2 $ $7$ $2$ $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)$
$ 2, 2, 2, 2, 2, 2, 2 $ $7$ $2$ $( 1, 2)( 3,14)( 4,13)( 5,12)( 6,11)( 7,10)( 8, 9)$
$ 14 $ $14$ $14$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14)$
$ 14 $ $14$ $14$ $( 1, 2, 3,14, 5,12, 7,10, 9, 8,11, 6,13, 4)$
$ 14 $ $14$ $14$ $( 1, 2, 5, 6, 9,10,13,14, 3, 4, 7, 8,11,12)$
$ 14 $ $14$ $14$ $( 1, 2, 5,12, 9, 8,13, 4, 3,14, 7,10,11, 6)$
$ 14 $ $14$ $14$ $( 1, 2, 7, 8,13,14, 5, 6,11,12, 3, 4, 9,10)$
$ 14 $ $14$ $14$ $( 1, 2, 7,10,13, 4, 5,12,11, 6, 3,14, 9, 8)$
$ 7, 7 $ $2$ $7$ $( 1, 3, 5, 7, 9,11,13)( 2, 4, 6, 8,10,12,14)$
$ 7, 7 $ $4$ $7$ $( 1, 3, 5, 7, 9,11,13)( 2, 6,10,14, 4, 8,12)$
$ 7, 7 $ $4$ $7$ $( 1, 3, 5, 7, 9,11,13)( 2, 8,14, 6,12, 4,10)$
$ 7, 7 $ $4$ $7$ $( 1, 3, 5, 7, 9,11,13)( 2,10, 4,12, 6,14, 8)$
$ 7, 7 $ $4$ $7$ $( 1, 3, 5, 7, 9,11,13)( 2,12, 8, 4,14,10, 6)$
$ 7, 7 $ $2$ $7$ $( 1, 3, 5, 7, 9,11,13)( 2,14,12,10, 8, 6, 4)$
$ 7, 7 $ $2$ $7$ $( 1, 5, 9,13, 3, 7,11)( 2, 6,10,14, 4, 8,12)$
$ 7, 7 $ $4$ $7$ $( 1, 5, 9,13, 3, 7,11)( 2, 8,14, 6,12, 4,10)$
$ 7, 7 $ $4$ $7$ $( 1, 5, 9,13, 3, 7,11)( 2,10, 4,12, 6,14, 8)$
$ 7, 7 $ $2$ $7$ $( 1, 5, 9,13, 3, 7,11)( 2,12, 8, 4,14,10, 6)$
$ 7, 7 $ $2$ $7$ $( 1, 7,13, 5,11, 3, 9)( 2, 8,14, 6,12, 4,10)$
$ 7, 7 $ $2$ $7$ $( 1, 7,13, 5,11, 3, 9)( 2,10, 4,12, 6,14, 8)$

Group invariants

Order:  $196=2^{2} \cdot 7^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [196, 9]
Character table: Data not available.