Properties

Label 28T34
Degree $28$
Order $196$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{14}\times D_7$

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Group action invariants

Degree $n$:  $28$
Transitive number $t$:  $34$
Group:  $C_{14}\times D_7$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $14$
Generators:  (1,26,22,18,13,10,6,2,25,21,17,14,9,5)(3,8,12,16,20,23,28,4,7,11,15,19,24,27), (1,11,25,8,22,4,17,27,13,23,9,19,6,16)(2,12,26,7,21,3,18,28,14,24,10,20,5,15)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$7$:  $C_7$
$14$:  $D_{7}$, $C_{14}$ x 3
$28$:  $D_{14}$, 28T2
$98$:  $C_7 \wr C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$ x 3

Degree 4: $C_2^2$

Degree 7: None

Degree 14: $C_7 \wr C_2$

Low degree siblings

28T34 x 2

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 70 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $196=2^{2} \cdot 7^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [196, 10]
Character table: not available.