Galois group: 28T34

• Label: 28T34
• Degree: $28$
• Order: $196$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $C_7\times D_{14}$

Group invariants

Abstract group:		$C_7\times D_{14}$
Order:		$196=2^{2} \cdot 7^{2}$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$28$
Transitive number $t$:		$34$
Parity:		$1$
Primitive:		no
$\card{\Aut(F/K)}$:		$14$
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

$\card{(G/N)}$	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

Conjugacy classes not computed

Character table

70 x 70 character table

Regular extensions

Data not computed