Galois group: 26T13

• Label: 26T13
• Degree: $26$
• Order: $676$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $D_{13}^2$

Group invariants

Abstract group:		$D_{13}^2$
Order:		$676=2^{2} \cdot 13^{2}$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$26$
Transitive number $t$:		$13$
Parity:		$-1$
Primitive:		no
$\card{\Aut(F/K)}$:		$1$
Generators:		$(1,17,9,21,4,25,12,16,7,20,2,24,10,15,5,19,13,23,8,14,3,18,11,22,6,26)$, $(1,24,3,23,5,22,7,21,9,20,11,19,13,18,2,17,4,16,6,15,8,14,10,26,12,25)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 3
$4$:	$C_2^2$
$26$:	$D_{13}$ x 2
$52$:	$D_{26}$ x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 13: None

Low degree siblings

26T13 x 5

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

64 x 64 character table

Regular extensions

Data not computed