Galois group: 2T1

• Label: 2T1
• Degree: $2$
• Order: $2$
• Cyclic: yes
• Abelian: yes
• Solvable: yes
• Primitive: yes
• pp-group: yes
• Group: $C_2$

Group action invariants

Degree $n$:		$2$
Transitive number $t$:		$1$
Group:		$C_2$
CHM label:		$S2$
Parity:		$-1$
Primitive:		yes
$\card{\Aut(F/K)}$:		$2$
Generators:		(1,2)

Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

Low degree siblings

There are no siblings with degree $\leq 47$

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

Conjugacy classes

Label	Cycle Type	Size	Order	Index	Representative
1A	$1^{2}$	$1$	$1$	$0$	$()$
2A	$2$	$1$	$2$	$1$	$(1,2)$

Malle's constant $a(G)$:     $1$

Group invariants

Order:		$2$ (is prime)
Cyclic:		yes
Abelian:		yes
Solvable:		yes
Nilpotency class:		$1$
Label:		2.1
Character table:

		1A	2A
	Size	1	1
	2 P	1A	1A
	Type
2.1.1a	R	$1$	$1$
2.1.1b	R	$1$	$-1$

Indecomposable integral representations

Complete list of indecomposable integral representations:

Name	Dim	$(1,2) \mapsto$
Triv	$1$	$\left(\begin{array}{r}1\end{array}\right)$
Sign	$1$	$\left(\begin{array}{r}-1\end{array}\right)$
$L$	$2$	$\left(\begin{array}{rr}0 & 1\\1 & 0\end{array}\right)$

The decomposition of an arbitrary integral representation as a direct sum of indecomposables is unique.