Properties

Label 2T1
Order \(2\)
n \(2\)
Cyclic Yes
Abelian Yes
Solvable Yes
Primitive Yes
$p$-group Yes
Group: $C_2$

Related objects

Group action invariants

Degree $n$ :  $2$
Transitive number $t$ :  $1$
Group :  $C_2$
CHM label :  $S2$
Parity:  $-1$
Primitive:  Yes
Generators:   (1,2)
$|\Aut(F/K)|$:  $2$
Low degree resolvents:  None

Subfields

Prime degree - none

Low degree siblings

There is no other low degree representation.
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

Cycle TypeSizeOrderRepresentative
$ 1, 1 $ $1$ $1$ $()$
$ 2 $ $1$ $2$ $(1,2)$

Group invariants

Order:  $2$ (is prime)
Cyclic:  Yes
Abelian:  Yes
Solvable:  Yes
GAP id:  [2, 1]
Character table:  
     2  1  1

       1a 2a
    2P 1a 1a

X.1     1 -1
X.2     1  1

Indecomposable integral representations

Complete list of indecomposable integral representations:

Name Dim $(1,2) \mapsto $
Triv $1$ $\left(\begin{array}{*{1}{r}}1\end{array}\right)$
Sign $1$ $\left(\begin{array}{*{1}{r}}-1\end{array}\right)$
$L$ $2$ $\left(\begin{array}{*{2}{r}}0 & 1\\1 & 0\end{array}\right)$
The decomposition of an arbitrary integral representation as a direct sum of indecomposables is unique.