none
Resolvents shown for degrees $\leq 47$
Prime degree - none
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Cycle Type | Size | Order | Representative |
$ 1, 1, 1, 1, 1 $ |
$1$ |
$1$ |
$()$ |
$ 5 $ |
$1$ |
$5$ |
$(1,2,3,4,5)$ |
$ 5 $ |
$1$ |
$5$ |
$(1,3,5,2,4)$ |
$ 5 $ |
$1$ |
$5$ |
$(1,4,2,5,3)$ |
$ 5 $ |
$1$ |
$5$ |
$(1,5,4,3,2)$ |
Character table:
| |
5 1 1 1 1 1
1a 5a 5b 5c 5d
X.1 1 1 1 1 1
X.2 1 A B /B /A
X.3 1 B /A A /B
X.4 1 /B A /A B
X.5 1 /A /B B A
A = E(5)
B = E(5)^2
|
Complete
list of indecomposable integral representations:
Name | Dim |
$(1,2,3,4,5) \mapsto $ |
Triv | $1$ |
$\left(\begin{array}{r}1\end{array}\right)$ |
$J$ | $4$ |
$\left(\begin{array}{rrrr}0 & 1 & 0 & 0\\0 & 0 & 1 & 0\\0 & 0 & 0 & 1\\-1 & -1 & -1 & -1\end{array}\right)$ |
$R$ | $5$ |
$\left(\begin{array}{rrrrr}0 & 1 & 0 & 0 & 0\\0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 1\\1 & 0 & 0 & 0 & 0\end{array}\right)$ |
|
The decomposition of an arbitrary integral representation as a direct
sum of indecomposables is unique.