Properties

Label 7T6-7_2.2.1.1.1_5.1.1
Group 7T6
Orders [7, 2, 5]
Genus 0
Size 2
Galois orbits 1

Learn more

Passport invariants

Degree:$7$
Monodromy group:$A_7$
Genus:$0$
Geometry type:hyperbolic
Primitive:yes

Conjugacy class data

The order and cycle type of an element in each of the conjugacy classes $C_0, C_1, C_{\infty}$ of the passport containing this orbit.

OrderPartition
$7$ $7$
$2$ $2, 2, 1, 1, 1$
$5$ $5, 1, 1$

Galois orbits

Passport size:  $2$
Number of Galois orbits:  $1$
LabelOrbit sizeBase fieldRepresentative triple
a $2$ \(\Q(\sqrt{21}) \) ; Generator \(\nu\), with minimal polynomial \( T^{2} - T - 5 \). $(1,2,7,6,5,4,3),(1,2)(3,4),(1,4,5,6,7)$