or, equivalently, defined by the multiplication table
where denotes the subgroup generated by and denotes the subgroup. Of those subgroups, the following are its proper normal subgroup: , , , and . In addition the center and commutator subgroup of the octic group is . It can also be shown that the automorphism of the octic group () is isomorphic to itself().[PJ] An additional property is that the subgroup of the general linear group of dimension 2 over the real numbers generated by: [ 0 1 -1 0 ],[ 0 1 1 0 ] is isomorphic to the octic group.
- PJ Pedersen, John: Groups of small order. http://www.math.usf.edu/ eclark/algctlg/small_groups.htmlhttp://www.math.usf.edu/ eclark/algctlg/small_groups.html
|Date of creation||2013-03-22 14:47:59|
|Last modified on||2013-03-22 14:47:59|
|Last modified by||Daume (40)|