Unitriangular matrix group:UT(4,2)

Definition
This group is defined in the following equivalent ways:


 * It is the unitriangular matrix group of degree four over the field of two elements.
 * It is a $$2$$-Sylow subgroup of the general linear group $$GL(4,2)$$, which turns out to be isomorphic to alternating group:A8.
 * It is the $$2$$-Sylow subgroup of the holomorph of the elementary abelian group of order eight, which is the general affine group.
 * It is the $$2$$-Sylow subgroup of the holomorph of the direct product of Z4 and Z2.