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Question: How to generate symmetric and rotational matrices of Dihedral group D8

Question:How to generate symmetric and rotational matrices of Dihedral group D8

sadiqa ilyas 20 Maple
group-theory
October 28 2019
1

Hi I want to generate dihedral group of order 8.I have given the commands
with (GroupTheory):

GroupTheory(DihedralGroup);

DihedralGroup(8, s);
                              D[8]
Elements(DihedralGroup(8, s));
{(), (12345678), (14725836), (16385274), (18765432), 

  (1357)(2468), (1753)(2864), (13)(48)(57), (15)(24)(68), 

  (17)(26)(35), (28)(37)(46), (12)(38)(47)(56), (14)(23)(58)(67), 

  (15)(26)(37)(48), (16)(25)(34)(78), (18)(27)(36)(45)}
but I need symmetric and rotation matrices like 

R0=[1,0;0 1],R1=[0,-1;1,0], R2=[-1,0;0,1], R3=[0 1;-1,0],S0=[1 0;0 -1], S1=[0 1 ;1 0], S2=[-1,0;0,1]; S3=[0,-1;-1,0]
 Can any one help me how to generate these matrices
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