Grupa D3 symetrii trójkąta równobocznego ma następującą tablicę Cayleya: {| border="2" cellpadding="8" !style="background:#efefef"| !style="background:#efefef"| R0 !style="background:#efefef"| R1 !style="background:#efefef"| R2 !style="background:#efefef"| S0 !style="background:#efefef"| S1 !style="background:#efefef"| S2 |- !style="background:#efefef"| R0 |style="background:#efefff"| R0 |style="background:#efefff"| R1 |style="background:#efefff"| R2 |style="background:#efffef"| S0 |style="background:#efffef"| S1 |style="background:#efffef"| S2 |- !style="background:#efefef"| R1 |style="background:#efefff"| R1 |style="background:#efefff"| R2 |style="background:#efefff"| R0 |style="background:#efffef"| S1 |style="background:#efffef"| S2 |style="background:#efffef"| S0 |- !style="background:#efefef"| R2 |style="background:#efefff"| R2 |style="background:#efefff"| R0 |style="background:#efefff"| R1 |style="background:#efffef"| S2 |style="background:#efffef"| S0 |style="background:#efffef"| S1 |- !style="background:#efefef"| S0 |style="background:#efffef"| S0 |style="background:#efffef"| S2 |style="background:#efffef"| S1 |style="background:#efefff"| R0 |style="background:#efefff"| R2 |style="background:#efefff"| R1 |- !style="background:#efefef"| S1 |style="background:#efffef"| S1 |style="background:#efffef"|