$Q^6_{1}\quad U=((2 3)(4 5) , (1 4)(3 6) , (1 5)(2 6) , (1 5)(2 6) , (1 4)(3 6) , (2 3)(4 5))\quad D=\iota\quad \hbox{order 6} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{2}\quad U=((2 3 5 6) , (1 4) , (1 4) , (2 3 5 6) , (1 4) , (1 4))\quad D=\iota\quad \hbox{order 8} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{3}\quad U=((2 3 5 6) , (1 4)(3 6) , (1 4)(2 5) , (2 6 5 3) , (1 4)(3 6) , (1 4)(2 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{4}\quad U=((2 4 5 3) , (1 3 6 4) , (1 5 6 2) , (1 2 6 5) , (1 4 6 3) , (2 3 5 4))\quad D=\iota\quad \hbox{order 6} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{5}\quad U=((3 4 6) , (3 4 6) , (1 5 2) , (1 5 2) , (3 4 6) , (1 5 2))\quad D=\iota\quad \hbox{order 6} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{6}\quad U=((3 4 6) , (3 4 6) , (1 5) , (1 5) , (3 4 6) , (1 5))\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{7}\quad U=((3 4 6) , (3 6 4) , (1 5) , (1 5) , (3 4 6) , (1 5))\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{8}\quad U=((2 3)(5 6) , (1 4)(3 5) , (1 4)(2 6) , (2 5)(3 6) , (1 4)(2 6) , (1 4)(3 5))\quad D=\iota\quad \hbox{order 8} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{9}\quad U=((2 3)(4 5) , (1 4)(3 5) , (1 5)(2 4) , (1 3)(2 5) , (1 2)(3 4) , \iota)\quad D=\iota\quad \hbox{order 10} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{10}\quad U=((2 4 5 3) , (1 5 4 3) , (1 4 2 5) , (1 3 5 2) , (1 2 3 4) , \iota)\quad D=\iota\quad \hbox{order 4} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{11}\quad U=((2 4)(3 6) , (1 5) , (1 5)(2 4) , (1 5) , (2 4)(3 6) , (1 5)(2 4))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{12}\quad U=((3 4 5 6) , \iota , \iota , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 8} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{13}\quad U=((3 4 5 6) , (3 4 5 6) , \iota , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 8} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{14}\quad U=((3 4 5 6) , (3 5)(4 6) , \iota , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 8} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{15}\quad U=((3 4 5 6) , (3 6 5 4) , \iota , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 8} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{16}\quad U=((4 5 6) , (1 3) , (4 5 6) , (1 3) , (1 3) , (1 3))\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{17}\quad U=((4 5 6) , (1 3)(4 5 6) , (4 5 6) , (1 3) , (1 3) , (1 3))\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{18}\quad U=((4 5 6) , (1 3)(4 6 5) , (4 5 6) , (1 3) , (1 3) , (1 3))\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{19}\quad U=(\iota , (1 3 4 5 6) , \iota , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 10} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{20}\quad U=((2 3 4)(5 6) , (1 4 3)(5 6) , (1 2 4)(5 6) , (1 3 2)(5 6) , \iota , \iota)\quad D=\iota\quad \hbox{order 12} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{21}\quad U=(\iota , (3 4 6) , (2 5) , (2 5) , (3 4 6) , (2 5))\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{22}\quad U=(\iota , (3 4 6) , (2 5)(4 6) , (2 5)(3 6) , (3 6 4) , (2 5)(3 4))\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{23}\quad U=((3 4 5) , \iota , (2 6) , (2 6) , (2 6) , \iota)\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{24}\quad U=((4 5) , (1 3) , (4 5) , (2 6) , (2 6) , (1 3))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{25}\quad U=((4 5) , (1 3)(4 5) , (4 5) , (2 6) , (2 6) , (1 3)(4 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{26}\quad U=((4 5 6) , (1 3) , (4 5 6) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{27}\quad U=((4 5 6) , (1 3)(4 5 6) , (4 5 6) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{28}\quad U=((4 5 6) , (1 3)(4 6 5) , (4 5 6) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{29}\quad U=((5 6) , (1 3 4)(5 6) , (5 6) , (5 6) , \iota , \iota)\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{30}\quad U=((2 3)(4 5 6) , \iota , \iota , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{31}\quad U=((2 3)(5 6) , (1 3)(4 5) , (1 2)(4 6) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 12} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{32}\quad U=((2 3)(5 6) , (1 3)(4 5) , (1 2)(4 6) , (2 5)(3 6) , (1 6)(2 4) , (1 5)(3 4))\quad D=\iota\quad \hbox{order 6} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{33}\quad U=((2 3)(4 5 6) , (1 3)(4 5 6) , (1 2)(4 5 6) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 6} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{34}\quad U=((2 3 4) , (1 4 3) , (1 2 4) , (1 3 2) , \iota , \iota)\quad D=\iota\quad \hbox{order 6} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{35}\quad U=((2 3)(4 5) , (1 3)(4 5) , (1 2)(4 5) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{36}\quad U=((2 3)(4 5) , (1 3)(4 5) , (1 2)(4 5) , \iota , \iota , (4 5))\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{37}\quad U=((2 4)(3 6) , (1 5) , (1 5) , (1 5) , (2 4)(3 6) , (1 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{38}\quad U=((2 4)(3 6) , (1 5)(3 6) , (1 5)(2 4) , (1 5)(3 6) , (2 4)(3 6) , (1 5)(2 4))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{39}\quad U=((3 4)(5 6) , (3 5)(4 6) , \iota , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{40}\quad U=((2 3)(4 5) , \iota , \iota , (1 6) , (1 6) , (2 3)(4 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{41}\quad U=((2 3)(4 5) , \iota , \iota , (1 6)(2 3) , (1 6)(2 3) , (2 3)(4 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{42}\quad U=((2 4) , (1 5) , (2 4) , (1 5) , (2 4) , \iota)\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{43}\quad U=((2 4) , (1 5) , (2 4) , (1 5) , (2 4) , (2 4))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{44}\quad U=((2 4) , (1 5) , (2 4) , (1 5) , (2 4) , (1 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{45}\quad U=((2 4) , (1 5) , (2 4) , (1 5) , (2 4) , (1 5)(2 4))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{46}\quad U=((4 5 6) , \iota , \iota , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 6} \quad c_1 = 9, c_2 = 3$\hfil\break $Q^6_{47}\quad U=((4 5 6) , \iota , (4 5 6) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 6} \quad c_1 = 9, c_2 = 3$\hfil\break $Q^6_{48}\quad U=((4 5 6) , \iota , (4 6 5) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 6} \quad c_1 = 9, c_2 = 3$\hfil\break $Q^6_{49}\quad U=((4 5 6) , (4 5 6) , (4 5 6) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 6} \quad c_1 = 9, c_2 = 3$\hfil\break $Q^6_{50}\quad U=((4 5 6) , (4 5 6) , (4 6 5) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 6} \quad c_1 = 9, c_2 = 3$\hfil\break $Q^6_{51}\quad U=((4 5) , (1 3) , (4 5) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{52}\quad U=((4 5) , (1 3) , (4 5) , \iota , \iota , (4 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{53}\quad U=((4 5) , (1 3) , (4 5) , \iota , \iota , (1 3))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{54}\quad U=((4 5) , (1 3) , (4 5) , \iota , \iota , (1 3)(4 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{55}\quad U=((4 5) , (1 3)(4 5) , (4 5) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{56}\quad U=((4 5) , (1 3)(4 5) , (4 5) , \iota , \iota , (4 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{57}\quad U=((4 5) , (1 3)(4 5) , (4 5) , \iota , \iota , (1 3)(4 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{58}\quad U=((4 5) , (1 3)(4 5) , (4 5) , (1 3) , (1 3) , \iota)\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{59}\quad U=((4 5) , (1 3)(4 5) , (4 5) , (1 3) , (1 3) , (1 3)(4 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{60}\quad U=((2 3)(4 5) , \iota , \iota , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{61}\quad U=((2 3)(4 5) , \iota , \iota , \iota , \iota , (4 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{62}\quad U=((2 3)(4 5) , \iota , \iota , \iota , \iota , (2 3)(4 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{63}\quad U=((2 3) , (1 3) , (1 2) , \iota , (4 6) , \iota)\quad D=\iota\quad \hbox{order 12} \quad c_1 = 7, c_2 = 5$\hfil\break $Q^6_{64}\quad U=((2 3) , (1 3) , (1 2) , (5 6) , (4 6) , (4 5))\quad D=\iota\quad \hbox{order 6} \quad c_1 = 6, c_2 = 6$\hfil\break $Q^6_{65}\quad U=((5 6) , \iota , (2 4) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{66}\quad U=((2 3) , (1 4) , (1 4) , (2 3) , \iota , \iota)\quad D=\iota\quad \hbox{order 4} \quad c_1 = 8, c_2 = 4$\hfil\break $Q^6_{67}\quad U=((2 3) , (1 3) , (1 2) , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 6} \quad c_1 = 9, c_2 = 3$\hfil\break $Q^6_{68}\quad U=((4 5) , \iota , \iota , \iota , \iota , \iota)\quad D=\iota\quad \hbox{order 4} \quad c_1 = 10, c_2 = 2$\hfil\break $Q^6_{69}\quad U=((4 5) , \iota , \iota , \iota , \iota , (4 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 10, c_2 = 2$\hfil\break $Q^6_{70}\quad U=((4 5) , \iota , (4 5) , \iota , \iota , (4 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 10, c_2 = 2$\hfil\break $Q^6_{71}\quad U=((4 5) , (4 5) , (4 5) , \iota , \iota , (4 5))\quad D=\iota\quad \hbox{order 4} \quad c_1 = 10, c_2 = 2$\hfil\break $Q^6_{72}\quad U=\iota\quad D=\iota\quad \hbox{order 2} \quad S, c_1 = 12, c_2 = 0$\hfil\break