= Solution
The table describes the <symmetry group> of a regular <hexagon>. Choose $R$ as a counterclockwise rotation through $\pi/3$ and $m_1$ as reflection in one symmetry axis. With $s=m_1$, the relations are
$$
R^6=I,\qquad s^2=I,\qquad sRs=R^{-1}.
$$
The rotation entries already are $I,R,\ldots,R^5$, and the table gives $Rm_j=m_{j+1}$ with indices modulo six. Therefore
$$
\boxed{m_j=R^{j-1}s\quad(j=1,\ldots,6),\qquad G=\{R^k,R^ks:0\leq k<6\}.}
$$
The source writes $D_6$ with the subscript counting polygon vertices; this <dihedral group> has order 12.
Back to article page
