Item $3$

Cyclopropane is a compound once used as an anesthetic. It belongs under the D$3$h point group whose character table is shown below.

$\backslash$table$[[D_{3h},$E$,2C_3(z),3C_2,{}_h(xy),2S_3,3a_v,\backslash$table$[[$linear functions,$],[$rotations$]],\backslash$table$[[$quadratic$],[$functions$]],\backslash$table$[[$cubic$],[$functions$]]],[A_1^{\text{'}},+1,+1,+1,+1,+1,+1,-,x^2+y^2,z^2,x(x^2-3y^2)$