Question

Write out the operation table for the symmetry groups of the following figures:

a)

Short answer

$o$	$r_0$	$r_1$	v	h
$r_0$	$r_0$	$r_1$	v	h
$r_1$	$r_1$	$r_0$	h	v
v	v	h	$r_0$	$r_1$
h	h	v	$r_1$	$r_0$

Step-by-step solution

Determine operation table

Consider that,$r_0$ is the identity of symmetries of the oblong,$r_1$ is thedata-custom-editor="chemistry" ${180}^{°}$ rotation, v is the vertical reflection and h is the horizontal reflection.

Result

Then the operation table is,

o	$r_0$	$r_1$	v	h
$r_0$	$r_0$	$r_1$	v	h
$r_1$	$r_1$	$r_0$	h	v
v	v	h	$r_0$	$r_1$
h	h	v	role="math" localid="1653378717339" $r_1$	$r_0$