The priests carried out the religious ritual carefully.

[W]e behold two men with lion-look, with alert attitude, side foremost, right foot advanced; flourishing and thrusting, stoccado and passado, in tierce and quart; intent to skewer one another.

So finite groups often appear as subgroups of permutation groups or linear groups. The “geometry” of a group (as permutation group or linear group, or as a group of Lie type etc.) should be used in order to describe basic invariants.

What is the selective advantage of height?