Ambulacraria Ambulacraria Ambulacraria or Coelomopora is a Superphylum of invertebrate phyla which includes echinoderms and hemichordates; a member of this group is called an ambulacrarian. Phylogenetic analysis suggest the echinoderms and hemichordates separated around 533 million years ago. The Ambulacraria are part of the deuterostomes, a larger clade that also includes the Chordata, Vetulicolia and Saccorhytus. The two living clades with representative organisms are: The group Xenoturbellida (two species of worm-like animals) has previously been considered to be in this clade, but is now considered to be placed more basally among Metazoans. Fossil taxa that may lie on the stem lineage:
Klein four-group representation on four points: In this representation, V is a normal subgroup of the alternating group A (and also the symmetric group S) on four letters. In fact, it is the kernel of a surjective group homomorphism from S to S. Other representations within S are: They are not normal subgroups of S According to Galois theory, the existence of the Klein four-group (and in particular, the permutation representation of it) explains the existence of the formula for calculating the roots of quartic equations in terms of radicals, as established by Lodovico Ferrari: the map corresponds to the resolvent cubic,