Maotianshan Shales fossil record. Phylum Porifera (sponges; 15 species) and Priapulida (16 species) are also well represented. Other phyla represented are Brachiopoda, Chaetognatha, Cnidaria, Ctenophora, Echinodermata, Hyolitha, Nematomorpha, Phoronida, and Chordata. Possible molluscs include "Wiwaxia" and "Nectocaris". About one in eight animals are problematic forms of uncertain affinity, some of which may have been evolutionary experiments that survived for only a brief period as benthic environments rapidly changed in the Cambrian. Chengjiang is the richest source of the lobopodia, a group including many early panarthropods, with six genera represented: "Luolishania", "Paucipodia", "Cardiodictyon"," Hallucigenia" (also known from the Burgess Shale), "Microdictyon", and "Onychodictyon".
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,