## CAS

swMATH ID: | 7634 |

Software Authors: | Neubüser, J.; Pahlings, H.; Plesken, W. |

Description: | CAS; Design and use of a system for the handling of characters of finite groups. CAS is a system for handling characters of finite groups, including irrationalities, and partially defined characters. The commands allow: Generation of complete character tables: from generic formulae, eg. PSL(2,q); from matrix of class-multiplication coefficients; from other character tables, e.g. direct products, quotients. Generation of characters: as a Galois conjugate; using an outer automorphism; powering, tensoring, inducing, extending; extracting irreducible components (using several techniques). Tests: orthogonality relations; Schur-Frobenius indicator; block orthogonality relations; checking power maps. Other information: central characters; structure constants of the centre of the group algebra; kernel of a character; p-blocks; power maps; decomposition matrix; Molien series; detecting subgroups. The paper discusses the design of CAS, the available commands (with comments on their application), and presents several realistic examples of character table construction, the determination of irrationalities of the Baby Monster, and the decomposition matrix of PS p (4,3) at the prime p=3. The examples clearly indicate how useful CAS would be for use in a course on character theory, and for researchers in group theory. The CAS system makes a major contribution, by incorporating the experience of many people, who have worked on character tables, into a powerful, portable, available software tool. The associated library of character tables greatly enhances the usefulness of the system |

Homepage: | http://www.math.rwth-aachen.de/~Joachim.Neubueser/schrift.html |

Keywords: | CAS; characters of finite groups; character tables; block orthogonality relations; group algebra; p-blocks; decomposition matrix; Molien series; Baby Monster; software |

Related Software: | GAP; ATLAS Group Representations; Magma; Cayley; Maple; MeatAxe; CHEVIE; IBM Scratchpad |

Referenced in: | 22 Publications |

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### Referenced by 27 Authors

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### Referenced in 11 Serials

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