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

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  1. Unger, W.R.: Computing the character table of a finite group. (2006)
  2. Vavilov, N.A.; Mysovskikh, V.I.; Teterin, Yu.G.: Computational group theory in St. Petersburg (1997)
  3. Hiss, Gerhard; Lübeck, Frank; Malle, Gunter: The Brauer trees of the exceptional Chevalley groups of type $E\sb 6$ (1995)
  4. Hiss, Gerhard: The $3$-modular characters of the Rudvalis sporadic simple group and its covering group (1994)
  5. Hiss, Gerhard; Lux, Klaus; Parker, Richard: The 5-modular characters of the McLaughlin group and its covering group (1991)
  6. Conder, Marston: Hurwitz groups: A brief survey (1990)
  7. Michler, Gerhard O.: Some problems in computational representation theory (1990)
  8. Pahlings, H.: Computing with characters of finite groups (1990)
  9. Schneider, Gerhard J.A.: Dixon’s character table algorithm revisited (1990)
  10. Pahlings, H.: Some sporadic groups as Galois groups. II (1989)
  11. Abduh, A.; List, R.J.: The characters of the centralizer of an involution in $C\sb 1$ (1988)
  12. Blau, Harvey I.: On linear groups with a cyclic or T.I. Sylow subgroup (1988)
  13. Hiss, Gerhard; Lux, Klaus: The Brauer characters of the Hall-Janko group (1988)
  14. Kostrikin, A.I.; Chubarov, I.A.: Representations of finite groups (1988)
  15. Pahlings, H.: Some sporadic groups as Galois groups (1988)
  16. Willems, Wolfgang: Blocks of defect zero in finite simple groups of Lie type (1988)
  17. Atkinson, M.D.; Hassan, R.A.: On the computation of group characters (1986)
  18. Hoyden-Siedersleben, Gudrun; Matzat, B.Heinrich: Realization of sporadic simple groups as Galois groups over cyclotomic fields. (1986)
  19. Michler, Gerhard O.: A finite simple group of Lie type has p-blocks with different defects, $p\ne 2$ (1986)
  20. Hiss, Gerhard: Groups whose Brauer-characters are liftable (1985)

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