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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The character table of an eight-dimensional orthogonal group


Author: David C. Hunt
Journal: Math. Comp. 28 (1974), 659-660
MSC: Primary 20C15; Secondary 20D05
MathSciNet review: 0369493
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Abstract: This paper describes the calculation of the character table of the 8-dimensional orthogonal group of maximal index over the field with 3 elements. The group is of interest as it is a subgroup of relatively small index in the sporadic simple group $ M(23)$ defined by B. Fischer [2]. The group also has an outer automorphism group of order 24, isomorphic to the symmetric group on 4 symbols.


References [Enhancements On Off] (What's this?)

  • [1] R. H. Dye, "The simple group $ FH(8,2)$ of order $ {2^{12}} \cdot {3^5} \cdot {5^2} \cdot 7$ and the associated geometry of triality," Proc. London Math. Soc. (3), v. 18, 1968, pp. 521-562. MR 37 #1468. MR 0225877 (37:1468)
  • [2] B. Fischer, "Finite groups generated by 3-transpositions. I," Invent. Math., v. 13, 1971, pp. 232-246. MR 45 #3557. MR 0294487 (45:3557)
  • [3] D. C. Hunt, "Character tables of certain finite simple groups," Bull. Austral. Math. Soc., v. 5, 1971, pp. 1-42. MR 46 #1896. MR 0302753 (46:1896)
  • [4] G. E. Wall, "On the conjugacy classes in the unitary, symplectic and orthogonal groups," J. Austral. Math. Soc., v. 3, 1963, pp. 1-62. MR 27 #212. MR 0150210 (27:212)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1974-0369493-5
PII: S 0025-5718(1974)0369493-5
Article copyright: © Copyright 1974 American Mathematical Society