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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.

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  • [1] R. H. Dye, The simple group 𝐹𝐻(8,2) of order 2¹²⋅3⁵⋅5²⋅7 and the associated geometry of triality, Proc. London Math. Soc. (3) 18 (1968), 521–562. MR 0225877
  • [2] Bernd Fischer, Finite groups generated by 3-transpositions. I, Invent. Math. 13 (1971), 232–246. MR 0294487
  • [3] David C. Hunt, Character tables of certain finite simple groups, Bull. Austral. Math. Soc. 5 (1971), 1–42. MR 0302753
  • [4] G. E. Wall, On the conjugacy classes in the unitary, symplectic and orthogonal groups, J. Austral. Math. Soc. 3 (1963), 1–62. MR 0150210

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Article copyright: © Copyright 1974 American Mathematical Society