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

DOI:
https://doi.org/10.1090/S0025-5718-1974-0369493-5

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.

- 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)**18**(1968), 521โ562. MR**225877**, DOI https://doi.org/10.1112/plms/s3-18.3.521 - Bernd Fischer,
*Finite groups generated by $3$-transpositions. I*, Invent. Math.**13**(1971), 232โ246. MR**294487**, DOI https://doi.org/10.1007/BF01404633 - David C. Hunt,
*Character tables of certain finite simple groups*, Bull. Austral. Math. Soc.**5**(1971), 1โ42. MR**302753**, DOI https://doi.org/10.1017/S0004972700046852 - G. E. Wall,
*On the conjugacy classes in the unitary, symplectic and orthogonal groups*, J. Austral. Math. Soc.**3**(1963), 1โ62. MR**0150210**

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Article copyright:
© Copyright 1974
American Mathematical Society