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The Fischer-Clifford matrices of the group \(2^6:\text{SP}_6(2)\). (English) Zbl 0944.20010

The authors use the techniques of Clifford theory to build the character table of the split extension of the simple group \(\text{Sp}(6,2)\) acting on its natural module. This group is of interest since it is a maximal subgroup of the smallest sporadic Fischer group \(\text{Fi}_{22}\).
The character table in question has been independently calculated by Oliver Bonten of RWTH Aachen (Thesis, 1987), and Bonten’s table has been available in the CAS library, and now in GAP, since 1987.

MSC:

20C33 Representations of finite groups of Lie type
20C15 Ordinary representations and characters
20D08 Simple groups: sporadic groups
20E22 Extensions, wreath products, and other compositions of groups

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References:

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[6] DOI: 10.1007/BF01206468 · Zbl 0628.20015 · doi:10.1007/BF01206468
[7] DOI: 10.1007/BF01196499 · Zbl 0628.20016 · doi:10.1007/BF01196499
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[9] DOI: 10.1112/jlms/s2-23.1.61 · Zbl 0443.20016 · doi:10.1112/jlms/s2-23.1.61
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[15] DOI: 10.1017/S0305004100061491 · Zbl 0551.20010 · doi:10.1017/S0305004100061491
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