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Construction of the fourfold cover of the Mathieu group \(M_{22}\). (English) Zbl 0805.20014

Summary: We give an explicit construction for the two faithful, irreducible, 16- dimensional representations of \(4 \cdot M_{22}\) over the field \(\text{GF}(49)\). Then we extend them to the 32-dimensional representation of \(4 \cdot M_{22} : 2\) over \(\text{GF}(7)\). Explicit matrices are given.

MSC:

20C34 Representations of sporadic groups
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References:

[1] Burgoyne N., Nagoya Math. J. 27 pp 733– (1966)
[2] Conway J. H., Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups (1985) · Zbl 0568.20001
[3] DOI: 10.1017/S0305004100052075 · Zbl 0321.05018 · doi:10.1017/S0305004100052075
[4] DOI: 10.1016/0021-8693(82)90003-5 · Zbl 0479.20005 · doi:10.1016/0021-8693(82)90003-5
[5] Parker, R. A. ”The computer calculation of modular characters (The ’Meat-axe’)”. Symposium on Computational Group Theory. Edited by: Atkinson, M. D. pp.267–274. Orlando, FL: Academic Press. [Parker 1984]
[6] Parker R. A., An Atlas of Modular Character Tables
[7] DOI: 10.1016/S0747-7171(08)80075-2 · Zbl 0742.20018 · doi:10.1016/S0747-7171(08)80075-2
[8] DOI: 10.1016/0021-8693(92)90244-G · Zbl 0783.20010 · doi:10.1016/0021-8693(92)90244-G
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