Brauer trees of \(2.F_ 4(2)\). (English) Zbl 0808.20018
Let \(F\) be the finite Chevalley group \(F_ 4(2)\) of type \(F_ 4\) over the field of 2 elements, and let \(G = 2.F_ 4(2)\) be the double cover of \(F\) (the universal covering group of \(F\)). The order of \(G\) is \(2^{25} \cdot 3^ 6 \cdot 5^ 2 \cdot 7^ 2 \cdot 13 \cdot 17\). We determine here the Brauer trees of \(G\), and hence \(F\), and their planar embeddings for all odd primes dividing \(| G|\).
MSC:
| 20C33 | Representations of finite groups of Lie type |
| 20C20 | Modular representations and characters |
Keywords:
finite Chevalley group; double cover; universal covering group; Brauer trees; planar embeddingsReferences:
| [1] | Conway J.H., ”An ATLAS of finite groups,” (1985) |
| [2] | Feit W., ”The representation theory of finite groups,” (1982) · Zbl 0493.20007 |
| [3] | Hiss, G. 1989. Edited by: Lux, K. England |
| [4] | Neubëser J., ”Computational group theory” pp 195– (1984) |
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