The Projective Character Tables of a Solvable Group 26:6×2
The Chevalley–Dickson simple group G24 of Lie type G2 over the Galois field GF4 and of order 251596800=212.33.52.7.13 has a class of maximal subgroups of the form 24+6:A5×3, where 24+6 is a special 2-group with center Z24+6=24. Since 24 is normal in 24+6:A5×3, the group 24+6:A5×3 can be constructed...
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Wiley
2019-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2019/8684742 |
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| author | Abraham Love Prins |
| author_facet | Abraham Love Prins |
| author_sort | Abraham Love Prins |
| collection | DOAJ |
| description | The Chevalley–Dickson simple group G24 of Lie type G2 over the Galois field GF4 and of order 251596800=212.33.52.7.13 has a class of maximal subgroups of the form 24+6:A5×3, where 24+6 is a special 2-group with center Z24+6=24. Since 24 is normal in 24+6:A5×3, the group 24+6:A5×3 can be constructed as a nonsplit extension group of the form G¯=24·26:A5×3. Two inertia factor groups, H1=26:A5×3 and H2=26:6×2, are obtained if G¯ acts on 24. In this paper, the author presents a method to compute all projective character tables of H2. These tables become very useful if one wants to construct the ordinary character table of G¯ by means of Fischer–Clifford theory. The method presented here is very effective to compute the irreducible projective character tables of a finite soluble group of manageable size. |
| format | Article |
| id | doaj-art-089d397964cc47cebcd5dfd1702d5ccd |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-089d397964cc47cebcd5dfd1702d5ccd2025-02-03T06:07:24ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252019-01-01201910.1155/2019/86847428684742The Projective Character Tables of a Solvable Group 26:6×2Abraham Love Prins0Department of Mathematics and Physics, Faculty of Applied Sciences, Cape Peninsula University of Technology, P.O. Box 1906, Bellville 7535, South AfricaThe Chevalley–Dickson simple group G24 of Lie type G2 over the Galois field GF4 and of order 251596800=212.33.52.7.13 has a class of maximal subgroups of the form 24+6:A5×3, where 24+6 is a special 2-group with center Z24+6=24. Since 24 is normal in 24+6:A5×3, the group 24+6:A5×3 can be constructed as a nonsplit extension group of the form G¯=24·26:A5×3. Two inertia factor groups, H1=26:A5×3 and H2=26:6×2, are obtained if G¯ acts on 24. In this paper, the author presents a method to compute all projective character tables of H2. These tables become very useful if one wants to construct the ordinary character table of G¯ by means of Fischer–Clifford theory. The method presented here is very effective to compute the irreducible projective character tables of a finite soluble group of manageable size.http://dx.doi.org/10.1155/2019/8684742 |
| spellingShingle | Abraham Love Prins The Projective Character Tables of a Solvable Group 26:6×2 International Journal of Mathematics and Mathematical Sciences |
| title | The Projective Character Tables of a Solvable Group 26:6×2 |
| title_full | The Projective Character Tables of a Solvable Group 26:6×2 |
| title_fullStr | The Projective Character Tables of a Solvable Group 26:6×2 |
| title_full_unstemmed | The Projective Character Tables of a Solvable Group 26:6×2 |
| title_short | The Projective Character Tables of a Solvable Group 26:6×2 |
| title_sort | projective character tables of a solvable group 26 6 2 |
| url | http://dx.doi.org/10.1155/2019/8684742 |
| work_keys_str_mv | AT abrahamloveprins theprojectivecharactertablesofasolvablegroup2662 AT abrahamloveprins projectivecharactertablesofasolvablegroup2662 |