{"id":7417,"date":"2025-11-21T06:49:26","date_gmt":"2025-11-21T06:49:26","guid":{"rendered":"https:\/\/kibu.ac.ke\/sgs\/?p=7417"},"modified":"2025-11-21T06:50:50","modified_gmt":"2025-11-21T06:50:50","slug":"character-table-of-the-subgroup-27-g_22-of-the-automorphism-group-%e3%80%96fi%e3%80%97_22-by-fischer-clifford-matrices","status":"publish","type":"post","link":"https:\/\/kibu.ac.ke\/sgs\/character-table-of-the-subgroup-27-g_22-of-the-automorphism-group-%e3%80%96fi%e3%80%97_22-by-fischer-clifford-matrices\/","title":{"rendered":"Character Table of The Subgroup 2^7: G_2(2) of The Automorphism Group \u3016Fi\u3017_22 by Fischer Clifford Matrices"},"content":{"rendered":"\t\t
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Student\u2019s Name:
\nKhadioli Rose Khayere<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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Supervisors:
\n1.\tDr. Lucy Walingo Chikamai
\n2.\tProf. Abraham Love Prins
\n3.\tProf. Shem Aywa\n<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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Master of Science in Pure Mathematics<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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ABSTRACT<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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The subgroup\u00a0 :\u00a0of the Automorphism group\u00a0 \u00a0is a split extension group where the two component groups include the abelian group \u00a0with order 2 and dimension 7 and the Chevalley group\u00a0 \u00a0 over the finite field with 2 elements. From the ATLAS of Finite Groups, the order of the subgroup\u00a0 \u00a0\u00a0was calculated as 1,548,288. The character table for the group \u00a0was determined in the same ATLAS but the character table for \u00a0was not computed. The general objective of this research was to construct the Character table of the subgroup \u00a0of the Automorphism Group \u00a0using Fischer Clifford Matrices. The method employed was Fischer Clifford Matrices technique where the properties of Fischer Clifford Matrices were used to find the entries of the Fischer Clifford Matrices M\u00a0for each class representative \u00a0\u00a0G = . The character table of\u00a0 =:\u00a0was constructed from the Fischer Clifford Matrices of\u00a0 : \u00a0and the ordinary characters of the inertia factor groups . Therefore, the conjugacy classes of the subgroup : \u00a0were obtained and the Fischer Clifford Matrices were computed. Eventually, the ordinary Character table of \u00a0(2) associated with these matrices that contains information about the irreducible representations of the group, their dimensions and their characters was constructed. It was realized that the subgroup :(2) has 60 Conjugacy Classes, 16 sets of Fischer Clifford Matrices of dimensions varying between 2 and 8 and a character table which is a square matrix of order 60. The character table for the subgroup\u00a0 \u00a0= : would be important in coding theory\/error correcting codes (communication channel), crystallography and cryptography. It was recommended that the analysis of error-correcting codes based on the structure of : \u00a0be developed, possibility of using \u00a0(2) in new cryptographic and cryptollographic protocols be investigated and the methods used here be extended to the study of other maximal subgroups of Aut().<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Student\u2019s Name: Khadioli Rose Khayere Supervisors: 1. Dr. Lucy Walingo Chikamai 2. Prof. Abraham Love Prins 3. Prof. Shem Aywa Master of Science in Pure Mathematics ABSTRACT The subgroup\u00a0 :\u00a0of the Automorphism group\u00a0 \u00a0is a split extension group where the two component groups include the abelian group \u00a0with order 2 and dimension 7 and the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"class_list":["post-7417","post","type-post","status-publish","format-standard","hentry","category-theses"],"yoast_head":"\nCharacter Table of The Subgroup 2^7: G_2(2) of The Automorphism Group \u3016Fi\u3017_22 by Fischer Clifford Matrices - School of Graduate Studies<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/kibu.ac.ke\/sgs\/character-table-of-the-subgroup-27-g_22-of-the-automorphism-group-\u3016fi\u3017_22-by-fischer-clifford-matrices\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Character Table of The Subgroup 2^7: G_2(2) of The Automorphism Group \u3016Fi\u3017_22 by Fischer Clifford Matrices - School of Graduate Studies\" \/>\n<meta property=\"og:description\" content=\"Student\u2019s Name: Khadioli Rose Khayere Supervisors: 1. 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