{"id":6658,"date":"2025-10-21T06:30:01","date_gmt":"2025-10-21T06:30:01","guid":{"rendered":"https:\/\/sgs.kibu.ac.ke\/?p=6658"},"modified":"2025-11-21T04:49:20","modified_gmt":"2025-11-21T04:49:20","slug":"character-table-of-the-maximal-subgroup-27g_22-of-the-affine-subgroup-sp_82-by-fischer-clifford-matrices","status":"publish","type":"post","link":"https:\/\/kibu.ac.ke\/sgs\/character-table-of-the-maximal-subgroup-27g_22-of-the-affine-subgroup-sp_82-by-fischer-clifford-matrices\/","title":{"rendered":"CHARACTER TABLE OF THE MAXIMAL SUBGROUP 2^7:G_2(2) OF THE AFFINE SUBGROUP Sp_8(2) BY FISCHER-CLIFFORD MATRICES"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"6658\" class=\"elementor elementor-6658\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1725145a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1725145a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-427ae81f\" data-id=\"427ae81f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5579cb79 elementor-section-content-bottom elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5579cb79\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-1d6bed06\" data-id=\"1d6bed06\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-39b9f5db\" data-id=\"39b9f5db\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-368448c9 elementor-section-height-min-height elementor-section-items-stretch elementor-section-boxed elementor-section-height-default\" data-id=\"368448c9\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5b963c18\" data-id=\"5b963c18\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-23532d6a elementor-section-height-min-height elementor-section-content-middle elementor-section-boxed elementor-section-height-default\" data-id=\"23532d6a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-2a2d4c7a\" data-id=\"2a2d4c7a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4665249f elementor-widget elementor-widget-heading\" data-id=\"4665249f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Student\u2019s Name: <br>\nSIKOLIA MURUNGA JACINTA.<\/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<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-728b59a9\" data-id=\"728b59a9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5247af61 elementor-widget elementor-widget-heading\" data-id=\"5247af61\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Supervisors:<br>\n1. Dr . LUCY CHIKAMAI<br>\n2. VINCENT MARANI<br>\n3. A.L. PRINS\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<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-3d8f3fb9\" data-id=\"3d8f3fb9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6edbf50b elementor-widget elementor-widget-heading\" data-id=\"6edbf50b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7d503848 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7d503848\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-156067af\" data-id=\"156067af\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2245ef2a elementor-widget elementor-widget-spacer\" data-id=\"2245ef2a\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\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<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-3f865678\" data-id=\"3f865678\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-4d8c5c43 elementor-section-height-min-height elementor-section-boxed elementor-section-height-default\" data-id=\"4d8c5c43\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-5068b03d\" data-id=\"5068b03d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1cf15acc elementor-widget elementor-widget-heading\" data-id=\"1cf15acc\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">ABSTRACT<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-75c9e860 elementor-widget elementor-widget-text-editor\" data-id=\"75c9e860\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The group 2^7: G_2(2), is an extension of an elementary abelian group of order 2^7 by the exceptional group G_2(2). There are eleven maximal subgroup conjugacy classes in the simple symplectic group Sp_8(2). The split extension group of the 2^7: G_2(2) of order 1548288 is one of the maximal subgroups Sp_8(2). In this study, the theory of Fischer-Clifford matrices to construct the character table of the maximal subgroup 2^7: G_2(2) of the affine subgroup Sp_8(2) is used. The Fischer-Clifford matrices technique is based on Clifford theorem. To use this technique, the Fischer matrices, the conjugacy classes, the character tables of the inertia factor groups and the fusion maps of the inertia factor groups into G are needed. When the character of 2^7: G_2(2) has been obtained, finally we fuse it into Sp_8(2). Four inertia factor groups for 2^7: G_2(2) were identified H_1= G_2(2), H_2=3^ (1+2):8:2, H_3=L_2(7):2 and H_4=4^2: D_12. The Fischer matrices are all integer-valued matrices with sizes ranging from -48 to 63, whereas the character table of 2^7: G_2(2) is 53 \u00d753. The character table of finite group provides considerable amount of information about the group and hence is of great importance in group theory, dealing with the symmetry of objects or variables.<\/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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5be3ad4b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5be3ad4b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-27d57cf3\" data-id=\"27d57cf3\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\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<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Student\u2019s Name: SIKOLIA MURUNGA JACINTA. Supervisors: 1. Dr . LUCY CHIKAMAI 2. VINCENT MARANI 3. A.L. PRINS Master of Science in Pure Mathematics ABSTRACT The group 2^7: G_2(2), is an extension of an elementary abelian group of order 2^7 by the exceptional group G_2(2). There are eleven maximal subgroup conjugacy classes in the simple symplectic [&hellip;]<\/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-6658","post","type-post","status-publish","format-standard","hentry","category-theses"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>CHARACTER TABLE OF THE MAXIMAL SUBGROUP 2^7:G_2(2) OF THE AFFINE SUBGROUP Sp_8(2) 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-maximal-subgroup-27g_22-of-the-affine-subgroup-sp_82-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 MAXIMAL SUBGROUP 2^7:G_2(2) OF THE AFFINE SUBGROUP Sp_8(2) BY FISCHER-CLIFFORD MATRICES - School of Graduate Studies\" \/>\n<meta property=\"og:description\" content=\"Student\u2019s Name: SIKOLIA MURUNGA JACINTA. 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Supervisors: 1. Dr . LUCY CHIKAMAI 2. VINCENT MARANI 3. A.L. PRINS Master of Science in Pure Mathematics ABSTRACT The group 2^7: G_2(2), is an extension of an elementary abelian group of order 2^7 by the exceptional group G_2(2). There are eleven maximal subgroup conjugacy classes in the simple symplectic [&hellip;]","og_url":"https:\/\/kibu.ac.ke\/sgs\/character-table-of-the-maximal-subgroup-27g_22-of-the-affine-subgroup-sp_82-by-fischer-clifford-matrices\/","og_site_name":"School of Graduate Studies","article_published_time":"2025-10-21T06:30:01+00:00","article_modified_time":"2025-11-21T04:49:20+00:00","author":"kibabii","twitter_card":"summary_large_image","twitter_misc":{"Written by":"kibabii","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/kibu.ac.ke\/sgs\/character-table-of-the-maximal-subgroup-27g_22-of-the-affine-subgroup-sp_82-by-fischer-clifford-matrices\/#article","isPartOf":{"@id":"https:\/\/kibu.ac.ke\/sgs\/character-table-of-the-maximal-subgroup-27g_22-of-the-affine-subgroup-sp_82-by-fischer-clifford-matrices\/"},"author":{"name":"kibabii","@id":"https:\/\/kibu.ac.ke\/sgs\/#\/schema\/person\/3c7b50037f622e72b7023aafee6ed8f8"},"headline":"CHARACTER TABLE OF THE MAXIMAL SUBGROUP 2^7:G_2(2) OF THE AFFINE SUBGROUP Sp_8(2) BY FISCHER-CLIFFORD MATRICES","datePublished":"2025-10-21T06:30:01+00:00","dateModified":"2025-11-21T04:49:20+00:00","mainEntityOfPage":{"@id":"https:\/\/kibu.ac.ke\/sgs\/character-table-of-the-maximal-subgroup-27g_22-of-the-affine-subgroup-sp_82-by-fischer-clifford-matrices\/"},"wordCount":230,"commentCount":0,"publisher":{"@id":"https:\/\/kibu.ac.ke\/sgs\/#organization"},"articleSection":["Theses"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/kibu.ac.ke\/sgs\/character-table-of-the-maximal-subgroup-27g_22-of-the-affine-subgroup-sp_82-by-fischer-clifford-matrices\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/kibu.ac.ke\/sgs\/character-table-of-the-maximal-subgroup-27g_22-of-the-affine-subgroup-sp_82-by-fischer-clifford-matrices\/","url":"https:\/\/kibu.ac.ke\/sgs\/character-table-of-the-maximal-subgroup-27g_22-of-the-affine-subgroup-sp_82-by-fischer-clifford-matrices\/","name":"CHARACTER TABLE OF THE MAXIMAL SUBGROUP 2^7:G_2(2) OF THE AFFINE SUBGROUP Sp_8(2) BY FISCHER-CLIFFORD MATRICES - 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