{"id":5243,"date":"2025-06-25T12:00:52","date_gmt":"2025-06-25T12:00:52","guid":{"rendered":"https:\/\/fs.kibu.ac.ke\/?p=5243"},"modified":"2025-12-26T22:52:54","modified_gmt":"2025-12-26T22:52:54","slug":"conjugacy-classes-of-the-maximal-subgroup-28-g22-in-o_102","status":"publish","type":"post","link":"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-maximal-subgroup-28-g22-in-o_102\/","title":{"rendered":"Conjugacy Classes of the Maximal Subgroup 28: G2(2) in O+_10(2)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"5243\" class=\"elementor elementor-5243\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-324697fc elementor-section-full_width elementor-section-height-min-height elementor-section-items-stretch elementor-section-height-default\" data-id=\"324697fc\" data-element_type=\"section\" id=\"ourgoal\">\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-7a1a1afc\" data-id=\"7a1a1afc\" 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-7d311a75 elementor-widget elementor-widget-theme-post-title elementor-page-title elementor-widget-heading\" data-id=\"7d311a75\" data-element_type=\"widget\" data-widget_type=\"theme-post-title.default\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Conjugacy Classes of the Maximal Subgroup 28: G2(2) in O+_10(2)<\/h1>\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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7601955f elementor-section-height-min-height elementor-section-boxed elementor-section-height-default elementor-section-items-middle\" data-id=\"7601955f\" 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-100 elementor-top-column elementor-element elementor-element-760997d2\" data-id=\"760997d2\" 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<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-7debe97d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7debe97d\" 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-6ef1326 elementor-invisible\" data-id=\"6ef1326\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&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-130469ec elementor-widget__width-auto elementor-widget elementor-widget-heading\" data-id=\"130469ec\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">2024<\/h2>\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-30b37b76 elementor-invisible\" data-id=\"30b37b76\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&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-1450d562 elementor-widget elementor-widget-heading\" data-id=\"1450d562\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">KIBU Authors<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7bf64805 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"7bf64805\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeIn&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Lucy Walingo Chikamai<\/p><p>Vincent Marani<\/p>\t\t\t\t\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-2a6ff03b elementor-invisible\" data-id=\"2a6ff03b\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&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-30cc838e elementor-tablet-align-left elementor-invisible elementor-widget elementor-widget-button\" data-id=\"30cc838e\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInLeft&quot;}\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-shrink\" href=\"https:\/\/www.irejournals.com\/paper-details\/1706170\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">VIEW ON PUBLISHER SITE<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\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<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-6cbf9431 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6cbf9431\" 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-inner-column elementor-element elementor-element-3a8ed19e elementor-invisible\" data-id=\"3a8ed19e\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&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-64cd161b elementor-widget elementor-widget-heading\" data-id=\"64cd161b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\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 class=\"elementor-element elementor-element-73978a38 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"73978a38\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeIn&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>This study investigates the conjugacy class structure of the maximal subgroup 28: G2(2) within the orthogonal group O+_10(2). Using a combination of theoretical techniques from group extension theory and Clifford theory, along with computational methods implemented in GAP and Magma, we determine and classify all conjugacy classes of 28: G2(2). Our analysis reveals a total of 82 distinct conjugacy classes, significantly more than the 16 classes of G2(2) alone, reflecting the complex structure introduced by the 28 normal subgroup. We observe intricate fusion patterns from G2(2) to 28: G2(2), with some classes splitting and others lifting directly. Notably, we identify 57 new classes unique to the extension, showcasing the non-trivial interaction between 28 and G2(2). The centralizer structures of class representatives are analyzed, revealing a rich subgroup landscape within 28: G2(2). We also compare our results with the known conjugacy class structure of O+_10(2), providing insights into the embedding of 28: G2(2) as a maximal subgroup. This study contributes to the understanding of group extensions involving exceptional groups and classical groups, and lays groundwork for future investigations into the representation theory of 28: G2(2). Our findings have potential applications in coding theory, algebraic geometry, and cryptography.<\/p>\t\t\t\t\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<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>2024 KIBU Authors Lucy Walingo Chikamai Vincent Marani VIEW ON PUBLISHER SITE Abstract This study investigates the conjugacy class structure of the maximal subgroup 28: G2(2) within the orthogonal group O+_10(2). Using a combination of theoretical techniques from group extension theory and Clifford theory, along with computational methods implemented in GAP and Magma, we determine [&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":[9],"tags":[],"class_list":["post-5243","post","type-post","status-publish","format-standard","hentry","category-research-list"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Conjugacy Classes of the Maximal Subgroup 28: G2(2) in O+_10(2) - Faculty of Science<\/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\/fs\/conjugacy-classes-of-the-maximal-subgroup-28-g22-in-o_102\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Conjugacy Classes of the Maximal Subgroup 28: G2(2) in O+_10(2) - Faculty of Science\" \/>\n<meta property=\"og:description\" content=\"2024 KIBU Authors Lucy Walingo Chikamai Vincent Marani VIEW ON PUBLISHER SITE Abstract This study investigates the conjugacy class structure of the maximal subgroup 28: G2(2) within the orthogonal group O+_10(2). Using a combination of theoretical techniques from group extension theory and Clifford theory, along with computational methods implemented in GAP and Magma, we determine [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-maximal-subgroup-28-g22-in-o_102\/\" \/>\n<meta property=\"og:site_name\" content=\"Faculty of Science\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-25T12:00:52+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-12-26T22:52:54+00:00\" \/>\n<meta name=\"author\" content=\"kibabii\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"kibabii\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-maximal-subgroup-28-g22-in-o_102\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-maximal-subgroup-28-g22-in-o_102\/\"},\"author\":{\"name\":\"kibabii\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/#\/schema\/person\/fc9b7f13eeb65cf0be520197c35b17d6\"},\"headline\":\"Conjugacy Classes of the Maximal Subgroup 28: G2(2) in O+_10(2)\",\"datePublished\":\"2025-06-25T12:00:52+00:00\",\"dateModified\":\"2025-12-26T22:52:54+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-maximal-subgroup-28-g22-in-o_102\/\"},\"wordCount\":206,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/#organization\"},\"articleSection\":[\"Research List\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-maximal-subgroup-28-g22-in-o_102\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-maximal-subgroup-28-g22-in-o_102\/\",\"url\":\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-maximal-subgroup-28-g22-in-o_102\/\",\"name\":\"Conjugacy Classes of the Maximal Subgroup 28: G2(2) in O+_10(2) - 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