{"id":5252,"date":"2025-06-25T12:03:49","date_gmt":"2025-06-25T12:03:49","guid":{"rendered":"https:\/\/fs.kibu.ac.ke\/?p=5252"},"modified":"2025-12-26T22:51:14","modified_gmt":"2025-12-26T22:51:14","slug":"conjugacy-classes-of-the-split-extension-28-u42","status":"publish","type":"post","link":"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-split-extension-28-u42\/","title":{"rendered":"Conjugacy Classes of the Split Extension 28: U4(2)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"5252\" class=\"elementor elementor-5252\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-73e8c48a elementor-section-full_width elementor-section-height-min-height elementor-section-items-stretch elementor-section-height-default\" data-id=\"73e8c48a\" 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-4ec72885\" data-id=\"4ec72885\" 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-7346d64c elementor-widget elementor-widget-theme-post-title elementor-page-title elementor-widget-heading\" data-id=\"7346d64c\" 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 Split Extension 28: U4(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-2e20eac5 elementor-section-height-min-height elementor-section-boxed elementor-section-height-default elementor-section-items-middle\" data-id=\"2e20eac5\" 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-7d2b3a54\" data-id=\"7d2b3a54\" 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-31214310 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"31214310\" 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-5c05409 elementor-invisible\" data-id=\"5c05409\" 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-d795ec3 elementor-widget__width-auto elementor-widget elementor-widget-heading\" data-id=\"d795ec3\" 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-77d4d34c elementor-invisible\" data-id=\"77d4d34c\" 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-44c684fc elementor-widget elementor-widget-heading\" data-id=\"44c684fc\" 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-25bcad45 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"25bcad45\" 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 Nyongesa 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-6bbf806f elementor-invisible\" data-id=\"6bbf806f\" 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-459495 elementor-tablet-align-left elementor-invisible elementor-widget elementor-widget-button\" data-id=\"459495\" 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\/1706209\">\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-54184891 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"54184891\" 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-2a8a6ac0 elementor-invisible\" data-id=\"2a8a6ac0\" 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-21490b93 elementor-widget elementor-widget-heading\" data-id=\"21490b93\" 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-31806682 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"31806682\" 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 presents a comprehensive analysis of the conjugacy classes of the split extension 28: U4(2), where U4(2) is the unitary group of degree 4 over the field with 2 elements. Using a combination of theoretical techniques, including Fischer-Clifford matrices and character theory, along with computational tools such as GAP and MAGMA, we determined and classified all 49 conjugacy classes of this group. Our analysis revealed complex fusion patterns from U4(2) to 28: U4(2), including class splitting and the introduction of new element orders. We found that 28: U4(2) has more than double the number of conjugacy classes compared to U4(2) alone, with class sizes ranging from 5 to over 1.3 million elements. This work addresses significant gaps in the existing literature regarding this specific group extension and provides insights into its structure, representations, and automorphisms. The methodology and results presented here contribute to the broader understanding of group extensions and lay the groundwork for further investigations into the properties and applications of 28: U4(2) in areas such as coding theory and quantum mechanics.<\/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 Nyongesa Marani VIEW ON PUBLISHER SITE Abstract This study presents a comprehensive analysis of the conjugacy classes of the split extension 28: U4(2), where U4(2) is the unitary group of degree 4 over the field with 2 elements. Using a combination of theoretical techniques, including Fischer-Clifford matrices and [&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-5252","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 Split Extension 28: U4(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-split-extension-28-u42\/\" \/>\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 Split Extension 28: U4(2) - Faculty of Science\" \/>\n<meta property=\"og:description\" content=\"2024 KIBU Authors Lucy Walingo Chikamai Vincent Nyongesa Marani VIEW ON PUBLISHER SITE Abstract This study presents a comprehensive analysis of the conjugacy classes of the split extension 28: U4(2), where U4(2) is the unitary group of degree 4 over the field with 2 elements. Using a combination of theoretical techniques, including Fischer-Clifford matrices and [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-split-extension-28-u42\/\" \/>\n<meta property=\"og:site_name\" content=\"Faculty of Science\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-25T12:03:49+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-12-26T22:51:14+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-split-extension-28-u42\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-split-extension-28-u42\/\"},\"author\":{\"name\":\"kibabii\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/#\/schema\/person\/fc9b7f13eeb65cf0be520197c35b17d6\"},\"headline\":\"Conjugacy Classes of the Split Extension 28: U4(2)\",\"datePublished\":\"2025-06-25T12:03:49+00:00\",\"dateModified\":\"2025-12-26T22:51:14+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-split-extension-28-u42\/\"},\"wordCount\":185,\"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-split-extension-28-u42\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-split-extension-28-u42\/\",\"url\":\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-split-extension-28-u42\/\",\"name\":\"Conjugacy Classes of the Split Extension 28: U4(2) - 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