{"id":5190,"date":"2025-06-25T11:26:47","date_gmt":"2025-06-25T11:26:47","guid":{"rendered":"https:\/\/fs.kibu.ac.ke\/?p=5190"},"modified":"2025-12-26T22:59:29","modified_gmt":"2025-12-26T22:59:29","slug":"conjugacy-classes-of-the-group-extension-27-g22","status":"publish","type":"post","link":"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-group-extension-27-g22\/","title":{"rendered":"Conjugacy Classes of the Group Extension 27: G2(2)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"5190\" class=\"elementor elementor-5190\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-34fac5d3 elementor-section-full_width elementor-section-height-min-height elementor-section-items-stretch elementor-section-height-default\" data-id=\"34fac5d3\" 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-3a8a163c\" data-id=\"3a8a163c\" 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-23249b92 elementor-widget elementor-widget-theme-post-title elementor-page-title elementor-widget-heading\" data-id=\"23249b92\" 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 Group Extension 27: G2(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-4f7ad57e elementor-section-height-min-height elementor-section-boxed elementor-section-height-default elementor-section-items-middle\" data-id=\"4f7ad57e\" 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-764dbab5\" data-id=\"764dbab5\" 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-4f5206f8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4f5206f8\" 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-1ee221f0 elementor-invisible\" data-id=\"1ee221f0\" 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-5f924886 elementor-widget__width-auto elementor-widget elementor-widget-heading\" data-id=\"5f924886\" 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-315a5c4d elementor-invisible\" data-id=\"315a5c4d\" 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-65bd608b elementor-widget elementor-widget-heading\" data-id=\"65bd608b\" 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-4d13f6f2 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"4d13f6f2\" 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 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-59bc53aa elementor-invisible\" data-id=\"59bc53aa\" 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-140e6d40 elementor-tablet-align-left elementor-invisible elementor-widget elementor-widget-button\" data-id=\"140e6d40\" 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\/1706108\">\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-5118b9b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5118b9b\" 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-7e703b35 elementor-invisible\" data-id=\"7e703b35\" 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-6fc67f7b elementor-widget elementor-widget-heading\" data-id=\"6fc67f7b\" 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-40036169 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"40036169\" 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 group extension 27: G2(2), a maximal subgroup of both the symplectic group Sp8(2) and the automorphism group of the sporadic Fischer group Fi22. Using the Fischer-Clifford matrix technique and computational methods, we determine and analyze the conjugacy classes of 27: G2(2), their sizes, and centralizer orders. Our results reveal that 27: G2(2) has 111 conjugacy classes, with sizes ranging from 1 to 1,548,288. We construct Fischer-Clifford matrices for each conjugacy class representative in G2(2) and establish a fusion map from 27: G2(2) into Sp8(2). The analysis shows a strong influence of the normal subgroup 27 on the overall group structure, with many class sizes being powers of 2. We also compare the conjugacy class structure of 27: G2(2) with related groups, highlighting its unique features. This comprehensive analysis contributes to the broader understanding of group extensions, their relationship to larger structures like symplectic and sporadic groups, and lays the groundwork for future studies on the representations and character theory of 27: G2(2).<\/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 Chikamai Vincent Marani VIEW ON PUBLISHER SITE Abstract This study investigates the conjugacy class structure of the group extension 27: G2(2), a maximal subgroup of both the symplectic group Sp8(2) and the automorphism group of the sporadic Fischer group Fi22. Using the Fischer-Clifford matrix technique and computational methods, we determine 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-5190","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 Group Extension 27: G2(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-group-extension-27-g22\/\" \/>\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 Group Extension 27: G2(2) - Faculty of Science\" \/>\n<meta property=\"og:description\" content=\"2024 KIBU Authors Lucy Chikamai Vincent Marani VIEW ON PUBLISHER SITE Abstract This study investigates the conjugacy class structure of the group extension 27: G2(2), a maximal subgroup of both the symplectic group Sp8(2) and the automorphism group of the sporadic Fischer group Fi22. Using the Fischer-Clifford matrix technique and computational methods, we determine and [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-group-extension-27-g22\/\" \/>\n<meta property=\"og:site_name\" content=\"Faculty of Science\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-25T11:26:47+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-12-26T22:59:29+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-group-extension-27-g22\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-group-extension-27-g22\/\"},\"author\":{\"name\":\"kibabii\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/#\/schema\/person\/fc9b7f13eeb65cf0be520197c35b17d6\"},\"headline\":\"Conjugacy Classes of the Group Extension 27: G2(2)\",\"datePublished\":\"2025-06-25T11:26:47+00:00\",\"dateModified\":\"2025-12-26T22:59:29+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-group-extension-27-g22\/\"},\"wordCount\":178,\"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-group-extension-27-g22\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-group-extension-27-g22\/\",\"url\":\"https:\/\/kibu.ac.ke\/fs\/conjugacy-classes-of-the-group-extension-27-g22\/\",\"name\":\"Conjugacy Classes of the Group Extension 27: G2(2) - 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