Conjugacy Class Determination of the Split Extension Group 28: A10 Using Coset Analysis Techniques

• Author(s): Muchanga Redempta Namalwa ; Lucy Chikamai ; Shem Aywa
• Paper ID: 1709580
• Page: 305-309
• Published Date: 09-07-2025
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 9 Issue 1 July-2025

Abstract

This paper presents a comprehensive determination of the conjugacy class structure of the split extension group G = 2?:A??, which represents a maximal subgroup of the affine group Sp(8,2). Using the coset analysis technique pioneered by Moori, we systematically compute all 75 conjugacy classes of this extension group. The methodology involves analyzing the action of the alternating group A?? on the elementary abelian normal subgroup 2?, determining fixed point structures, and computing fusion parameters for each conjugacy class of A??. Our results reveal that the 24 conjugacy classes of A?? expand to 75 conjugacy classes in the extension, with centralizer orders ranging from 9 to 464,486,400. The conjugacy class structure exhibits a systematic relationship between fixed point counts and fusion parameters, with all fixed point values being powers of 2, reflecting the elementary abelian structure of the normal subgroup. These findings provide essential groundwork for character table construction and contribute to the broader classification of maximal subgroups in finite simple groups.

Keywords

Conjugacy Classes, Split Extension, Alternating Group, Coset Analysis

Citations

IRE Journals:
Muchanga Redempta Namalwa , Lucy Chikamai , Shem Aywa "Conjugacy Class Determination of the Split Extension Group 28: A10 Using Coset Analysis Techniques" Iconic Research And Engineering Journals Volume 9 Issue 1 2025 Page 305-309

IEEE:
Muchanga Redempta Namalwa , Lucy Chikamai , Shem Aywa "Conjugacy Class Determination of the Split Extension Group 28: A10 Using Coset Analysis Techniques" Iconic Research And Engineering Journals, 9(1)