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Simple fusion system for dihedral group:D8

769 bytes added, 18:50, 26 April 2012
Fusion of elements
==Realization in groups==
<section begin="realization"/>
{| class="sortable" border="1"
! Group !! Order !! [[Dihedral group:D8]] as a subgroup of this group !! Comment
| [[alternating group:A6]] || 360 || [[D8 in A6]] || also a ''minimal'' example
|}
<section end="realization"/>
==Element structure==
===Fusion of elements=== As far as elements are concerned, this fusion system is as rich as possible: ''any two elements of the same order get fused with each other''. Below is some information. Each equivalence class under fusion is presented in terms of its conjugacy classes in the original group: {| class="sortable" border="1"! Equivalence class under fusion, i.e., equivalence class under conjugacy in the fusion system !! Order of elements !! Number of elements !! Number of conjugacy classes|-| <math>\{filline \}</math> || 1 || 1 || 1|-| <math>\{ a^2 \}</math>, <math>\{ x, a^2x \}</math>, <math>\{ ax, a^3x \}</math> || 2 || 5 || 3|-| <math>\{ a, a^3 \}</math> || 4 || 2 || 1|-! Total !! -- !! 8 !! 5|}
==Fusion subsystem structure==
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