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		<id>http://wiki.manchester.ac.uk/blocks/api.php?action=feedcontributions&amp;feedformat=atom&amp;user=Pete+Gautam</id>
		<title>Block library - User contributions [en-gb]</title>
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		<updated>2026-04-27T01:31:20Z</updated>
		<subtitle>User contributions</subtitle>
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	<entry>
		<id>http://wiki.manchester.ac.uk/blocks/index.php?title=Classification_by_p-group&amp;diff=1249</id>
		<title>Classification by p-group</title>
		<link rel="alternate" type="text/html" href="http://wiki.manchester.ac.uk/blocks/index.php?title=Classification_by_p-group&amp;diff=1249"/>
				<updated>2025-09-09T11:50:13Z</updated>
		
		<summary type="html">&lt;p&gt;Pete Gautam: /* Blocks for  p=2  */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;'''Classification of Morita equivalences for blocks with a given defect group'''&lt;br /&gt;
&lt;br /&gt;
On this page we list classifications of Morita equivalence classes for each isomorphism class of p-groups in turn. [[Generic classifications by p-group class|Generic classifications for classes of p-groups can be found here]].&lt;br /&gt;
&lt;br /&gt;
See [[Labelling for Morita equivalence classes|this page]] for a description of the labelling conventions.&lt;br /&gt;
&lt;br /&gt;
== Blocks for &amp;lt;math&amp;gt; p=2 &amp;lt;/math&amp;gt; ==&lt;br /&gt;
&lt;br /&gt;
{| role=&amp;quot;presentation&amp;quot; class=&amp;quot;wikitable mw-collapsible mw-collapsed&amp;quot;&lt;br /&gt;
| &amp;lt;strong&amp;gt;&amp;lt;math&amp;gt;1 \leq |D| \leq 8&amp;lt;/math&amp;gt; &amp;amp;nbsp;&amp;lt;/strong&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| &amp;lt;math&amp;gt;|D|&amp;lt;/math&amp;gt;&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| SmallGroup &lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Isotype&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Known &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;-(&amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt;-)classes&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Complete (w.r.t.)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Derived equiv classes (w.r.t)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| References&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Notes&lt;br /&gt;
|- &lt;br /&gt;
| 1 || 1 || &amp;lt;math&amp;gt;1&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || &lt;br /&gt;
|- &lt;br /&gt;
| 2 || [[C2|1]] || [[C2|&amp;lt;math&amp;gt;C_2&amp;lt;/math&amp;gt;]] || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|- &lt;br /&gt;
| 4 || [[C4|1]] || [[C4|&amp;lt;math&amp;gt;C_4&amp;lt;/math&amp;gt;]] || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|- &lt;br /&gt;
| 4 || [[C2xC2|2]] || [[C2xC2|&amp;lt;math&amp;gt;C_2 \times C_2&amp;lt;/math&amp;gt;]] || 3(3) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References|[Er82], [Li94] ]] ||&lt;br /&gt;
|- &lt;br /&gt;
|8 || [[C8|1]] || [[C8|&amp;lt;math&amp;gt;C_8&amp;lt;/math&amp;gt;]] ||1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|-&lt;br /&gt;
|8 || [[C4xC2|2]] || [[C4xC2|&amp;lt;math&amp;gt;C_4 \times C_2&amp;lt;/math&amp;gt;]] ||1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|-&lt;br /&gt;
|8 || [[D8|3]] || [[D8|&amp;lt;math&amp;gt;D_8&amp;lt;/math&amp;gt;]] ||6(?) || &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt; || [[References|[Er87] ]] || Principal blocks classified up to source algebra equivalence in [[References#K|[KoLa20]]] &lt;br /&gt;
|-&lt;br /&gt;
|8 || [[Q8|4]] || [[Q8|&amp;lt;math&amp;gt;Q_8&amp;lt;/math&amp;gt;]] ||3(3) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt; || [[References|[Er88a], [Er88b], [HKL07], [Ei16]]] || &lt;br /&gt;
|-&lt;br /&gt;
|8 || [[C2xC2xC2|5]] || [[C2xC2xC2|&amp;lt;math&amp;gt;C_2 \times C_2 \times C_2&amp;lt;/math&amp;gt;]] || 8(8) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References| [Ea16]]] || Uses CFSG&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
{| role=&amp;quot;presentation&amp;quot; class=&amp;quot;wikitable mw-collapsible mw-collapsed&amp;quot;&lt;br /&gt;
| &amp;lt;strong&amp;gt;&amp;lt;math&amp;gt;|D|=16&amp;lt;/math&amp;gt; &amp;amp;nbsp;&amp;lt;/strong&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| &amp;lt;math&amp;gt;|D|&amp;lt;/math&amp;gt;&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| SmallGroup &lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Isotype&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Donovan (w.r.t)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Known &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;-(&amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt;-)classes&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Complete (w.r.t.)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Derived equiv classes (w.r.t)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| References&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Notes&lt;br /&gt;
|- &lt;br /&gt;
|16 || [[C16|1]] || [[C16|&amp;lt;math&amp;gt;C_{16}&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; ||1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|-&lt;br /&gt;
|16 || [[C4xC4|2]] || [[C4xC4|&amp;lt;math&amp;gt;C_4 \times C_4&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 2(2) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References|[EKKS14] ]] ||&lt;br /&gt;
|-&lt;br /&gt;
|16 || [[MNA(2,1)|3]] || [[MNA(2,1)]] || No || 3(?) || No || || [[References|[Sa11] ]] || Block invariants known&lt;br /&gt;
|-&lt;br /&gt;
|16 || [[C4:C4|4]] || [[C4:C4|&amp;lt;math&amp;gt;C_4:C_4&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt;|| 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References|[CG12], [Sa12b]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|16 || [[C8xC2|5]] || [[C8xC2|&amp;lt;math&amp;gt;C_8 \times C_2&amp;lt;/math&amp;gt;]]|| &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|-&lt;br /&gt;
|16 || [[M16|6]] || [[M16|&amp;lt;math&amp;gt;M_{16}&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References|[CG12], [Sa12b] ]] || &lt;br /&gt;
|-&lt;br /&gt;
|16 || [[D16|7]] || [[D16|&amp;lt;math&amp;gt;D_{16}&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;|| 5(?) || &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt; || [[References|[Er87]]] || Principal blocks classified up to source algebra equivalence in [[References#K|[KoLa20]]] &lt;br /&gt;
|-&lt;br /&gt;
|16 || [[SD16|8]] || [[SD16|&amp;lt;math&amp;gt;SD_{16}&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt; || 7(?) || || || [[References|[Er88c], [Er90b]]] || Two other possible classes&lt;br /&gt;
|-&lt;br /&gt;
|16 || [[Q16|9]] || [[Q16|&amp;lt;math&amp;gt;Q_{16}&amp;lt;/math&amp;gt;]] || No || 6(?) || || &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt; || [[References|[Er88a], [Er88b], [Ho97]]] || Two possibly infinite families when &amp;lt;math&amp;gt;l(B)=2&amp;lt;/math&amp;gt;. Classified over &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; when &amp;lt;math&amp;gt;l(B)=3&amp;lt;/math&amp;gt; in [[References#E|[Ei16]]]. Principal blocks classified up to source algebra equivalence in [[References#K|[KoLa20b]]]&lt;br /&gt;
|-&lt;br /&gt;
|16 || [[C4xC2xC2|10]] || [[C4xC2xC2|&amp;lt;math&amp;gt;C_4 \times C_2 \times C_2&amp;lt;/math&amp;gt;]]|| &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 3(3) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References|[EL18a]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|16 || [[D8xC2|11]] || [[D8xC2|&amp;lt;math&amp;gt;D_8 \times C_2&amp;lt;/math&amp;gt;]] || No || || || || [[References|[Sa12] ]] || Block invariants known&lt;br /&gt;
|-&lt;br /&gt;
|16 || [[Q8xC2|12]] || [[Q8xC2|&amp;lt;math&amp;gt;Q_8 \times C_2&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 3(3) || No || || [[References#E|[EL20]]] || Block invariants known by [[References#S|[Sa13]]]&lt;br /&gt;
|-&lt;br /&gt;
|16 || [[D8*C4|13]] || [[D8*C4|&amp;lt;math&amp;gt;D_8*C_4&amp;lt;/math&amp;gt;]] || No || 3(?) || No || || [[References|[Sa13b] ]] || Block invariants known&lt;br /&gt;
|-&lt;br /&gt;
|16 || [[(C2)^4|14]] || [[(C2)^4|&amp;lt;math&amp;gt;(C_2)^4&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 16(16) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References|[Ea18] ]] ||&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The table for defect groups of order 32 takes as its starting point Table 13.1 of Sambale's book [[References|[Sa14]]].&lt;br /&gt;
&lt;br /&gt;
{| role=&amp;quot;presentation&amp;quot; class=&amp;quot;wikitable mw-collapsible mw-collapsed&amp;quot;&lt;br /&gt;
| &amp;lt;strong&amp;gt;&amp;lt;math&amp;gt;|D|=32&amp;lt;/math&amp;gt; &amp;amp;nbsp;&amp;lt;/strong&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| &amp;lt;math&amp;gt;|D|&amp;lt;/math&amp;gt;&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| SmallGroup &lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Isotype&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Donovan (w.r.t)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Known &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;-(&amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt;-)classes&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Complete (w.r.t.)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Derived equiv classes (w.r.t)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| References&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Notes&lt;br /&gt;
|- &lt;br /&gt;
|32 || [[C32|1]] || [[C32|&amp;lt;math&amp;gt;C_{32}&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; ||1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[MNA(2,2)|2]] || [[MNA(2,2)|&amp;lt;math&amp;gt;MNA(2,2)&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 2(2) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#E|[EKS12]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[C8xC4|3]] || [[C8xC4|&amp;lt;math&amp;gt;C_8 \times C_4&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || &lt;br /&gt;
|-&lt;br /&gt;
|32 || [[C8:C4|4]] || [[C8:C4|&amp;lt;math&amp;gt;C_8:C_4&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#C|[CG12], [Sa12b]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[MNA(3,1)|5]] || [[MNA(3,1)|&amp;lt;math&amp;gt;MNA(3,1)&amp;lt;/math&amp;gt;]] || No || || || || [[References#S|[Sa11] ]] || Invariants known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[MNA(2,1):C2|6]] || [[MNA(3,1):C2|&amp;lt;math&amp;gt;MNA(2,1):C_2&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#S|[Sa14]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[SmallGroup(32,7)|7]] || [[SmallGroup(32,7)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#S|[Sa14]]] || &amp;lt;math&amp;gt;M_{16}:C_2&amp;lt;/math&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[2.MNA(2,1)|8]] || [[2.MNA(2,1)|&amp;lt;math&amp;gt;2.MNA(2,1)&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#S|[Sa14]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[D8:C4|9]] || [[D8:C4|&amp;lt;math&amp;gt;D_8:C_4&amp;lt;/math&amp;gt;]] || No || || || || [[References#S|[Sa14,10.23]]] || Invariants known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[Q8:C4|10]] || [[Q8:C4|&amp;lt;math&amp;gt;Q_8:C_4&amp;lt;/math&amp;gt;]] || No || || || || [[References#S|[Sa14,10.25]]] || Invariants known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[C4wrC2|11]] || [[C4wrC2|&amp;lt;math&amp;gt;C_4 \wr C_2&amp;lt;/math&amp;gt;]] || No || 6(6) || No || || [[References#K|[Ku80]]], [[References#K|[KoLaSa23]]] || Invariants known. Principal blocks classified up to source algebra equivalence in [[References#K|[KoLaSa23]]]&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[C4:C8|12]] || [[C4:C8|&amp;lt;math&amp;gt;C_4:C_8&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#C|[CG12], [Sa12b]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[C8:C4a|13]] || [[C8:C4a|&amp;lt;math&amp;gt;C_8:C_4=\langle a,b|a^8=b^4=1, ba=a^3b \rangle&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#C|[CG12], [Sa12b]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[C8:C4b|14]] || [[C8:C4b|&amp;lt;math&amp;gt;C_8:C_4=\langle a,b|a^8=b^4=1, ba=a^7b \rangle&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#C|[CG12], [Sa12b]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[SmallGroup(32,15)|15]] || [[SmallGroup(32,15)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#C|[CG12], [Sa12b]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[C16xC2|16]] || [[C16xC2|&amp;lt;math&amp;gt;C_{16} \times C_2&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[M32|17]] || [[M32|&amp;lt;math&amp;gt;M_{32}&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#C|[CG12], [Sa12b]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[D32|18]] || [[D32|&amp;lt;math&amp;gt;D_{32}&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt; || 5(?) || &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt; || [[References#E|[Er87]]] || Principal blocks classified up to source algebra equivalence in [[References#K|[KoLa20]]] &lt;br /&gt;
|-&lt;br /&gt;
|32 || [[SD32|19]] || [[SD32|&amp;lt;math&amp;gt;SD_{32}&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt; || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[Q32|20]] || [[Q32|&amp;lt;math&amp;gt;Q_{32}&amp;lt;/math&amp;gt;]] || No || || || || [[References#E|[Er88a], [Er88b], [Ho97]]] || Two possibly infinite families when &amp;lt;math&amp;gt;l(B)=2&amp;lt;/math&amp;gt;. Classified over &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; when &amp;lt;math&amp;gt;l(B)=3&amp;lt;/math&amp;gt; in [[References#E|[Ei16]]]. Principal blocks classified up to source algebra equivalence in [[References#K|[KoLa20b]]]&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[C4xC4xC2|21]] || [[C4xC4xC2|&amp;lt;math&amp;gt;C_4 \times C_4 \times C_2&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 2(2) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#E|[EKKS14]]] &lt;br /&gt;
|-&lt;br /&gt;
|32 || [[MNA(2,1)xC2|22]] || [[MNA(2,1)xC2|&amp;lt;math&amp;gt;MNA(2,1) \times C_2&amp;lt;/math&amp;gt;]] || No || || || || [[References#S|[Sa14,10.25]]] || Invariants known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[(C4:C4)xC2|23]] || [[(C4:C4)xC2|&amp;lt;math&amp;gt;(C_4:C_4) \times C_2&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#S|[Sa14]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[SmallGroup(32,24)|24]] || [[SmallGroup(32,24)]]&amp;lt;!--&amp;lt;math&amp;gt;(C_4 \times C_4):C_2=\langle a,b,c \mid a^4 = b^4 = c^2 = e, ab = ba, ac = ca, cb = a^2bc \rangle&amp;lt;/math&amp;gt;]]--&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#S|[Sa14]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[D8xC4|25]] || [[D8xC4|&amp;lt;math&amp;gt;D_8 \times C_4&amp;lt;/math&amp;gt;]] || No || || || || [[References#S|[Sa14,9.7]]] ||&lt;br /&gt;
Invariants known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[Q8xC4|26]] || [[Q8xC4|&amp;lt;math&amp;gt;Q_8 \times C_4&amp;lt;/math&amp;gt;]] ||  &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 3(3) || No || || [[References#E|[EL20]]] || Invariants known by [[References#S|[Sa14,9.28]]]&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[SmallGroup(32,27)|27]] || [[SmallGroup(32,27)]]&amp;lt;!--|&amp;lt;math&amp;gt;(C_4 \times C_4):C_2=\langle x,y,z,a,b \mid x^2 = y^2 = z^2 = a^2 = b^2 = e, xy = yx, xz, = zx, yz = zy, aza^{-1} = xz, bzb^{-1} = yz, ax = xa, ay = ya, bx = xb, by = yb \rangle&amp;lt;/math&amp;gt;]]--&amp;gt; || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[SmallGroup(32,28)|28]] || [[SmallGroup(32,28)]] || No || || || || [[References#S|[Sa14,13.11]]] || Invariants known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[SmallGroup(32,29)|29]] || [[SmallGroup(32,29)]] || No || || || || [[References#S|[Sa14,13.11]]] || Invariants known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[SmallGroup(32,30)|30]] || [[SmallGroup(32,30)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#S|[Sa14]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[SmallGroup(32,31)|31]] || [[SmallGroup(32,31)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#S|[Sa14]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[SmallGroup(32,32)|32]] || [[SmallGroup(32,32)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#S|[Sa14]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[SmallGroup(32,33)|33]] || [[SmallGroup(32,33)]] || No || || || || [[References|[Sa14,13.12]]] || Invariants partly known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[SmallGroup(32,34)|34]] || [[SmallGroup(32,34)]] || No || || || || [[References|[Sa14,13.12]]] || Invariants partly known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[C4:Q8|35]] || [[C4:Q8|&amp;lt;math&amp;gt;C_4:Q_8&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#S|[Sa14]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[C8xC2xC2|36]] || [[C8xC2xC2|&amp;lt;math&amp;gt;C_8 \times C_2 \times C_2&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 3(3) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#E|[EL18a]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[M16xC2|37]] || [[M16xC2|&amp;lt;math&amp;gt;M_{16} \times C_2&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#S|[Sa14]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[D8*C8|38]] || [[D8*C8|&amp;lt;math&amp;gt;D_8*C_8&amp;lt;/math&amp;gt;]] || No || || || || [[References#S|[Sa14,9.18]]] || Invariants known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[D16xC2|39]] || [[D16xC2|&amp;lt;math&amp;gt;D_{16} \times C_2&amp;lt;/math&amp;gt;]] || No || || || || [[References#S|[Sa14,9.7]]] || Invariants known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[SD16xC2|40]] || [[SD16xC2|&amp;lt;math&amp;gt;SD_{16} \times C_2&amp;lt;/math&amp;gt;]] || No || || || || [[References#S|[Sa14,9.37]]] || Invariants known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[Q16xC2|41]] || [[Q16xC2|&amp;lt;math&amp;gt;Q_{16} \times C_2&amp;lt;/math&amp;gt;]] || No || || || || [[References#S|[Sa14,9.28]]] || Invariants known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[D16*C4|42]] || [[D16*C4|&amp;lt;math&amp;gt;D_{16}*C_4&amp;lt;/math&amp;gt;]] || No || || || || [[References|[Sa14,9.18]]] || Invariants known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[SmallGroup(32,43)|43]] || [[SmallGroup(32,43)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[SmallGroup(32,44)|44]] || [[SmallGroup(32,44)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[C4xC2xC2xC2|45]] || [[C4xC2xC2xC2|&amp;lt;math&amp;gt;C_4 \times C_2 \times C_2 \times C_2&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 8(8) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#E|[EL23]]] ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[D8xC2xC2|46]] || [[D8xC2xC2|&amp;lt;math&amp;gt;D_8 \times C_2 \times C_2&amp;lt;/math&amp;gt;]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[Q8xC2xC2|47]] || [[Q8xC2xC2|&amp;lt;math&amp;gt;Q_8 \times C_2 \times C_2&amp;lt;/math&amp;gt;]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[D8*C4xC2|48]] || [[D8*C4xC2|&amp;lt;math&amp;gt;(D_8*C_4) \times C_2&amp;lt;/math&amp;gt;]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[D8*D8|49]] || [[D8*D8|&amp;lt;math&amp;gt;D_8*D_8&amp;lt;/math&amp;gt;]] || No || || || || [[References#S|[Sa13c]]] || Invariants partly known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[D8*Q8|50]] || [[D8*Q8|&amp;lt;math&amp;gt;D_8*Q_8&amp;lt;/math&amp;gt;]] || No || || || || [[References#S|[Sa13c]]] || Invariants partly known&lt;br /&gt;
|-&lt;br /&gt;
|32 || [[(C2)^5|51]] || [[(C2)^5|&amp;lt;math&amp;gt;(C_2)^5&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 34 (34) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; ||  || [[References#A|[Ar19]]] || Derived eq. classes determined for 30 of the 34 Morita eq. classes. &lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--&lt;br /&gt;
{| role=&amp;quot;presentation&amp;quot; class=&amp;quot;wikitable mw-collapsible mw-collapsed&amp;quot;&lt;br /&gt;
| &amp;lt;strong&amp;gt;&amp;lt;math&amp;gt;|D|=64&amp;lt;/math&amp;gt; &amp;amp;nbsp;&amp;lt;/strong&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| &amp;lt;math&amp;gt;|D|&amp;lt;/math&amp;gt;&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| SmallGroup &lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Isotype&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Donovan (w.r.t)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Known &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;-(&amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt;-)classes&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Complete (w.r.t.)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Derived equiv classes (w.r.t)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| References&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Notes&lt;br /&gt;
|- &lt;br /&gt;
|64 || [[C64|1]] || [[C64|&amp;lt;math&amp;gt;C_{64}&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; ||1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|- &lt;br /&gt;
|64 || [[C8xC8|2]] || [[C8xC8|&amp;lt;math&amp;gt;C_8 \times C_8&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; ||2(2) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#E|[EKKS14]]]||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,3)|3]] || [[SmallGroup(64,3)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#C|[CG12], [Sa12b]]] || &amp;lt;math&amp;gt;C_8:C_8&amp;lt;/math&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[(C2xC2xC2):C8|4]] || [[(C2xC2xC2):C8|&amp;lt;math&amp;gt;(C_2)^3:C_8&amp;lt;/math&amp;gt;]] || No || || || || || FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,5)|5]] || [[SmallGroup(64,5)]] || No || || || || || FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[(D8:C8|6]] || [[D8:C8|&amp;lt;math&amp;gt;D_8:C_8&amp;lt;/math&amp;gt;]] || No || || || || || FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[(Q8:C8|7]] || [[Q8:C8|&amp;lt;math&amp;gt;Q_8:C_8&amp;lt;/math&amp;gt;]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,8)|8]] || [[SmallGroup(64,8)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,9)|9]] || [[SmallGroup(64,9)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,10)|10]] || [[SmallGroup(64,10)]] || No || || || || || FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,11)|11]] || [[SmallGroup(64,11)]] || No || || || || || FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,12)|12]] || [[SmallGroup(64,12)]] || No || || || || || FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,13)|13]] || [[SmallGroup(64,13)]] || No || || || || || FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,14)|14]] || [[SmallGroup(64,14)]] || No || || || || || FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,15)|15]] || [[SmallGroup(64,15)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#C|[CG12], [Sa12b]]] || &amp;lt;math&amp;gt;C_8:C_8&amp;lt;/math&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,16)|16]] || [[SmallGroup(64,16)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#C|[CG12], [Sa12b]]] || &amp;lt;math&amp;gt;C_8:C_8&amp;lt;/math&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,17)|17]] || [[SmallGroup(64,17)]] || No || || || || || FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,18)|18]] || [[SmallGroup(64,18)]] || No || || || || || &amp;lt;math&amp;gt;(C_4 \times C_4):C_4&amp;lt;/math&amp;gt; FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,19)|19]] || [[SmallGroup(64,19)]] || No || || || || || Maxperm&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,20)|20]] || [[SmallGroup(64,20)]] || No || || || || || &amp;lt;math&amp;gt;(C_4 \times C_4):C_4&amp;lt;/math&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,21)|21]] || [[SmallGroup(64,21)]] || No || || || || || FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,22)|22]] || [[SmallGroup(64,22)]] || No || || || || || FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,23)|23]] || [[SmallGroup(64,23)]] || No || || || || || FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,24)|24]] || [[SmallGroup(64,24)]] || No || || || || || &amp;lt;math&amp;gt;M_{16}:C_4&amp;lt;/math&amp;gt; FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,25)|25]] || [[SmallGroup(64,25)]] || No || || || || || &amp;lt;math&amp;gt;M_{16}:C_4&amp;lt;/math&amp;gt; FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[C16xC4|26]] || [[C16xC4|&amp;lt;math&amp;gt;C_{16} \times C_4&amp;lt;/math&amp;gt;]]|| &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,27)|27]] || [[SmallGroup(64,27)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#C|[CG12], [Sa12b]]] || &amp;lt;math&amp;gt;C_{16}:C_4&amp;lt;/math&amp;gt; FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,28)|28]] || [[SmallGroup(64,28)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#C|[CG12], [Sa12b]]] || &amp;lt;math&amp;gt;C_{16}:C_4&amp;lt;/math&amp;gt; FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[(C2xC2):C16|29]] || [[(C2xC2):C16|&amp;lt;math&amp;gt;(C_2)^2:C_{16}&amp;lt;/math&amp;gt;]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,30)|30]] || [[SmallGroup(64,30)]] || No || || || || || &amp;lt;math&amp;gt;M_{32}:C_2&amp;lt;/math&amp;gt; FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,31)|31]] || [[SmallGroup(64,31)]] || No || || || || || &amp;lt;math&amp;gt;M_{32}:C_2&amp;lt;/math&amp;gt; &lt;br /&gt;
|-&lt;br /&gt;
|64 || [[C2wrC4|32]] || [[(C2wrC4|&amp;lt;math&amp;gt;C_2 \wr C_4&amp;lt;/math&amp;gt;]] || No || || || || || &lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,33)|33]] || [[SmallGroup(64,33)]] || No || || || || || FT&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,34)|34]] || [[SmallGroup(64,31)]] || No || || || || ||  &amp;lt;math&amp;gt;(C_4 \times C_4):C_4&amp;lt;/math&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,35)|35]] || [[SmallGroup(64,35)]] || No || || || || ||  &amp;lt;math&amp;gt;(C_4 \times C_4):C_4&amp;lt;/math&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,36)|36]] || [[SmallGroup(64,36)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,37)|37]] || [[SmallGroup(64,37)]] || No || || || || || &amp;lt;math&amp;gt;C_4:Q_8&amp;lt;/math&amp;gt;, fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,38)|38]] || [[SmallGroup(64,38)]] || No || || || || || &amp;lt;math&amp;gt;D_{16}:C_4&amp;lt;/math&amp;gt;, fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,39)|39]] || [[SmallGroup(64,39)]] || No || || || || || &amp;lt;math&amp;gt;Q_{16}:C_2&amp;lt;/math&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,40)|40]] || [[SmallGroup(64,40)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,41)|41]] || [[SmallGroup(64,41)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,42)|42]] || [[SmallGroup(64,42)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,43)|43]] || [[SmallGroup(64,43)]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[C4:C16|44]] || [[C4:C16|&amp;lt;math&amp;gt;C_4:C_{16}&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#C|[CG12], [Sa12b]]] || &amp;lt;math&amp;gt;C_4:C_{16}&amp;lt;/math&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,45)|45]] || [[SmallGroup(64,45)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,46)|46]] || [[SmallGroup(64,46)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,47)|47]] || [[SmallGroup(64,47)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#C|[CG12], [Sa12b]]] || &amp;lt;math&amp;gt;C_{16}:C_4&amp;lt;/math&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,48)|48]] || [[SmallGroup(64,48)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#C|[CG12], [Sa12b]]] || &amp;lt;math&amp;gt;C_{16}:C_4&amp;lt;/math&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,48)|49]] || [[SmallGroup(64,49)]] || No || || || || ||&lt;br /&gt;
|- &lt;br /&gt;
|64 || [[C32xC2|50]] || [[C32xC2|&amp;lt;math&amp;gt;C_{32} \times C_2&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; ||1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[M6(2)|51]] || [[M6(2)|&amp;lt;math&amp;gt;M_6(2)&amp;lt;/math&amp;gt;]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[D64|52]] || [[D64|&amp;lt;math&amp;gt;D_{64}&amp;lt;/math&amp;gt;]] || No || &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt; || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SD64|53]] || [[SD64|&amp;lt;math&amp;gt;SD_{64}&amp;lt;/math&amp;gt;]] || No || &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt; || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[Q64|54]] || [[Q64|&amp;lt;math&amp;gt;Q_{64}&amp;lt;/math&amp;gt;]] || No || || || || ||&lt;br /&gt;
|- &lt;br /&gt;
|64 || [[C4xC4xC4|55]] || [[C4xC4xC4|&amp;lt;math&amp;gt;C_4 \times C_4 \times C_4&amp;lt;/math&amp;gt;]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; ||4(4) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#E|[EL18a]]]||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,56)|56]] || [[SmallGroup(64,56)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,57)|57]] || [[SmallGroup(64,57)]] || No || || || || ||&lt;br /&gt;
|- &lt;br /&gt;
|64 || [[C4x(C2xC2):C4|58]] || [[C4x(C2xC2):C4|&amp;lt;math&amp;gt;C_{4} \times (C_2 \times C_2):C_4&amp;lt;/math&amp;gt;]] || || || || || || Fusion trivial?&lt;br /&gt;
|- &lt;br /&gt;
|64 || [[C4x(C4:C4)|59]] || [[C4x(C4:C4)|&amp;lt;math&amp;gt;C_{4} \times (C_4:C_4)&amp;lt;/math&amp;gt;]] || || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,60)|60]] || [[SmallGroup(64,60)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,61)|61]] || [[SmallGroup(64,61)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,62)|62]] || [[SmallGroup(64,62)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,63)|63]] || [[SmallGroup(64,63)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || Resistant group with automorphism group a 2-group&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,64)|64]] || [[SmallGroup(64,64)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,65)|65]] || [[SmallGroup(64,65)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,66)|66]] || [[SmallGroup(64,66)]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,67)|67]] || [[SmallGroup(64,67)]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,68)|68]] || [[SmallGroup(64,68)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || Resistant group with automorphism group a 2-group&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,69)|69]] || [[SmallGroup(64,69)]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,70)|70]] || [[SmallGroup(64,70)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || Resistant group with automorphism group a 2-group&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,71)|71]] || [[SmallGroup(64,71)]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,72)|72]] || [[SmallGroup(64,72)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || Resistant group with automorphism group a 2-group&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,73)|73]] || [[SmallGroup(64,73)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[(C2)^3:Q8|74]] || [[(C2)^3:Q8|&amp;lt;math&amp;gt;(C_2)^3:Q_8&amp;lt;/math&amp;gt;]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,75)|75]] || [[SmallGroup(64,75)]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,76)|76]] || [[SmallGroup(64,76)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || Resistant group with automorphism group a 2-group&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,77)|77]] || [[SmallGroup(64,77)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,78)|78]] || [[SmallGroup(64,78)]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,79)|79]] || [[SmallGroup(64,79)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || Resistant group with automorphism group a 2-group&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,80)|80]] || [[SmallGroup(64,80)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,81)|81]] || [[SmallGroup(64,81)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || Resistant group with automorphism group a 2-group&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,82)|82]] || [[SmallGroup(64,82)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 6(6) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#E|[Ea24]]] || Sylow 2-subgroup of &amp;lt;math&amp;gt;Sz(8)&amp;lt;/math&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[C8xC4xC2|83]] || [[C8xC4xC2|&amp;lt;math&amp;gt;C_{8} \times C_4 \times C_2&amp;lt;/math&amp;gt;]]|| &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[C2x(C8:C4)|84]] || [[C2x(C8:C4)|&amp;lt;math&amp;gt;C_{2} \times (C_8:C_4)&amp;lt;/math&amp;gt;]]|| No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[M4(2)xC4|85]] || [[M4(2)xC4|&amp;lt;math&amp;gt;M_4(2) \times C_4&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,86)|86]] || [[SmallGroup(64,86)]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[C2x(C2xC2):C8|87]] || [[C2x(C2xC2):C8|&amp;lt;math&amp;gt;C_{2} \times (C_2 \times C_2):C_8&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,88)|88]] || [[SmallGroup(64,88)]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[(C8xC2xC2):C2|89]] || [[(C8xC2xC2):C2|&amp;lt;math&amp;gt;(C_8 \times C_2 \times C_2):C_2&amp;lt;/math&amp;gt;]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[C2x(C2xC2xC2):C4|90]] || [[C2x(C2xC2xC2):C4|&amp;lt;math&amp;gt;C_2 \times (C_2 \times C_2 \times C_2):C_4&amp;lt;/math&amp;gt;]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,91)|91]] || [[SmallGroup(64,91)]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,92)|92]] || [[SmallGroup(64,92)]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,93)|93]] || [[SmallGroup(64,93)]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,94)|94]] || [[SmallGroup(64,94)]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[C2x(D_8:C4)|95]] || [[C2x(D_8:C4)|&amp;lt;math&amp;gt;C_{2} \times (D_8:C_4)&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[C2x(Q_8:C4)|96]] || [[C2x(Q_8:C4)|&amp;lt;math&amp;gt;C_{2} \times (Q_8:C_4)&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,97)|97]] || [[SmallGroup(64,97)]] || No || || || || || &lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,98)|98]] || [[SmallGroup(64,98)]] || No || || || || || &lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,99)|99]] || [[SmallGroup(64,99)]] || No || || || || || &lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,100)|100]] || [[SmallGroup(64,100)]] || No || || || || || &lt;br /&gt;
|-&lt;br /&gt;
|64 || [[C2x(C4wrC2)|101]] || [[C2x(C4wrC2)|&amp;lt;math&amp;gt;C_{2} \times (C_4 \wr C_2)&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[(C4xC4)(C2:C2)|102]] || [[(C4xC4)(C2:C2)|&amp;lt;math&amp;gt;(C_4 \times C_4):(C_2 \times C_2)&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[C2x(C4:C8)|103]] || [[C2x(C4:C8)|&amp;lt;math&amp;gt;C_{2} \times (C_4:C_8)&amp;lt;/math&amp;gt;]]|| No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[C4:M4(2)|104]] || [[C4:M4(2)|&amp;lt;math&amp;gt;C_{4}:M_4(2)&amp;lt;/math&amp;gt;]]|| No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,105)|105]] || [[SmallGroup(64,105)]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,106)|106]] || [[SmallGroup(64,106)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,107)|107]] || [[SmallGroup(64,107)]] || No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,108)|108]] || [[SmallGroup(64,108)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[M4(2):C4|109]] || [[M4(2):C4|&amp;lt;math&amp;gt;M_4(2):C_4&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,110)|110]] || [[SmallGroup(64,110)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,111)|111]] || [[SmallGroup(64,111)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,112)|112]] || [[SmallGroup(64,112)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || Resistant group with automorphism group a 2-group&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,113)|113]] || [[SmallGroup(64,113)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,114)|114]] || [[SmallGroup(64,114)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[D8xC8|115]] || [[D8xC8|&amp;lt;math&amp;gt;D_8 \times C_8&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,116)|116]] || [[SmallGroup(64,116)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,117)|117]] || [[SmallGroup(64,117)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[D16xC4|118]] || [[D16xC4|&amp;lt;math&amp;gt;D_{16} \times C_4&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SD16xC4|119]] || [[SD16xC4|&amp;lt;math&amp;gt;SD_{16} \times C_4&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[Q16xC4|120]] || [[Q16xC4|&amp;lt;math&amp;gt;Q_{16} \times C_4&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SD16:C4|121]] || [[SD16:C4|&amp;lt;math&amp;gt;SD_{16}:C_4&amp;lt;/math&amp;gt;]]|| No || || || || || Fusion trivial?&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[Q16:C4|122]] || [[Q16:C4|&amp;lt;math&amp;gt;Q_{16}:C_4&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[D16:C4|123]] || [[D16:C4|&amp;lt;math&amp;gt;D_{16}:C_4&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,124)|124]] || [[SmallGroup(64,124)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,125)|125]] || [[SmallGroup(64,125)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[Q8xC8|126]] || [[Q8xC8|&amp;lt;math&amp;gt;Q_{8} \times C_8&amp;lt;/math&amp;gt;]]|| &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 3(3) || || || [[References#E|[EL20]]] || Invariants known by [[References#S|[Sa14,9.28]]]&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,127)|127]] || [[SmallGroup(64,127)]] || No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[(C2xC2):D16|128]] || [[(C2xC2)D16|&amp;lt;math&amp;gt;(C_2 \times C_2):D_{16}&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[Q8:D8|129]] || [[Q8:D8|&amp;lt;math&amp;gt;Q_8:D_{8}&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[D8:D8|130]] || [[D8:D8|&amp;lt;math&amp;gt;D_8:D_{8}&amp;lt;/math&amp;gt;]]|| No || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|64 || [[Q8xQ8|239]] || [[Q8xQ8|&amp;lt;math&amp;gt;Q_{8} \times Q_8&amp;lt;/math&amp;gt;]]|| &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || || || [[References#E|[EL20]]] || &lt;br /&gt;
|-&lt;br /&gt;
|64 || [[SmallGroup(64,245)|245]] || [[SmallGroup(64,245)]] || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || 3(3) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || [[References#E|[Ea24]]] || Sylow 2-subgroup of &amp;lt;math&amp;gt;PSU_3(4)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|}--&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Blocks for &amp;lt;math&amp;gt;p=3&amp;lt;/math&amp;gt;==&lt;br /&gt;
&lt;br /&gt;
{| role=&amp;quot;presentation&amp;quot; class=&amp;quot;wikitable mw-collapsible mw-collapsed&amp;quot;&lt;br /&gt;
| &amp;lt;strong&amp;gt;&amp;lt;math&amp;gt;1 \leq |D| \leq 27&amp;lt;/math&amp;gt; &amp;amp;nbsp;&amp;lt;/strong&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| &amp;lt;math&amp;gt;|D|&amp;lt;/math&amp;gt;&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| SmallGroup &lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Isotype&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Known &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;-(&amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt;-)classes&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Complete (w.r.t.)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Derived equiv classes (w.r.t)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| References&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Notes&lt;br /&gt;
|- &lt;br /&gt;
| 1 || 1 || &amp;lt;math&amp;gt;1&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || &lt;br /&gt;
|- &lt;br /&gt;
| 3 || [[C3|1]] || [[C3|&amp;lt;math&amp;gt;C_3&amp;lt;/math&amp;gt;]] || 2(2) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|- &lt;br /&gt;
|9 || [[C9|1]] ||[[C9|&amp;lt;math&amp;gt;C_9&amp;lt;/math&amp;gt;]] || 3(3) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || &lt;br /&gt;
|-&lt;br /&gt;
|9 || [[C3xC3|2]] || [[C3xC3|&amp;lt;math&amp;gt;C_3 \times C_3&amp;lt;/math&amp;gt;]] || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|27 || [[C27|1]] || [[C27|&amp;lt;math&amp;gt;C_{27}&amp;lt;/math&amp;gt;]] || 3(3) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|-&lt;br /&gt;
|27 || [[C9xC3|2]] || [[C9xC3|&amp;lt;math&amp;gt;C_9 \times C_3&amp;lt;/math&amp;gt;]] || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|27 || [[3_+^3|3]] || [[3_+^3|&amp;lt;math&amp;gt;3_+^{1+2}&amp;lt;/math&amp;gt;]] || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|27 || [[3_-^3|4]] || [[3_-^3|&amp;lt;math&amp;gt;3_-^{1+2}&amp;lt;/math&amp;gt;]] || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|27 || [[C3xC3xC3|5]] || [[C3xC3xC3|&amp;lt;math&amp;gt;C_3 \times C_3 \times C_3&amp;lt;/math&amp;gt;]] || || || || ||&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
==Blocks for &amp;lt;math&amp;gt;p=5&amp;lt;/math&amp;gt;==&lt;br /&gt;
&lt;br /&gt;
{| role=&amp;quot;presentation&amp;quot; class=&amp;quot;wikitable mw-collapsible mw-collapsed&amp;quot;&lt;br /&gt;
| &amp;lt;strong&amp;gt;&amp;lt;math&amp;gt;5 \leq |D| \leq 125&amp;lt;/math&amp;gt; &amp;amp;nbsp;&amp;lt;/strong&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| &amp;lt;math&amp;gt;|D|&amp;lt;/math&amp;gt;&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| SmallGroup &lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Isotype&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Known &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;-(&amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt;-)classes&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Complete (w.r.t.)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Derived equiv classes (w.r.t)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| References&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Notes&lt;br /&gt;
|- &lt;br /&gt;
| 1 || 1 || &amp;lt;math&amp;gt;1&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || &lt;br /&gt;
|- &lt;br /&gt;
|5 || [[C5|1]] || [[C5|&amp;lt;math&amp;gt;C_5&amp;lt;/math&amp;gt;]] ||6(6) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|- &lt;br /&gt;
|25 || [[C25|1]] ||[[C25|&amp;lt;math&amp;gt;C_{25}&amp;lt;/math&amp;gt;]] || 6(6) || No || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || Max 12 classes &lt;br /&gt;
|-&lt;br /&gt;
|25 || [[C5xC5|2]] || [[C5xC5|&amp;lt;math&amp;gt;C_5 \times C_5&amp;lt;/math&amp;gt;]] || ||  || || ||&lt;br /&gt;
|- &lt;br /&gt;
|125 || [[C125|1]] ||[[C125|&amp;lt;math&amp;gt;C_{125}&amp;lt;/math&amp;gt;]] || || || || || &lt;br /&gt;
|-&lt;br /&gt;
|125 || [[C25xC5|2]] || [[C25xC5|&amp;lt;math&amp;gt;C_{25} \times C_5&amp;lt;/math&amp;gt;]] || || || || || &lt;br /&gt;
|-&lt;br /&gt;
|125 || [[5_+^3|3]] || [[5_+^3|&amp;lt;math&amp;gt;5_+^{1+2}&amp;lt;/math&amp;gt;]] || 62(62) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || [[References#A|[AE23]]] || Inertial quotients are consistent within classes&lt;br /&gt;
|-&lt;br /&gt;
|125 || [[5_-^3|4]] || [[5_-^3|&amp;lt;math&amp;gt;5_-^{1+2}&amp;lt;/math&amp;gt;]] || || || || ||&lt;br /&gt;
|-&lt;br /&gt;
|125 || [[C5xC5xC5|5]] || [[C5xC5xC5|&amp;lt;math&amp;gt;C_5 \times C_5 \times C_5&amp;lt;/math&amp;gt;]] || || || || ||&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
==Blocks for &amp;lt;math&amp;gt;p\geq 7&amp;lt;/math&amp;gt;==&lt;br /&gt;
&lt;br /&gt;
{| role=&amp;quot;presentation&amp;quot; class=&amp;quot;wikitable mw-collapsible mw-collapsed&amp;quot;&lt;br /&gt;
| &amp;lt;strong&amp;gt;&amp;lt;math&amp;gt;|D|&amp;lt;/math&amp;gt; &amp;amp;nbsp;&amp;lt;/strong&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| &amp;lt;math&amp;gt;|D|&amp;lt;/math&amp;gt;&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| SmallGroup &lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Isotype&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Known &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt;-(&amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt;-)classes&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Complete (w.r.t.)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Derived equiv classes (w.r.t)?&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| References&lt;br /&gt;
! scope=&amp;quot;col&amp;quot;| Notes&lt;br /&gt;
|- &lt;br /&gt;
| 1 || 1 || &amp;lt;math&amp;gt;1&amp;lt;/math&amp;gt; || 1(1) || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || || &lt;br /&gt;
|- &lt;br /&gt;
|7 || [[C7|1]] || [[C7|&amp;lt;math&amp;gt;C_7&amp;lt;/math&amp;gt;]] ||14(14) ||No || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||Max 21 classes &lt;br /&gt;
|- &lt;br /&gt;
|11|| [[C11|1]] || [[C11|&amp;lt;math&amp;gt;C_{11}&amp;lt;/math&amp;gt;]] || ||No || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|- &lt;br /&gt;
|13 || [[C13|1]] || [[C13|&amp;lt;math&amp;gt;C_{13}&amp;lt;/math&amp;gt;]] || ||No || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|-&lt;br /&gt;
|17|| [[C17|1]] || [[C17|&amp;lt;math&amp;gt;C_{17}&amp;lt;/math&amp;gt;]] || ||No || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|- &lt;br /&gt;
|19 || [[C19|1]] || [[C19|&amp;lt;math&amp;gt;C_{19}&amp;lt;/math&amp;gt;]] || ||No || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|-&lt;br /&gt;
|23 || [[C23|1]] || [[C23|&amp;lt;math&amp;gt;C_{23}&amp;lt;/math&amp;gt;]] || ||No || &amp;lt;math&amp;gt;\mathcal{O}&amp;lt;/math&amp;gt; || ||&lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>Pete Gautam</name></author>	</entry>

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