Finite Group Databasebeta

Isoclinism class

Groups whose commutator structure agrees: there are isomorphisms G/Z(G) → H/Z(H) and G′ → H′ carrying one commutator map to the other. The class spans orders — G × A is isoclinic to G for every abelian A.

Stem order 64: every member's order is a multiple of it, and the members attaining it — the stem groups — are marked ◆.

5,176 groups of the catalog are in this class; the 4,902 with an abelian direct factor are hidden.

grouporder× stem
#39264×1◆ stem
#39364×1◆ stem
#39464×1◆ stem
#39564×1◆ stem
#39664×1◆ stem
#39764×1◆ stem
#39864×1◆ stem
#39964×1◆ stem
#40064×1◆ stem
#40164×1◆ stem
#1438128×2
#1439128×2
#1440128×2
#1441128×2
#1442128×2
#1443128×2
#1444128×2
#1445128×2
#1446128×2
#1780128×2
#1798128×2
#1818128×2
#1832128×2
#1840128×2
#1843128×2
#1851128×2
#1870128×2
#1917128×2
#1924128×2
#1940128×2
#1955128×2
#1985128×2
#2388128×2
#2392128×2
#2395128×2
#2396128×2
#2397128×2
#2398128×2
#2399128×2
#2401128×2
#2402128×2
#7555256×4
#7556256×4
#7557256×4
#7850256×4
#7851256×4
#7852256×4
#8134256×4
#8135256×4
#8136256×4
#8147256×4
#8149256×4
#8263256×4
#8265256×4
#10713256×4
#10715256×4
#10796256×4
#10798256×4
#10833256×4
#10835256×4
#10875256×4
#10877256×4
#10922256×4
#10964256×4
#11042256×4
#11147256×4
#11202256×4
#11255256×4
#11298256×4
#11322256×4
#11346256×4
#11380256×4
#12680256×4
#12784256×4
#12845256×4
#12880256×4
#12895256×4
#12899256×4
#12913256×4
#12977256×4
#13105256×4
#13121256×4
#13160256×4
#13190256×4
#13264256×4
#13839256×4
#13842256×4
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#13846256×4
#13847256×4
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#13850256×4
#13851256×4
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#20718256×4
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#21431256×4
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#21491256×4
#21566256×4
#21601256×4
#21635256×4
#21668256×4
#21676256×4
#21683256×4
#21715256×4
#34547256×4
#34551256×4
#34552256×4
#94849512×8
#94858512×8
#94859512×8
#94860512×8
#94861512×8
#105248512×8
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#105250512×8
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#105481512×8
#105482512×8
#108387512×8
#108388512×8
#108765512×8
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#109461512×8
#109462512×8
#110043512×8
#123423512×8
#123425512×8
#123507512×8
#123648512×8
#123852512×8
#123853512×8
#126561512×8
#126573512×8
#128210512×8
#128215512×8
#128252512×8
#128264512×8
#128272512×8
#128283512×8
#129046512×8
#129058512×8
#129066512×8
#129071512×8
#146365512×8
#146391512×8
#146809512×8
#146833512×8
#146943512×8
#146962512×8
#147112512×8
#147138512×8
#147350512×8
#147528512×8
#147955512×8
#148440512×8
#148663512×8
#148916512×8
#149101512×8
#149178512×8
#149291512×8
#149416512×8
#152002512×8
#152198512×8
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#152378512×8
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#152397512×8
#152411512×8
#152487512×8
#152791512×8
#152807512×8
#152846512×8
#152876512×8
#152998512×8
#153734512×8
#153736512×8
#153737512×8
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#153739512×8
#181859512×8
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#181869512×8
#181907512×8
#181922512×8
#183303512×8
#183318512×8
#183732512×8
#183741512×8
#183752512×8
#183775512×8
#183846512×8
#184055512×8
#184382512×8
#353564512×8
#353572512×8
#353717512×8
#353725512×8
#353759512×8
#353766512×8
#353836512×8
#353840512×8
#353987512×8
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#354127512×8
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#354295512×8
#354387512×8
#354466512×8
#354521512×8
#354619512×8
#354694512×8
#354759512×8
#354780512×8
#354838512×8
#354894512×8
#354967512×8
#355003512×8
#355041512×8
#358113512×8
#358372512×8
#358490512×8
#358617512×8
#358644512×8
#358724512×8
#358800512×8
#358838512×8
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#358920512×8
#358947512×8
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#493932512×8
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#6371227512×8
#6372546512×8
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#6373886512×8
#6374056512×8
#7627707512×8

The class itself is infinite — G × A is isoclinic to G for every abelian A, and there are abelian groups of every order — so a table shows the part of it the catalog names, never the whole.