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 ◆.

1,428 groups of the catalog are in this class; the 1,277 with an abelian direct factor are hidden.

grouporder× stem
#45364×1◆ stem
#45464×1◆ stem
#45564×1◆ stem
#45664×1◆ stem
#1792128×2
#1793128×2
#1794128×2
#1856128×2
#1857128×2
#1858128×2
#1859128×2
#1860128×2
#1861128×2
#1881128×2
#1882128×2
#1883128×2
#1884128×2
#1885128×2
#1886128×2
#1887128×2
#1888128×2
#3018128×2
#8318256×4
#8319256×4
#8835256×4
#8836256×4
#8839256×4
#8840256×4
#8953256×4
#8954256×4
#8957256×4
#8958256×4
#8959256×4
#8960256×4
#10749256×4
#10750256×4
#10751256×4
#10752256×4
#10753256×4
#10779256×4
#10780256×4
#10781256×4
#10782256×4
#10891256×4
#10892256×4
#10893256×4
#10894256×4
#10899256×4
#10900256×4
#10901256×4
#10902256×4
#10956256×4
#10957256×4
#10958256×4
#10959256×4
#12685256×4
#12916256×4
#12918256×4
#12979256×4
#12982256×4
#20615256×4
#20855256×4
#20863256×4
#20942256×4
#20952256×4
#21477256×4
#106350512×8
#106351512×8
#106354512×8
#106356512×8
#106357512×8
#106360512×8
#106362512×8
#106363512×8
#106366512×8
#106404512×8
#106406512×8
#106408512×8
#106410512×8
#106412512×8
#106414512×8
#109498512×8
#109499512×8
#109502512×8
#109504512×8
#109505512×8
#109508512×8
#109522512×8
#109524512×8
#109526512×8
#109528512×8
#109530512×8
#109532512×8
#110062512×8
#110063512×8
#110066512×8
#110068512×8
#110070512×8
#110071512×8
#123487512×8
#123488512×8
#123489512×8
#123490512×8
#123491512×8
#123492512×8
#129647512×8
#129665512×8
#135853512×8
#135859512×8
#135864512×8
#135870512×8
#136743512×8
#136755512×8
#136767512×8
#136777512×8
#136787512×8
#136797512×8
#146377512×8
#146389512×8
#146403512×8
#146411512×8
#146417512×8
#146418512×8
#147120512×8
#147124512×8
#147141512×8
#147152512×8
#147153512×8
#147361512×8
#147368512×8
#152007512×8
#152414512×8
#152416512×8
#152489512×8
#152492512×8
#184929512×8
#191756512×8
#191808512×8
#193726512×8
#193788512×8
#353437512×8
#353458512×8
#353908512×8
#353926512×8
#354046512×8
#354311512×8
#354320512×8
#354475512×8
#354483512×8
#354829512×8
#495679512×8

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.