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 ◆.

1,319 groups of the catalog are in this class; the 1,174 with an abelian direct factor are hidden.

grouporder× stem
#47164×1◆ stem
#47264×1◆ stem
#47364×1◆ stem
#1814128×2
#1815128×2
#1816128×2
#1906128×2
#1907128×2
#1908128×2
#1930128×2
#1931128×2
#1932128×2
#1951128×2
#1952128×2
#1953128×2
#1976128×2
#1977128×2
#1978128×2
#1979128×2
#3067128×2
#8604256×4
#8605256×4
#9095256×4
#9096256×4
#9549256×4
#9550256×4
#9607256×4
#9608256×4
#9667256×4
#9668256×4
#9669256×4
#10772256×4
#10773256×4
#10774256×4
#10826256×4
#10827256×4
#10828256×4
#10869256×4
#10870256×4
#10871256×4
#10872256×4
#10873256×4
#10895256×4
#10896256×4
#10897256×4
#10898256×4
#10942256×4
#10943256×4
#10944256×4
#10945256×4
#10946256×4
#12792256×4
#12987256×4
#13123256×4
#13164256×4
#13197256×4
#20678256×4
#21003256×4
#21075256×4
#21181256×4
#21248256×4
#21558256×4
#105632512×8
#105634512×8
#105636512×8
#105638512×8
#108546512×8
#108548512×8
#108550512×8
#108552512×8
#109158512×8
#109159512×8
#109162512×8
#109164512×8
#109165512×8
#109168512×8
#109170512×8
#109171512×8
#109174512×8
#109510512×8
#109512512×8
#109514512×8
#109516512×8
#109518512×8
#109520512×8
#110327512×8
#110328512×8
#110331512×8
#110333512×8
#110334512×8
#110337512×8
#110339512×8
#110340512×8
#110343512×8
#123467512×8
#123468512×8
#123469512×8
#123470512×8
#123471512×8
#123472512×8
#134715512×8
#134723512×8
#137860512×8
#137872512×8
#140154512×8
#140158512×8
#140409512×8
#140413512×8
#140795512×8
#140803512×8
#140811512×8
#146386512×8
#146414512×8
#146826512×8
#146844512×8
#146956512×8
#146974512×8
#146975512×8
#147122512×8
#147145512×8
#147148512×8
#147359512×8
#147366512×8
#147371512×8
#152206512×8
#152497512×8
#152809512×8
#152850512×8
#152883512×8
#188780512×8
#196172512×8
#202478512×8
#203710512×8
#204429512×8
#353356512×8
#353548512×8
#353708512×8
#353918512×8
#354109512×8
#354318512×8
#354399512×8
#354641512×8
#354711512×8
#354955512×8
#495804512×8

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.