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

485 groups of the catalog are in this class; the 401 with an abelian direct factor are hidden.

group	order	× stem
#1902	128	×1	◆ stem
#1903	128	×1	◆ stem
#1904	128	×1	◆ stem
#1905	128	×1	◆ stem
#9087	256	×2
#9088	256	×2
#9089	256	×2
#9090	256	×2
#10783	256	×2
#10784	256	×2
#10785	256	×2
#10786	256	×2
#10787	256	×2
#10903	256	×2
#10904	256	×2
#10905	256	×2
#10906	256	×2
#10951	256	×2
#10952	256	×2
#10953	256	×2
#10954	256	×2
#10955	256	×2
#12986	256	×2
#20995	256	×2
#20998	256	×2
#106416	512	×4
#106418	512	×4
#106419	512	×4
#106422	512	×4
#106423	512	×4
#106426	512	×4
#106428	512	×4
#106430	512	×4
#106431	512	×4
#109534	512	×4
#109536	512	×4
#109538	512	×4
#109540	512	×4
#109542	512	×4
#109544	512	×4
#110345	512	×4
#110346	512	×4
#110349	512	×4
#110351	512	×4
#110353	512	×4
#110354	512	×4
#110357	512	×4
#110359	512	×4
#110360	512	×4
#123499	512	×4
#123500	512	×4
#123501	512	×4
#123502	512	×4
#123503	512	×4
#123504	512	×4
#123505	512	×4
#123506	512	×4
#137820	512	×4
#137830	512	×4
#137840	512	×4
#137850	512	×4
#146388	512	×4
#146416	512	×4
#146419	512	×4
#147123	512	×4
#147143	512	×4
#147150	512	×4
#147356	512	×4
#147365	512	×4
#147370	512	×4
#152496	512	×4
#196078	512	×4
#196079	512	×4
#196080	512	×4
#196081	512	×4
#196082	512	×4
#353465	512	×4
#353468	512	×4
#353936	512	×4
#353938	512	×4
#354122	512	×4
#354124	512	×4
#354322	512	×4
#494428	512	×4

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.