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 ◆.

458 groups of the catalog are in this class; the 388 with an abelian direct factor are hidden.

group	order	× stem
#2121	128	×1	◆ stem
#2122	128	×1	◆ stem
#2123	128	×1	◆ stem
#11426	256	×2
#11427	256	×2
#11428	256	×2
#11436	256	×2
#11453	256	×2
#11454	256	×2
#11458	256	×2
#11473	256	×2
#11474	256	×2
#11484	256	×2
#12574	256	×2
#12575	256	×2
#12577	256	×2
#12579	256	×2
#12621	256	×2
#12622	256	×2
#12624	256	×2
#33347	256	×2
#122225	512	×4
#122226	512	×4
#122227	512	×4
#122314	512	×4
#122315	512	×4
#122360	512	×4
#122361	512	×4
#126909	512	×4
#126910	512	×4
#126912	512	×4
#126920	512	×4
#126922	512	×4
#126948	512	×4
#126950	512	×4
#126958	512	×4
#127067	512	×4
#127068	512	×4
#127071	512	×4
#127072	512	×4
#127082	512	×4
#128306	512	×4
#128307	512	×4
#128309	512	×4
#128317	512	×4
#128319	512	×4
#128343	512	×4
#128345	512	×4
#128351	512	×4
#128353	512	×4
#128451	512	×4
#128452	512	×4
#128462	512	×4
#146349	512	×4
#146351	512	×4
#146353	512	×4
#146361	512	×4
#149524	512	×4
#149608	512	×4
#149670	512	×4
#479996	512	×4
#480039	512	×4
#480093	512	×4
#480094	512	×4
#480095	512	×4
#480096	512	×4
#480124	512	×4
#492886	512	×4
#492990	512	×4
#492999	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.