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 ◆.

324 groups of the catalog are in this class; the 262 with an abelian direct factor are hidden.

group	order	× stem
#2199	128	×1	◆ stem
#2200	128	×1	◆ stem
#2201	128	×1	◆ stem
#12762	256	×2
#12763	256	×2
#12764	256	×2
#12766	256	×2
#12960	256	×2
#12961	256	×2
#12963	256	×2
#12966	256	×2
#12967	256	×2
#12969	256	×2
#13043	256	×2
#13044	256	×2
#13046	256	×2
#13049	256	×2
#13050	256	×2
#13052	256	×2
#33550	256	×2
#129610	512	×4
#129611	512	×4
#129612	512	×4
#129616	512	×4
#135940	512	×4
#135941	512	×4
#135947	512	×4
#135954	512	×4
#135955	512	×4
#135957	512	×4
#136819	512	×4
#136820	512	×4
#136823	512	×4
#136824	512	×4
#136830	512	×4
#136832	512	×4
#146601	512	×4
#146602	512	×4
#146604	512	×4
#146606	512	×4
#146608	512	×4
#146636	512	×4
#146638	512	×4
#146641	512	×4
#146642	512	×4
#146644	512	×4
#147330	512	×4
#147332	512	×4
#147334	512	×4
#147336	512	×4
#147338	512	×4
#147340	512	×4
#147342	512	×4
#147489	512	×4
#147491	512	×4
#147493	512	×4
#493581	512	×4
#494348	512	×4
#494369	512	×4
#494574	512	×4
#494595	512	×4
#495755	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.