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 ◆.

343 groups of the catalog are in this class; the 297 with an abelian direct factor are hidden.

group	order	× stem
#1828	128	×1	◆ stem
#1829	128	×1	◆ stem
#1830	128	×1	◆ stem
#8734	256	×2
#8735	256	×2
#10768	256	×2
#10769	256	×2
#10770	256	×2
#10771	256	×2
#10829	256	×2
#10830	256	×2
#10831	256	×2
#12851	256	×2
#20710	256	×2
#20713	256	×2
#105604	512	×4
#105605	512	×4
#105608	512	×4
#105610	512	×4
#105612	512	×4
#105613	512	×4
#108554	512	×4
#108556	512	×4
#108558	512	×4
#108560	512	×4
#123477	512	×4
#123478	512	×4
#123479	512	×4
#123480	512	×4
#135457	512	×4
#135463	512	×4
#146382	512	×4
#146406	512	×4
#146827	512	×4
#146845	512	×4
#152309	512	×4
#190012	512	×4
#190013	512	×4
#190014	512	×4
#190015	512	×4
#353346	512	×4
#353349	512	×4
#353553	512	×4
#353555	512	×4
#354856	512	×4
#493848	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.