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 ◆.

258 groups of the catalog are in this class; the 221 with an abelian direct factor are hidden.

group	order	× stem
#2263	128	×1	◆ stem
#2264	128	×1	◆ stem
#13616	256	×2
#13617	256	×2
#13618	256	×2
#13620	256	×2
#13634	256	×2
#13636	256	×2
#13652	256	×2
#13653	256	×2
#13654	256	×2
#13656	256	×2
#33981	256	×2
#150057	512	×4
#150058	512	×4
#150059	512	×4
#150067	512	×4
#151033	512	×4
#151035	512	×4
#151078	512	×4
#151079	512	×4
#151080	512	×4
#151082	512	×4
#151766	512	×4
#151768	512	×4
#151772	512	×4
#151959	512	×4
#151960	512	×4
#151962	512	×4
#151964	512	×4
#151992	512	×4
#151994	512	×4
#151996	512	×4
#512690	512	×4
#512716	512	×4
#512761	512	×4
#512773	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.