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

203 groups of the catalog are in this class; the 181 with an abelian direct factor are hidden.

group	order	× stem
D₄₈	96	×1	◆ stem
#800	96	×1	◆ stem
Dic₂₄	96	×1	◆ stem
#4503	192	×2
#4504	192	×2
#4505	192	×2
#4506	192	×2
#4509	192	×2
#4510	192	×2
#4904	192	×2
#67441	384	×4
#67500	384	×4
#67501	384	×4
#67502	384	×4
#67504	384	×4
#67505	384	×4
#67806	384	×4
#67807	384	×4
#67808	384	×4
#69067	384	×4
#71404	384	×4
#71412	384	×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.