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

1,158 groups of the catalog are in this class; the 1,118 with an abelian direct factor are hidden.

group	order	× stem
D₃₂	64	×1	◆ stem
SD₆₄	64	×1	◆ stem
Q₆₄	64	×1	◆ stem
#1415	128	×2
#1416	128	×2
#1417	128	×2
#1423	128	×2
#1424	128	×2
#1425	128	×2
#2262	128	×2
#7383	256	×4
#7384	256	×4
#7387	256	×4
#7460	256	×4
#7461	256	×4
#7462	256	×4
#7471	256	×4
#7472	256	×4
#7473	256	×4
#13615	256	×4
#13633	256	×4
#13655	256	×4
#93747	512	×8
#93748	512	×8
#93751	512	×8
#93880	512	×8
#93881	512	×8
#93882	512	×8
#94021	512	×8
#94022	512	×8
#94027	512	×8
#94044	512	×8
#94045	512	×8
#94052	512	×8
#150056	512	×8
#151032	512	×8
#151081	512	×8
#151765	512	×8
#151963	512	×8
#151995	512	×8

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.