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

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

group	order	× stem
D₃×D₅	60	×1	◆ stem
D₅×Dic₃	120	×2
D₃×Dic₅	120	×2
#1200	120	×2
D₅×C₃⋊C₈	240	×4
D₃×#168	240	×4
#6648	240	×4
Dic₃×Dic₅	240	×4
D₅×C₃⋊C₁₆	480	×8
D₃×#672	480	×8
#90933	480	×8
Dic₅×C₃⋊C₈	480	×8
Dic₃×#168	480	×8
#90951	480	×8
D₅×C₃⋊C₃₂	960	×16
D₃×#3926	960	×16
#11745814	960	×16
C₃⋊C₈×#168	960	×16
Dic₅×C₃⋊C₁₆	960	×16
Dic₃×#672	960	×16
#11745872	960	×16
#168×C₃⋊C₁₆	1,920	×32
#14277445	1,920	×32
C₃⋊C₈×#672	1,920	×32
Dic₅×C₃⋊C₃₂	1,920	×32
#14279193	1,920	×32
Dic₃×#3926	1,920	×32
D₅×C₃⋊C₆₄	1,920	×32
#14279786	1,920	×32
D₃×#64663	1,920	×32

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.