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

862 groups of the catalog are in this class; the 822 with an abelian direct factor are hidden.

group	order	× stem
Dic₁₀	40	×1	◆ stem
D₂₀	40	×1	◆ stem
C₂²⋊D₅	40	×1	◆ stem
#676	80	×2
#681	80	×2
#683	80	×2
C₄⋊Dic₅	80	×2
#685	80	×2
C₂²⋊Dic₅	80	×2
#709	80	×2
#3930	160	×4
#3935	160	×4
C₄⋊#168	160	×4
#3944	160	×4
#3946	160	×4
#3947	160	×4
#3952	160	×4
C₂²⋊#168	160	×4
#3963	160	×4
#4018	160	×4
#4047	160	×4
#4072	160	×4
#64667	320	×8
#64674	320	×8
#64675	320	×8
#64681	320	×8
C₄⋊#672	320	×8
#64719	320	×8
#64721	320	×8
#64722	320	×8
#64727	320	×8
#64744	320	×8
C₂²⋊#672	320	×8
#64770	320	×8
#64974	320	×8
#64978	320	×8
#65190	320	×8
#65214	320	×8
#65221	320	×8
#65390	320	×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.