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

120 groups of the catalog are in this class; the 87 with an abelian direct factor are hidden.

group	order	× stem
D₃×AGL(1,𝔽₅)	120	×1	◆ stem
Dic₃×AGL(1,𝔽₅)	240	×2
D₃×#170	240	×2
#6738	240	×2
AGL(1,𝔽₅)×C₃⋊C₈	480	×4
ΓL(1,𝔽₁₆)⋊C₈	480	×4
D₃×#674	480	×4
#91164	480	×4
Dic₃×#170	480	×4
D₃×D₅⋊C₈	480	×4
AGL(1,𝔽₅)×C₃⋊C₁₆	960	×8
ΓL(1,𝔽₁₆)⋊C₁₆	960	×8
D₃×#3928	960	×8
#11746481	960	×8
C₃⋊C₈×#170	960	×8
Dic₃×#674	960	×8
#11746541	960	×8
D₃×D₅⋊C₁₆	960	×8
Dic₃×D₅⋊C₈	960	×8
#170×C₃⋊C₁₆	1,920	×16
#14277448	1,920	×16
C₃⋊C₈×#674	1,920	×16
AGL(1,𝔽₅)×C₃⋊C₃₂	1,920	×16
ΓL(1,𝔽₁₆)⋊C₃₂	1,920	×16
Dic₃×#3928	1,920	×16
#14279198	1,920	×16
D₃×#64665	1,920	×16
#14279789	1,920	×16
C₃⋊C₈×D₅⋊C₈	1,920	×16
D₃×#64885	1,920	×16
#14312537	1,920	×16
Dic₃×D₅⋊C₁₆	1,920	×16
D₃×D₅⋊C₃₂	1,920	×16

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.