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

77 groups of the catalog are in this class; the 63 with an abelian direct factor are hidden.

group	order	× stem
AΓL(1,𝔽₉)	144	×1	◆ stem
GO⁺(4,𝔽₂)⋊C₄	288	×2
PSU(3,𝔽₂)⋊C₄	288	×2
AGL(1,𝔽₉)⋊C₄	288	×2
GO⁺(4,𝔽₂)⋊C₈	576	×4
PSU(3,𝔽₂)⋊C₈	576	×4
AGL(1,𝔽₉)⋊C₈	576	×4
#10593166	576	×4
#11770760	1,152	×8
#11770801	1,152	×8
#11770802	1,152	×8
GO⁺(4,𝔽₂)⋊C₁₆	1,152	×8
PSU(3,𝔽₂)⋊C₁₆	1,152	×8
AGL(1,𝔽₉)⋊C₁₆	1,152	×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.