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

1,468 groups of the catalog are in this class; the 1,403 with an abelian direct factor are hidden.

group	order	× stem
Dic₆	24	×1	◆ stem
D₁₂	24	×1	◆ stem
#67	24	×1	◆ stem
ΓL(1,𝔽₂₅)	48	×2
#208	48	×2
Dic₃⋊C₄	48	×2
C₄⋊Dic₃	48	×2
(C₂×D₃)⋊C₄	48	×2
#217	48	×2
#235	48	×2
#798	96	×4
#803	96	×4
C₄⋊(C₃⋊C₈)	96	×4
#812	96	×4
Dic₃⋊C₈	96	×4
#815	96	×4
(C₂×D₃)⋊C₈	96	×4
#830	96	×4
C₃⋊#95	96	×4
#872	96	×4
#901	96	×4
#926	96	×4
#4447	192	×8
#4454	192	×8
#4455	192	×8
#4461	192	×8
C₄⋊(C₃⋊C₁₆)	192	×8
#4499	192	×8
Dic₃⋊C₁₆	192	×8
#4502	192	×8
(C₂×D₃)⋊C₁₆	192	×8
#4524	192	×8
#4549	192	×8
#4550	192	×8
#4685	192	×8
#4689	192	×8
#4901	192	×8
#4925	192	×8
#4932	192	×8
#5101	192	×8
#67432	384	×16
#67437	384	×16
#67438	384	×16
#67498	384	×16
#67499	384	×16
#67508	384	×16
C₄⋊(C₃⋊C₃₂)	384	×16
#67587	384	×16
#67589	384	×16
Dic₃⋊C₃₂	384	×16
(C₂×D₃)⋊C₃₂	384	×16
C₃⋊#1273	384	×16
#67657	384	×16
#67803	384	×16
#67804	384	×16
#68047	384	×16
#69051	384	×16
#69052	384	×16
#69366	384	×16
#69388	384	×16
#69724	384	×16
#69744	384	×16
#69749	384	×16
#69750	384	×16
#71399	384	×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.