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

572 groups of the catalog are in this class; the 532 with an abelian direct factor are hidden.

group	order	× stem
#204	48	×1	◆ stem
D₂₄	48	×1	◆ stem
Dic₁₂	48	×1	◆ stem
#805	96	×2
#816	96	×2
#817	96	×2
#818	96	×2
#819	96	×2
#821	96	×2
#904	96	×2
#4456	192	×4
#4457	192	×4
#4458	192	×4
#4459	192	×4
#4463	192	×4
#4508	192	×4
#4523	192	×4
#4551	192	×4
#4552	192	×4
#4700	192	×4
#5106	192	×4
#5113	192	×4
#67439	384	×8
#67440	384	×8
#67503	384	×8
#67506	384	×8
#67510	384	×8
#67595	384	×8
#67611	384	×8
#67654	384	×8
#67655	384	×8
#67656	384	×8
#67658	384	×8
#67805	384	×8
#69056	384	×8
#69729	384	×8
#69734	384	×8
#69779	384	×8
#69789	384	×8
#71969	384	×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.