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 ◆.

799 groups of the catalog are in this class; the 742 with an abelian direct factor are hidden.

group	order	× stem
#213	48	×1	◆ stem
#214	48	×1	◆ stem
#215	48	×1	◆ stem
#216	48	×1	◆ stem
#807	96	×2
#808	96	×2
#809	96	×2
#810	96	×2
#822	96	×2
#825	96	×2
#832	96	×2
#835	96	×2
#837	96	×2
#950	96	×2
#4479	192	×4
#4480	192	×4
#4483	192	×4
#4484	192	×4
#4511	192	×4
#4515	192	×4
#4529	192	×4
#4532	192	×4
D₄⋊(C₃⋊C₈)	192	×4
#4535	192	×4
#4555	192	×4
#4558	192	×4
#4561	192	×4
#4998	192	×4
#5002	192	×4
#5144	192	×4
#5233	192	×4
#67554	384	×8
#67555	384	×8
#67556	384	×8
#67558	384	×8
#67599	384	×8
#67603	384	×8
#67619	384	×8
#67667	384	×8
#67671	384	×8
#67703	384	×8
#67704	384	×8
#67736	384	×8
#67739	384	×8
D₄⋊(C₃⋊C₁₆)	384	×8
#67768	384	×8
#67810	384	×8
#67815	384	×8
#67823	384	×8
#69887	384	×8
#69889	384	×8
#70745	384	×8
#70754	384	×8
#71452	384	×8
#71580	384	×8
#71638	384	×8
#72008	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.