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

369 groups of the catalog are in this class; the 357 with an abelian direct factor are hidden.

group	order	× stem
#157	36	×1	◆ stem
#622	72	×2
#3708	144	×4
#3787	144	×4
#63540	288	×8
#63764	288	×8
#10589065	576	×16
#10590132	576	×16
#10590174	576	×16
#11770649	1,152	×32
#11772651	1,152	×32
#11773089	1,152	×32

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.