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 ◆.

291 groups of the catalog are in this class; the 270 with an abelian direct factor are hidden.

group	order	× stem
D₃²	36	×1	◆ stem
D₃×Dic₃	72	×2
#624	72	×2
D₃×C₃⋊C₈	144	×4
#3710	144	×4
Dic₃²	144	×4
D₃×C₃⋊C₁₆	288	×8
#63542	288	×8
Dic₃×C₃⋊C₈	288	×8
#63553	288	×8
D₃×C₃⋊C₃₂	576	×16
#10589067	576	×16
C₃⋊C₈²	576	×16
Dic₃×C₃⋊C₁₆	576	×16
#10589102	576	×16
C₃⋊C₈×C₃⋊C₁₆	1,152	×32
#11771290	1,152	×32
Dic₃×C₃⋊C₃₂	1,152	×32
#11772653	1,152	×32
D₃×C₃⋊C₆₄	1,152	×32
#11773091	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.