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 ◆.

272 groups of the catalog are in this class; the 258 with an abelian direct factor are hidden.

group	order	× stem
#226	48	×1	◆ stem
GL(2,𝔽₃)	48	×1	◆ stem
#859	96	×2
GU(2,𝔽₃)	96	×2
#985	96	×2
SL(2,𝔽₃)⋊C₈	192	×4
#4628	192	×4
#5404	192	×4
#5424	192	×4
SL(2,𝔽₃)⋊C₁₆	384	×8
#68006	384	×8
#73038	384	×8
#73068	384	×8
#73121	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.