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

371 groups of the catalog are in this class; the 309 with an abelian direct factor are hidden.

group	order	× stem
#2196	128	×1	◆ stem
#2197	128	×1	◆ stem
#2198	128	×1	◆ stem
#12759	256	×2
#12760	256	×2
#12761	256	×2
#12765	256	×2
#12958	256	×2
#12959	256	×2
#12962	256	×2
#12964	256	×2
#12965	256	×2
#12968	256	×2
#13041	256	×2
#13042	256	×2
#13045	256	×2
#13047	256	×2
#13048	256	×2
#13051	256	×2
#33546	256	×2
#129607	512	×4
#129608	512	×4
#129609	512	×4
#129615	512	×4
#135938	512	×4
#135939	512	×4
#135946	512	×4
#135952	512	×4
#135953	512	×4
#135956	512	×4
#136817	512	×4
#136818	512	×4
#136821	512	×4
#136822	512	×4
#136829	512	×4
#136831	512	×4
#146599	512	×4
#146600	512	×4
#146603	512	×4
#146605	512	×4
#146607	512	×4
#146635	512	×4
#146637	512	×4
#146639	512	×4
#146640	512	×4
#146643	512	×4
#147329	512	×4
#147331	512	×4
#147333	512	×4
#147335	512	×4
#147337	512	×4
#147339	512	×4
#147341	512	×4
#147488	512	×4
#147490	512	×4
#147492	512	×4
#493577	512	×4
#494345	512	×4
#494366	512	×4
#494571	512	×4
#494592	512	×4
#495753	512	×4

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.