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 ◆.

1,130 groups of the catalog are in this class; the 938 with an abelian direct factor are hidden.

group	order	× stem
#1284	128	×1	◆ stem
#1285	128	×1	◆ stem
#1286	128	×1	◆ stem
#1287	128	×1	◆ stem
#1288	128	×1	◆ stem
#1289	128	×1	◆ stem
#1290	128	×1	◆ stem
#1291	128	×1	◆ stem
#1292	128	×1	◆ stem
#1293	128	×1	◆ stem
#7017	256	×2
#7018	256	×2
#7019	256	×2
#7020	256	×2
#7021	256	×2
#7022	256	×2
#7023	256	×2
#7024	256	×2
#7143	256	×2
#7144	256	×2
#7146	256	×2
#7147	256	×2
#7149	256	×2
#7152	256	×2
#7164	256	×2
#7168	256	×2
#7184	256	×2
#7196	256	×2
#7200	256	×2
#7210	256	×2
#7940	256	×2
#7941	256	×2
#7942	256	×2
#7948	256	×2
#7949	256	×2
#7950	256	×2
#7956	256	×2
#7957	256	×2
#7958	256	×2
#7964	256	×2
#7965	256	×2
#7966	256	×2
#7972	256	×2
#7973	256	×2
#7974	256	×2
#7980	256	×2
#7981	256	×2
#7982	256	×2
#7986	256	×2
#7987	256	×2
#7988	256	×2
#7992	256	×2
#7993	256	×2
#7994	256	×2
#8000	256	×2
#8001	256	×2
#8002	256	×2
#8006	256	×2
#8007	256	×2
#8008	256	×2
#92806	512	×4
#92899	512	×4
#92900	512	×4
#92903	512	×4
#93250	512	×4
#93251	512	×4
#93258	512	×4
#93261	512	×4
#93275	512	×4
#93279	512	×4
#93288	512	×4
#93304	512	×4
#93315	512	×4
#93323	512	×4
#93339	512	×4
#93344	512	×4
#93352	512	×4
#93356	512	×4
#93999	512	×4
#94000	512	×4
#94006	512	×4
#94007	512	×4
#94011	512	×4
#94016	512	×4
#94033	512	×4
#94037	512	×4
#94061	512	×4
#94117	512	×4
#94123	512	×4
#94165	512	×4
#94955	512	×4
#94956	512	×4
#94957	512	×4
#94958	512	×4
#94959	512	×4
#94995	512	×4
#94996	512	×4
#94997	512	×4
#94998	512	×4
#94999	512	×4
#95031	512	×4
#95032	512	×4
#95033	512	×4
#95034	512	×4
#95035	512	×4
#95067	512	×4
#95068	512	×4
#95069	512	×4
#95070	512	×4
#95071	512	×4
#95072	512	×4
#95073	512	×4
#95423	512	×4
#95424	512	×4
#95425	512	×4
#95426	512	×4
#95427	512	×4
#95428	512	×4
#95429	512	×4
#95487	512	×4
#95488	512	×4
#95489	512	×4
#95490	512	×4
#95491	512	×4
#95492	512	×4
#95493	512	×4
#95551	512	×4
#95552	512	×4
#95553	512	×4
#95554	512	×4
#95555	512	×4
#95556	512	×4
#95557	512	×4
#95615	512	×4
#95616	512	×4
#95617	512	×4
#95618	512	×4
#95619	512	×4
#95620	512	×4
#95621	512	×4
#105313	512	×4
#105319	512	×4
#105321	512	×4
#105323	512	×4
#105325	512	×4
#105327	512	×4
#105398	512	×4
#105404	512	×4
#105406	512	×4
#126586	512	×4
#126589	512	×4
#126595	512	×4
#126598	512	×4
#126599	512	×4
#126606	512	×4
#126609	512	×4
#126615	512	×4
#126616	512	×4
#126618	512	×4
#126619	512	×4
#126626	512	×4
#126627	512	×4
#126646	512	×4
#126671	512	×4
#126672	512	×4
#126729	512	×4
#126730	512	×4
#126731	512	×4
#126761	512	×4
#126798	512	×4
#126799	512	×4
#126930	512	×4
#126940	512	×4
#126964	512	×4
#127029	512	×4
#127040	512	×4
#127055	512	×4
#127089	512	×4
#127091	512	×4
#127157	512	×4
#127171	512	×4
#127173	512	×4
#181116	512	×4
#181143	512	×4
#181167	512	×4
#181191	512	×4
#181212	512	×4
#181236	512	×4
#181262	512	×4
#181281	512	×4
#181302	512	×4
#181321	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.