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 ◆.

1,404 groups of the catalog are in this class; the 1,260 with an abelian direct factor are hidden.

group	order	× stem
#1343	128	×1	◆ stem
#1344	128	×1	◆ stem
#1345	128	×1	◆ stem
#1346	128	×1	◆ stem
#1351	128	×1	◆ stem
#1352	128	×1	◆ stem
#1353	128	×1	◆ stem
#1354	128	×1	◆ stem
#7058	256	×2
#7059	256	×2
#7060	256	×2
#7061	256	×2
#7065	256	×2
#7066	256	×2
#7067	256	×2
#7103	256	×2
#7104	256	×2
#7105	256	×2
#7122	256	×2
#7123	256	×2
#7124	256	×2
#7131	256	×2
#7132	256	×2
#7133	256	×2
#7250	256	×2
#7251	256	×2
#7252	256	×2
#7253	256	×2
#7282	256	×2
#7283	256	×2
#7284	256	×2
#7285	256	×2
#7286	256	×2
#7287	256	×2
#11691	256	×2
#11697	256	×2
#11715	256	×2
#11721	256	×2
#11725	256	×2
#11726	256	×2
#11727	256	×2
#11728	256	×2
#11733	256	×2
#11734	256	×2
#11735	256	×2
#11736	256	×2
#92815	512	×4
#92816	512	×4
#92871	512	×4
#92872	512	×4
#92886	512	×4
#92887	512	×4
#92987	512	×4
#92988	512	×4
#92989	512	×4
#92990	512	×4
#92991	512	×4
#92992	512	×4
#92993	512	×4
#92994	512	×4
#93007	512	×4
#93008	512	×4
#93009	512	×4
#93010	512	×4
#93372	512	×4
#93373	512	×4
#93374	512	×4
#93375	512	×4
#93398	512	×4
#93399	512	×4
#93400	512	×4
#93401	512	×4
#93412	512	×4
#93413	512	×4
#93414	512	×4
#93426	512	×4
#93427	512	×4
#93428	512	×4
#93670	512	×4
#93682	512	×4
#93688	512	×4
#93696	512	×4
#93718	512	×4
#93724	512	×4
#93731	512	×4
#93887	512	×4
#93929	512	×4
#93969	512	×4
#122260	512	×4
#122278	512	×4
#122328	512	×4
#122345	512	×4
#122398	512	×4
#122399	512	×4
#122414	512	×4
#122415	512	×4
#122416	512	×4
#122417	512	×4
#124049	512	×4
#124089	512	×4
#124121	512	×4
#124137	512	×4
#124138	512	×4
#124139	512	×4
#124140	512	×4
#124145	512	×4
#124149	512	×4
#124150	512	×4
#124151	512	×4
#124155	512	×4
#124167	512	×4
#124168	512	×4
#124169	512	×4
#124170	512	×4
#124175	512	×4
#124191	512	×4
#124192	512	×4
#124193	512	×4
#124194	512	×4
#124199	512	×4
#127492	512	×4
#127496	512	×4
#127529	512	×4
#127530	512	×4
#127533	512	×4
#127534	512	×4
#127537	512	×4
#127539	512	×4
#127792	512	×4
#127796	512	×4
#127800	512	×4
#127832	512	×4
#127836	512	×4
#127840	512	×4
#128767	512	×4
#128792	512	×4
#128959	512	×4
#128960	512	×4
#128963	512	×4
#128964	512	×4
#128967	512	×4
#128968	512	×4
#481511	512	×4
#481533	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.