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 ◆.

2,349 groups of the catalog are in this class; the 1,961 with an abelian direct factor are hidden.

group	order	× stem
#1595	128	×1	◆ stem
#1596	128	×1	◆ stem
#1597	128	×1	◆ stem
#1598	128	×1	◆ stem
#1599	128	×1	◆ stem
#1600	128	×1	◆ stem
#1601	128	×1	◆ stem
#1602	128	×1	◆ stem
#1603	128	×1	◆ stem
#1604	128	×1	◆ stem
#1605	128	×1	◆ stem
#1606	128	×1	◆ stem
#1607	128	×1	◆ stem
#1608	128	×1	◆ stem
#1609	128	×1	◆ stem
#1610	128	×1	◆ stem
#1611	128	×1	◆ stem
#1612	128	×1	◆ stem
#1613	128	×1	◆ stem
#1614	128	×1	◆ stem
#1615	128	×1	◆ stem
#1616	128	×1	◆ stem
#1617	128	×1	◆ stem
#1618	128	×1	◆ stem
#8399	256	×2
#8400	256	×2
#8401	256	×2
#8402	256	×2
#8403	256	×2
#8404	256	×2
#8405	256	×2
#8406	256	×2
#8407	256	×2
#8408	256	×2
#8409	256	×2
#8410	256	×2
#8411	256	×2
#8853	256	×2
#8854	256	×2
#8855	256	×2
#8856	256	×2
#8857	256	×2
#8858	256	×2
#8859	256	×2
#8860	256	×2
#8861	256	×2
#8862	256	×2
#8863	256	×2
#8864	256	×2
#8865	256	×2
#8866	256	×2
#8867	256	×2
#8868	256	×2
#8869	256	×2
#8870	256	×2
#8871	256	×2
#8872	256	×2
#8873	256	×2
#8874	256	×2
#8875	256	×2
#8876	256	×2
#8877	256	×2
#8878	256	×2
#8879	256	×2
#8880	256	×2
#8881	256	×2
#9009	256	×2
#9010	256	×2
#9011	256	×2
#9012	256	×2
#9013	256	×2
#9014	256	×2
#9015	256	×2
#9016	256	×2
#9017	256	×2
#9018	256	×2
#9019	256	×2
#9020	256	×2
#9021	256	×2
#9022	256	×2
#9023	256	×2
#9024	256	×2
#9025	256	×2
#9026	256	×2
#9027	256	×2
#9028	256	×2
#9029	256	×2
#9030	256	×2
#9031	256	×2
#9032	256	×2
#9033	256	×2
#9034	256	×2
#9035	256	×2
#9036	256	×2
#9037	256	×2
#9038	256	×2
#9039	256	×2
#9040	256	×2
#9041	256	×2
#9042	256	×2
#9043	256	×2
#9044	256	×2
#9045	256	×2
#9046	256	×2
#9047	256	×2
#9048	256	×2
#9049	256	×2
#9050	256	×2
#9051	256	×2
#9052	256	×2
#18100	256	×2
#18107	256	×2
#18114	256	×2
#18121	256	×2
#18122	256	×2
#18123	256	×2
#18124	256	×2
#18125	256	×2
#18126	256	×2
#18127	256	×2
#18128	256	×2
#18129	256	×2
#18130	256	×2
#18131	256	×2
#96950	512	×4
#96951	512	×4
#96952	512	×4
#96953	512	×4
#96954	512	×4
#96955	512	×4
#99313	512	×4
#99314	512	×4
#99315	512	×4
#99316	512	×4
#99317	512	×4
#99318	512	×4
#99423	512	×4
#99424	512	×4
#99425	512	×4
#99426	512	×4
#99427	512	×4
#99428	512	×4
#99429	512	×4
#99430	512	×4
#99547	512	×4
#99548	512	×4
#99549	512	×4
#99550	512	×4
#99551	512	×4
#99552	512	×4
#99553	512	×4
#99554	512	×4
#99555	512	×4
#99556	512	×4
#99557	512	×4
#99558	512	×4
#99559	512	×4
#99560	512	×4
#99561	512	×4
#99562	512	×4
#99579	512	×4
#99580	512	×4
#99581	512	×4
#99582	512	×4
#99583	512	×4
#99584	512	×4
#99585	512	×4
#99586	512	×4
#106822	512	×4
#106823	512	×4
#106824	512	×4
#106825	512	×4
#106826	512	×4
#106827	512	×4
#106828	512	×4
#106829	512	×4
#106830	512	×4
#106831	512	×4
#106832	512	×4
#106833	512	×4
#106834	512	×4
#106835	512	×4
#106836	512	×4
#106837	512	×4
#106838	512	×4
#106839	512	×4
#106840	512	×4
#106841	512	×4
#106842	512	×4
#106843	512	×4
#106844	512	×4
#106845	512	×4
#106846	512	×4
#106847	512	×4
#106848	512	×4
#106849	512	×4
#107986	512	×4
#107987	512	×4
#107988	512	×4
#107989	512	×4
#107990	512	×4
#107991	512	×4
#107992	512	×4
#107993	512	×4
#107994	512	×4
#107995	512	×4
#107996	512	×4
#107997	512	×4
#107998	512	×4
#107999	512	×4
#108000	512	×4
#108001	512	×4
#108002	512	×4
#108003	512	×4
#108004	512	×4
#108005	512	×4
#109916	512	×4
#109917	512	×4
#109918	512	×4
#109919	512	×4
#109920	512	×4
#109921	512	×4
#109922	512	×4
#109923	512	×4
#109924	512	×4
#109925	512	×4
#109926	512	×4
#109927	512	×4
#109928	512	×4
#109929	512	×4
#109930	512	×4
#109931	512	×4
#109932	512	×4
#109933	512	×4
#109934	512	×4
#109951	512	×4
#109952	512	×4
#109953	512	×4
#109954	512	×4
#109955	512	×4
#109956	512	×4
#109957	512	×4
#109958	512	×4
#109959	512	×4
#109960	512	×4
#109961	512	×4
#109962	512	×4
#109963	512	×4
#109964	512	×4
#109965	512	×4
#109966	512	×4
#109967	512	×4
#109968	512	×4
#109969	512	×4
#109970	512	×4
#110598	512	×4
#110599	512	×4
#110600	512	×4
#110601	512	×4
#110602	512	×4
#110603	512	×4
#110604	512	×4
#110605	512	×4
#110606	512	×4
#110607	512	×4
#110608	512	×4
#110609	512	×4
#110610	512	×4
#110611	512	×4
#110612	512	×4
#110613	512	×4
#110614	512	×4
#110615	512	×4
#110616	512	×4
#129498	512	×4
#129531	512	×4
#129547	512	×4
#129573	512	×4
#129574	512	×4
#129650	512	×4
#129668	512	×4
#135812	512	×4
#135825	512	×4
#135837	512	×4
#135857	512	×4
#135861	512	×4
#135868	512	×4
#135874	512	×4
#135879	512	×4
#135897	512	×4
#135902	512	×4
#135917	512	×4
#135936	512	×4
#135937	512	×4
#135950	512	×4
#135951	512	×4
#136576	512	×4
#136584	512	×4
#136592	512	×4
#136622	512	×4
#136651	512	×4
#136661	512	×4
#136671	512	×4
#136713	512	×4
#136748	512	×4
#136760	512	×4
#136771	512	×4
#136781	512	×4
#136791	512	×4
#136801	512	×4
#136809	512	×4
#136810	512	×4
#136811	512	×4
#136837	512	×4
#136838	512	×4
#136839	512	×4
#185853	512	×4
#185885	512	×4
#185921	512	×4
#185924	512	×4
#185927	512	×4
#185928	512	×4
#185929	512	×4
#185930	512	×4
#185931	512	×4
#186074	512	×4
#192061	512	×4
#192065	512	×4
#192066	512	×4
#192067	512	×4
#192068	512	×4
#192069	512	×4
#192070	512	×4
#192188	512	×4
#192221	512	×4
#192260	512	×4
#192298	512	×4
#192303	512	×4
#192304	512	×4
#192305	512	×4
#192306	512	×4
#192307	512	×4
#192308	512	×4
#192309	512	×4
#192456	512	×4
#192492	512	×4
#192534	512	×4
#194656	512	×4
#194704	512	×4
#194709	512	×4
#194714	512	×4
#194719	512	×4
#194720	512	×4
#194721	512	×4
#194722	512	×4
#194723	512	×4
#194724	512	×4
#194725	512	×4
#194726	512	×4
#194727	512	×4
#194964	512	×4
#195018	512	×4
#195064	512	×4
#195114	512	×4
#195119	512	×4
#195120	512	×4
#195121	512	×4
#195122	512	×4
#195123	512	×4
#195124	512	×4
#195125	512	×4
#195354	512	×4
#195424	512	×4
#209028	512	×4
#209029	512	×4
#209030	512	×4
#209031	512	×4
#209060	512	×4
#209061	512	×4
#209062	512	×4
#209063	512	×4
#209064	512	×4
#209065	512	×4
#209108	512	×4
#209109	512	×4
#209110	512	×4
#209111	512	×4
#6346371	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.