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 ◆.

3,141 groups of the catalog are in this class; the 500 smallest with no abelian direct factor are listed.

group	order	× stem
#3003	128	×1	◆ stem
#3004	128	×1	◆ stem
#3005	128	×1	◆ stem
#3006	128	×1	◆ stem
#3007	128	×1	◆ stem
#3036	128	×1	◆ stem
#3037	128	×1	◆ stem
#3038	128	×1	◆ stem
#3039	128	×1	◆ stem
#3040	128	×1	◆ stem
#3077	128	×1	◆ stem
#3078	128	×1	◆ stem
#3079	128	×1	◆ stem
#3080	128	×1	◆ stem
#3092	128	×1	◆ stem
#3093	128	×1	◆ stem
#3094	128	×1	◆ stem
#3095	128	×1	◆ stem
#3109	128	×1	◆ stem
#3110	128	×1	◆ stem
#3111	128	×1	◆ stem
#3112	128	×1	◆ stem
#3113	128	×1	◆ stem
#3114	128	×1	◆ stem
#3115	128	×1	◆ stem
#3116	128	×1	◆ stem
#3117	128	×1	◆ stem
#17448	256	×2
#17449	256	×2
#17450	256	×2
#17451	256	×2
#17452	256	×2
#17463	256	×2
#17464	256	×2
#17465	256	×2
#17466	256	×2
#17467	256	×2
#17807	256	×2
#17808	256	×2
#17809	256	×2
#17810	256	×2
#17869	256	×2
#17870	256	×2
#17871	256	×2
#17872	256	×2
#17905	256	×2
#17906	256	×2
#17907	256	×2
#17908	256	×2
#17909	256	×2
#17914	256	×2
#17915	256	×2
#17916	256	×2
#17917	256	×2
#20598	256	×2
#20599	256	×2
#20600	256	×2
#20601	256	×2
#20605	256	×2
#20646	256	×2
#20647	256	×2
#20648	256	×2
#20649	256	×2
#20654	256	×2
#20700	256	×2
#20701	256	×2
#20702	256	×2
#20705	256	×2
#20738	256	×2
#20739	256	×2
#20740	256	×2
#20741	256	×2
#20742	256	×2
#20743	256	×2
#20748	256	×2
#20844	256	×2
#20845	256	×2
#20846	256	×2
#20851	256	×2
#20873	256	×2
#20874	256	×2
#20875	256	×2
#20884	256	×2
#20902	256	×2
#20909	256	×2
#20910	256	×2
#20911	256	×2
#20912	256	×2
#20917	256	×2
#20925	256	×2
#20926	256	×2
#20927	256	×2
#20928	256	×2
#21033	256	×2
#21034	256	×2
#21041	256	×2
#21059	256	×2
#21060	256	×2
#21061	256	×2
#21070	256	×2
#21121	256	×2
#21122	256	×2
#21123	256	×2
#21124	256	×2
#21138	256	×2
#21170	256	×2
#21171	256	×2
#21172	256	×2
#21177	256	×2
#21252	256	×2
#21258	256	×2
#21259	256	×2
#21260	256	×2
#21261	256	×2
#21306	256	×2
#21312	256	×2
#21313	256	×2
#21314	256	×2
#21363	256	×2
#21364	256	×2
#21365	256	×2
#21366	256	×2
#21371	256	×2
#21383	256	×2
#21391	256	×2
#21392	256	×2
#21393	256	×2
#21394	256	×2
#21395	256	×2
#21396	256	×2
#21452	256	×2
#21453	256	×2
#21454	256	×2
#21455	256	×2
#21456	256	×2
#21457	256	×2
#21467	256	×2
#21503	256	×2
#21504	256	×2
#21505	256	×2
#21506	256	×2
#21507	256	×2
#21508	256	×2
#21518	256	×2
#21578	256	×2
#21579	256	×2
#21580	256	×2
#21581	256	×2
#21582	256	×2
#21583	256	×2
#21593	256	×2
#21613	256	×2
#21614	256	×2
#21615	256	×2
#21616	256	×2
#21617	256	×2
#21618	256	×2
#21628	256	×2
#60359	256	×2
#60415	256	×2
#60484	256	×2
#60511	256	×2
#60546	256	×2
#60558	256	×2
#60559	256	×2
#60560	256	×2
#60561	256	×2
#60562	256	×2
#60563	256	×2
#181431	512	×4
#181435	512	×4
#181436	512	×4
#181437	512	×4
#181438	512	×4
#181444	512	×4
#181445	512	×4
#181455	512	×4
#181456	512	×4
#181457	512	×4
#181458	512	×4
#181459	512	×4
#181460	512	×4
#181461	512	×4
#181462	512	×4
#182170	512	×4
#182171	512	×4
#182172	512	×4
#182182	512	×4
#182183	512	×4
#182184	512	×4
#182221	512	×4
#182222	512	×4
#182223	512	×4
#182227	512	×4
#182228	512	×4
#182229	512	×4
#182251	512	×4
#182252	512	×4
#182253	512	×4
#182257	512	×4
#182258	512	×4
#182259	512	×4
#182299	512	×4
#182302	512	×4
#182313	512	×4
#182321	512	×4
#182344	512	×4
#182349	512	×4
#182365	512	×4
#182367	512	×4
#182377	512	×4
#182379	512	×4
#182432	512	×4
#182433	512	×4
#182434	512	×4
#182447	512	×4
#182448	512	×4
#182449	512	×4
#182495	512	×4
#182496	512	×4
#182497	512	×4
#182501	512	×4
#182502	512	×4
#182503	512	×4
#182531	512	×4
#182532	512	×4
#182533	512	×4
#182537	512	×4
#182538	512	×4
#182539	512	×4
#183339	512	×4
#183347	512	×4
#183372	512	×4
#183373	512	×4
#183385	512	×4
#183386	512	×4
#183389	512	×4
#183390	512	×4
#183439	512	×4
#183440	512	×4
#183453	512	×4
#183454	512	×4
#183458	512	×4
#183459	512	×4
#183460	512	×4
#183506	512	×4
#183513	512	×4
#183515	512	×4
#184139	512	×4
#184140	512	×4
#184141	512	×4
#184142	512	×4
#184143	512	×4
#184144	512	×4
#184145	512	×4
#184146	512	×4
#184167	512	×4
#184168	512	×4
#184169	512	×4
#184170	512	×4
#184325	512	×4
#184326	512	×4
#184332	512	×4
#184333	512	×4
#184843	512	×4
#184844	512	×4
#184845	512	×4
#184846	512	×4
#188353	512	×4
#188354	512	×4
#188355	512	×4
#188356	512	×4
#189758	512	×4
#189759	512	×4
#189760	512	×4
#190820	512	×4
#190821	512	×4
#190822	512	×4
#190823	512	×4
#190824	512	×4
#190825	512	×4
#191658	512	×4
#191659	512	×4
#191660	512	×4
#191863	512	×4
#191864	512	×4
#191865	512	×4
#193423	512	×4
#193424	512	×4
#193425	512	×4
#193426	512	×4
#193537	512	×4
#193538	512	×4
#193539	512	×4
#193540	512	×4
#202185	512	×4
#202186	512	×4
#202321	512	×4
#202322	512	×4
#202323	512	×4
#203184	512	×4
#203185	512	×4
#203186	512	×4
#203187	512	×4
#203616	512	×4
#203617	512	×4
#203618	512	×4
#204486	512	×4
#204487	512	×4
#204488	512	×4
#204489	512	×4
#206708	512	×4
#206709	512	×4
#206710	512	×4
#207297	512	×4
#207298	512	×4
#207299	512	×4
#207300	512	×4
#207426	512	×4
#207427	512	×4
#207428	512	×4
#207429	512	×4
#207430	512	×4
#207431	512	×4
#208650	512	×4
#208651	512	×4
#208652	512	×4
#208653	512	×4
#208654	512	×4
#208655	512	×4
#210434	512	×4
#210435	512	×4
#210436	512	×4
#210437	512	×4
#210438	512	×4
#210439	512	×4
#212018	512	×4
#212019	512	×4
#212020	512	×4
#212021	512	×4
#212022	512	×4
#212023	512	×4
#212306	512	×4
#212307	512	×4
#212308	512	×4
#212309	512	×4
#212310	512	×4
#212311	512	×4
#353367	512	×4
#353368	512	×4
#353369	512	×4
#353374	512	×4
#353377	512	×4
#353392	512	×4
#353393	512	×4
#353394	512	×4
#353397	512	×4
#353400	512	×4
#353403	512	×4
#353503	512	×4
#353504	512	×4
#353508	512	×4
#353511	512	×4
#353593	512	×4
#353594	512	×4
#353598	512	×4
#353601	512	×4
#353677	512	×4
#353678	512	×4
#353679	512	×4
#353682	512	×4
#353685	512	×4
#353688	512	×4
#353810	512	×4
#353811	512	×4
#353812	512	×4
#353813	512	×4
#353816	512	×4
#353819	512	×4
#353822	512	×4
#353890	512	×4
#353891	512	×4
#353895	512	×4
#353898	512	×4
#353944	512	×4
#353945	512	×4
#353952	512	×4
#353956	512	×4
#353960	512	×4
#353995	512	×4
#354001	512	×4
#354017	512	×4
#354088	512	×4
#354089	512	×4
#354090	512	×4
#354095	512	×4
#354098	512	×4
#354145	512	×4
#354151	512	×4
#354152	512	×4
#354156	512	×4
#354213	512	×4
#354214	512	×4
#354215	512	×4
#354216	512	×4
#354220	512	×4
#354256	512	×4
#354257	512	×4
#354258	512	×4
#354259	512	×4
#354269	512	×4
#354308	512	×4
#354326	512	×4
#354343	512	×4
#354344	512	×4
#354352	512	×4
#354396	512	×4
#354422	512	×4
#354423	512	×4
#354427	512	×4
#354433	512	×4
#354434	512	×4
#354442	512	×4
#354473	512	×4
#354481	512	×4
#354501	512	×4
#354502	512	×4
#354510	512	×4
#354530	512	×4
#354565	512	×4
#354566	512	×4
#354567	512	×4
#354572	512	×4
#354631	512	×4
#354676	512	×4
#354677	512	×4
#354681	512	×4
#354709	512	×4
#354746	512	×4
#354747	512	×4
#354748	512	×4
#354752	512	×4
#354773	512	×4
#354808	512	×4
#354809	512	×4
#354810	512	×4
#354815	512	×4
#354818	512	×4
#354864	512	×4
#354865	512	×4
#354866	512	×4
#354870	512	×4
#354873	512	×4
#354943	512	×4
#354944	512	×4
#354945	512	×4
#354946	512	×4
#354950	512	×4
#354953	512	×4
#481116	512	×4
#481118	512	×4
#481138	512	×4
#481140	512	×4
#481160	512	×4
#481162	512	×4
#481184	512	×4
#481185	512	×4
#481188	512	×4
#481190	512	×4
#483358	512	×4
#483360	512	×4
#483370	512	×4
#483372	512	×4
#483558	512	×4
#483560	512	×4
#483571	512	×4
#483581	512	×4
#483613	512	×4
#483619	512	×4
#483623	512	×4
#483626	512	×4
#483628	512	×4
#483643	512	×4
#483647	512	×4
#483650	512	×4
#483652	512	×4
#493340	512	×4
#493676	512	×4
#493841	512	×4
#493943	512	×4
#494222	512	×4
#494229	512	×4
#494407	512	×4
#494412	512	×4
#494773	512	×4
#494829	512	×4
#494950	512	×4
#495015	512	×4
#495093	512	×4
#495331	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.