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 ◆.

3,226 groups of the catalog are in this class; the 2,779 with an abelian direct factor are hidden.

group	order	× stem
#1619	128	×1	◆ stem
#1620	128	×1	◆ stem
#1621	128	×1	◆ stem
#1622	128	×1	◆ stem
#1623	128	×1	◆ stem
#1624	128	×1	◆ stem
#1625	128	×1	◆ stem
#1626	128	×1	◆ stem
#1627	128	×1	◆ stem
#1628	128	×1	◆ stem
#1629	128	×1	◆ stem
#1630	128	×1	◆ stem
#1631	128	×1	◆ stem
#1632	128	×1	◆ stem
#1633	128	×1	◆ stem
#1634	128	×1	◆ stem
#1635	128	×1	◆ stem
#1636	128	×1	◆ stem
#1637	128	×1	◆ stem
#1638	128	×1	◆ stem
#1639	128	×1	◆ stem
#1640	128	×1	◆ stem
#1641	128	×1	◆ stem
#1642	128	×1	◆ stem
#1643	128	×1	◆ stem
#1644	128	×1	◆ stem
#1645	128	×1	◆ stem
#1646	128	×1	◆ stem
#1647	128	×1	◆ stem
#1648	128	×1	◆ stem
#1649	128	×1	◆ stem
#1650	128	×1	◆ stem
#1651	128	×1	◆ stem
#1652	128	×1	◆ stem
#1653	128	×1	◆ stem
#1654	128	×1	◆ stem
#8436	256	×2
#8437	256	×2
#8438	256	×2
#8439	256	×2
#8440	256	×2
#8441	256	×2
#8442	256	×2
#8443	256	×2
#8444	256	×2
#8445	256	×2
#8446	256	×2
#8447	256	×2
#8448	256	×2
#8449	256	×2
#8450	256	×2
#8451	256	×2
#8452	256	×2
#8882	256	×2
#8883	256	×2
#8884	256	×2
#8885	256	×2
#8886	256	×2
#8887	256	×2
#8888	256	×2
#8889	256	×2
#8890	256	×2
#8891	256	×2
#8892	256	×2
#8893	256	×2
#8894	256	×2
#8895	256	×2
#8896	256	×2
#8897	256	×2
#8898	256	×2
#8899	256	×2
#8900	256	×2
#8901	256	×2
#8902	256	×2
#8903	256	×2
#8904	256	×2
#8905	256	×2
#8906	256	×2
#8907	256	×2
#8908	256	×2
#8909	256	×2
#8920	256	×2
#8921	256	×2
#8922	256	×2
#8923	256	×2
#8924	256	×2
#8925	256	×2
#8926	256	×2
#8927	256	×2
#8928	256	×2
#8929	256	×2
#8930	256	×2
#8931	256	×2
#8932	256	×2
#8933	256	×2
#8934	256	×2
#8935	256	×2
#8936	256	×2
#8969	256	×2
#8970	256	×2
#8971	256	×2
#8972	256	×2
#8973	256	×2
#8974	256	×2
#8975	256	×2
#8976	256	×2
#8977	256	×2
#8978	256	×2
#8979	256	×2
#8980	256	×2
#8981	256	×2
#8982	256	×2
#8983	256	×2
#8984	256	×2
#8985	256	×2
#8986	256	×2
#8987	256	×2
#8988	256	×2
#8989	256	×2
#8990	256	×2
#8991	256	×2
#8992	256	×2
#8993	256	×2
#8994	256	×2
#8995	256	×2
#8996	256	×2
#9053	256	×2
#9054	256	×2
#9055	256	×2
#9056	256	×2
#9057	256	×2
#9058	256	×2
#9059	256	×2
#9060	256	×2
#9061	256	×2
#9062	256	×2
#9063	256	×2
#9064	256	×2
#9065	256	×2
#9066	256	×2
#9067	256	×2
#9068	256	×2
#9069	256	×2
#9070	256	×2
#18480	256	×2
#18485	256	×2
#18494	256	×2
#18503	256	×2
#18510	256	×2
#18515	256	×2
#18516	256	×2
#18517	256	×2
#18518	256	×2
#18519	256	×2
#18520	256	×2
#18521	256	×2
#18522	256	×2
#18523	256	×2
#97658	512	×4
#97659	512	×4
#97660	512	×4
#97661	512	×4
#97662	512	×4
#97663	512	×4
#97664	512	×4
#97665	512	×4
#97666	512	×4
#97667	512	×4
#99337	512	×4
#99338	512	×4
#99339	512	×4
#99340	512	×4
#99341	512	×4
#99342	512	×4
#99343	512	×4
#99344	512	×4
#99345	512	×4
#99346	512	×4
#99439	512	×4
#99440	512	×4
#99441	512	×4
#99442	512	×4
#99443	512	×4
#99444	512	×4
#99445	512	×4
#99446	512	×4
#99447	512	×4
#99448	512	×4
#99449	512	×4
#99450	512	×4
#99451	512	×4
#99452	512	×4
#99453	512	×4
#99454	512	×4
#99503	512	×4
#99504	512	×4
#99505	512	×4
#99506	512	×4
#99507	512	×4
#99508	512	×4
#99509	512	×4
#99510	512	×4
#99511	512	×4
#99512	512	×4
#99513	512	×4
#99514	512	×4
#99515	512	×4
#99516	512	×4
#99517	512	×4
#99518	512	×4
#99595	512	×4
#99596	512	×4
#99597	512	×4
#99598	512	×4
#99599	512	×4
#99600	512	×4
#99601	512	×4
#99602	512	×4
#99603	512	×4
#99604	512	×4
#107046	512	×4
#107047	512	×4
#107048	512	×4
#107049	512	×4
#107050	512	×4
#107051	512	×4
#107052	512	×4
#107053	512	×4
#107054	512	×4
#107055	512	×4
#107056	512	×4
#107057	512	×4
#107058	512	×4
#107059	512	×4
#107060	512	×4
#107061	512	×4
#107062	512	×4
#107063	512	×4
#107064	512	×4
#107065	512	×4
#107066	512	×4
#107067	512	×4
#107068	512	×4
#107069	512	×4
#107070	512	×4
#107071	512	×4
#107072	512	×4
#107073	512	×4
#108334	512	×4
#108335	512	×4
#108336	512	×4
#108337	512	×4
#108338	512	×4
#108339	512	×4
#108340	512	×4
#108341	512	×4
#108342	512	×4
#108343	512	×4
#108344	512	×4
#108345	512	×4
#108346	512	×4
#108347	512	×4
#108348	512	×4
#108349	512	×4
#108350	512	×4
#108351	512	×4
#109971	512	×4
#109972	512	×4
#109973	512	×4
#109974	512	×4
#109975	512	×4
#109976	512	×4
#109977	512	×4
#109978	512	×4
#109979	512	×4
#109980	512	×4
#109981	512	×4
#109982	512	×4
#109983	512	×4
#109984	512	×4
#109985	512	×4
#109986	512	×4
#109987	512	×4
#109988	512	×4
#109989	512	×4
#109990	512	×4
#109991	512	×4
#109992	512	×4
#109993	512	×4
#109994	512	×4
#109995	512	×4
#109996	512	×4
#109997	512	×4
#109998	512	×4
#110012	512	×4
#110013	512	×4
#110014	512	×4
#110015	512	×4
#110016	512	×4
#110017	512	×4
#110018	512	×4
#110019	512	×4
#110020	512	×4
#110021	512	×4
#110022	512	×4
#110023	512	×4
#110024	512	×4
#110025	512	×4
#110026	512	×4
#110027	512	×4
#110028	512	×4
#110163	512	×4
#110164	512	×4
#110165	512	×4
#110166	512	×4
#110167	512	×4
#110168	512	×4
#110169	512	×4
#110170	512	×4
#110171	512	×4
#110172	512	×4
#110173	512	×4
#110174	512	×4
#110175	512	×4
#110176	512	×4
#110177	512	×4
#110178	512	×4
#110179	512	×4
#129514	512	×4
#129535	512	×4
#129541	512	×4
#129550	512	×4
#129653	512	×4
#129654	512	×4
#129679	512	×4
#135819	512	×4
#135831	512	×4
#135836	512	×4
#135838	512	×4
#135855	512	×4
#135856	512	×4
#135863	512	×4
#135866	512	×4
#135867	512	×4
#135872	512	×4
#135873	512	×4
#135878	512	×4
#135880	512	×4
#135896	512	×4
#135898	512	×4
#135901	512	×4
#135903	512	×4
#135916	512	×4
#135918	512	×4
#136575	512	×4
#136583	512	×4
#136591	512	×4
#136621	512	×4
#136649	512	×4
#136650	512	×4
#136659	512	×4
#136660	512	×4
#136669	512	×4
#136670	512	×4
#136711	512	×4
#136712	512	×4
#136745	512	×4
#136746	512	×4
#136757	512	×4
#136758	512	×4
#136769	512	×4
#136779	512	×4
#136789	512	×4
#136799	512	×4
#186491	512	×4
#186562	512	×4
#186601	512	×4
#186605	512	×4
#186608	512	×4
#186610	512	×4
#186611	512	×4
#186612	512	×4
#186613	512	×4
#192594	512	×4
#192599	512	×4
#192604	512	×4
#192609	512	×4
#192610	512	×4
#192611	512	×4
#192612	512	×4
#192613	512	×4
#192614	512	×4
#192615	512	×4
#192616	512	×4
#192617	512	×4
#192850	512	×4
#192902	512	×4
#192958	512	×4
#193180	512	×4
#193184	512	×4
#193187	512	×4
#193189	512	×4
#193190	512	×4
#193191	512	×4
#193192	512	×4
#193328	512	×4
#193387	512	×4
#193914	512	×4
#193974	512	×4
#193979	512	×4
#193984	512	×4
#193989	512	×4
#193990	512	×4
#193991	512	×4
#193992	512	×4
#193993	512	×4
#193994	512	×4
#193995	512	×4
#193996	512	×4
#193997	512	×4
#194294	512	×4
#194366	512	×4
#195474	512	×4
#195546	512	×4
#195550	512	×4
#195553	512	×4
#195555	512	×4
#195556	512	×4
#195557	512	×4
#195558	512	×4
#195559	512	×4
#195762	512	×4
#210188	512	×4
#210189	512	×4
#210190	512	×4
#210191	512	×4
#210192	512	×4
#210193	512	×4
#210260	512	×4
#210261	512	×4
#210262	512	×4
#210263	512	×4
#210264	512	×4
#210265	512	×4
#210266	512	×4
#210267	512	×4
#6348067	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.