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 64: every member's order is a multiple of it, and the members attaining it — the stem groups — are marked ◆.

7,552 groups of the catalog are in this class; the 500 smallest with no abelian direct factor are listed.

group	order	× stem
#447	64	×1	◆ stem
#448	64	×1	◆ stem
#449	64	×1	◆ stem
#450	64	×1	◆ stem
#451	64	×1	◆ stem
#452	64	×1	◆ stem
#459	64	×1	◆ stem
#460	64	×1	◆ stem
#461	64	×1	◆ stem
#462	64	×1	◆ stem
#463	64	×1	◆ stem
#464	64	×1	◆ stem
#474	64	×1	◆ stem
#475	64	×1	◆ stem
#476	64	×1	◆ stem
#477	64	×1	◆ stem
#478	64	×1	◆ stem
#479	64	×1	◆ stem
#480	64	×1	◆ stem
#481	64	×1	◆ stem
#482	64	×1	◆ stem
#483	64	×1	◆ stem
#484	64	×1	◆ stem
#485	64	×1	◆ stem
#1480	128	×2
#1481	128	×2
#1482	128	×2
#1483	128	×2
#1484	128	×2
#1485	128	×2
#1486	128	×2
#1487	128	×2
#1488	128	×2
#1489	128	×2
#1490	128	×2
#1491	128	×2
#1570	128	×2
#1571	128	×2
#1572	128	×2
#1573	128	×2
#1574	128	×2
#1581	128	×2
#1582	128	×2
#1583	128	×2
#1584	128	×2
#1585	128	×2
#1586	128	×2
#1587	128	×2
#1588	128	×2
#1786	128	×2
#1787	128	×2
#1788	128	×2
#1789	128	×2
#1802	128	×2
#1803	128	×2
#1804	128	×2
#1805	128	×2
#1806	128	×2
#1823	128	×2
#1824	128	×2
#1825	128	×2
#1826	128	×2
#1852	128	×2
#1853	128	×2
#1854	128	×2
#1855	128	×2
#1862	128	×2
#1863	128	×2
#1864	128	×2
#1865	128	×2
#1866	128	×2
#1871	128	×2
#1872	128	×2
#1873	128	×2
#1874	128	×2
#1875	128	×2
#1876	128	×2
#1877	128	×2
#1878	128	×2
#1879	128	×2
#1880	128	×2
#1918	128	×2
#1919	128	×2
#1920	128	×2
#1921	128	×2
#1922	128	×2
#1925	128	×2
#1926	128	×2
#1927	128	×2
#1928	128	×2
#1929	128	×2
#1947	128	×2
#1948	128	×2
#1949	128	×2
#1950	128	×2
#1980	128	×2
#1981	128	×2
#1982	128	×2
#1983	128	×2
#1986	128	×2
#1987	128	×2
#1988	128	×2
#1989	128	×2
#3002	128	×2
#3035	128	×2
#3076	128	×2
#3091	128	×2
#3100	128	×2
#3101	128	×2
#3102	128	×2
#3103	128	×2
#3104	128	×2
#3105	128	×2
#3106	128	×2
#3107	128	×2
#3108	128	×2
#7869	256	×4
#7870	256	×4
#7877	256	×4
#7878	256	×4
#7879	256	×4
#7880	256	×4
#7883	256	×4
#7884	256	×4
#7887	256	×4
#7888	256	×4
#7893	256	×4
#7894	256	×4
#7895	256	×4
#7896	256	×4
#7901	256	×4
#7902	256	×4
#7903	256	×4
#7904	256	×4
#8172	256	×4
#8173	256	×4
#8174	256	×4
#8175	256	×4
#8180	256	×4
#8181	256	×4
#8182	256	×4
#8183	256	×4
#8186	256	×4
#8189	256	×4
#8192	256	×4
#8193	256	×4
#8196	256	×4
#8197	256	×4
#8202	256	×4
#8203	256	×4
#8204	256	×4
#8205	256	×4
#8210	256	×4
#8211	256	×4
#8212	256	×4
#8213	256	×4
#8270	256	×4
#8277	256	×4
#8278	256	×4
#8279	256	×4
#8288	256	×4
#8289	256	×4
#8290	256	×4
#8291	256	×4
#8296	256	×4
#8297	256	×4
#8310	256	×4
#8311	256	×4
#8312	256	×4
#8563	256	×4
#8564	256	×4
#8565	256	×4
#8566	256	×4
#8706	256	×4
#8707	256	×4
#8708	256	×4
#8829	256	×4
#8830	256	×4
#8831	256	×4
#8843	256	×4
#8844	256	×4
#8845	256	×4
#8846	256	×4
#8937	256	×4
#8938	256	×4
#8939	256	×4
#8940	256	×4
#8945	256	×4
#8946	256	×4
#8947	256	×4
#8948	256	×4
#9533	256	×4
#9534	256	×4
#9535	256	×4
#9536	256	×4
#9541	256	×4
#9542	256	×4
#9543	256	×4
#9544	256	×4
#9601	256	×4
#9602	256	×4
#9603	256	×4
#9673	256	×4
#9674	256	×4
#9675	256	×4
#9864	256	×4
#9865	256	×4
#9866	256	×4
#10730	256	×4
#10731	256	×4
#10732	256	×4
#10733	256	×4
#10734	256	×4
#10788	256	×4
#10789	256	×4
#10790	256	×4
#10791	256	×4
#10806	256	×4
#10807	256	×4
#10808	256	×4
#10809	256	×4
#10849	256	×4
#10850	256	×4
#10851	256	×4
#10852	256	×4
#10853	256	×4
#10884	256	×4
#10885	256	×4
#10886	256	×4
#10887	256	×4
#10907	256	×4
#10908	256	×4
#10909	256	×4
#10910	256	×4
#10911	256	×4
#10931	256	×4
#10932	256	×4
#10933	256	×4
#10934	256	×4
#11582	256	×4
#11583	256	×4
#11606	256	×4
#11607	256	×4
#11614	256	×4
#11615	256	×4
#11622	256	×4
#11623	256	×4
#11630	256	×4
#11631	256	×4
#11638	256	×4
#11639	256	×4
#11997	256	×4
#12005	256	×4
#12014	256	×4
#12016	256	×4
#12018	256	×4
#12038	256	×4
#12049	256	×4
#12050	256	×4
#12053	256	×4
#12056	256	×4
#12057	256	×4
#12060	256	×4
#12063	256	×4
#12683	256	×4
#12787	256	×4
#12848	256	×4
#12914	256	×4
#12917	256	×4
#12978	256	×4
#12980	256	×4
#13106	256	×4
#13122	256	×4
#13163	256	×4
#13193	256	×4
#13265	256	×4
#17443	256	×4
#17447	256	×4
#17458	256	×4
#17462	256	×4
#17803	256	×4
#17806	256	×4
#17863	256	×4
#17868	256	×4
#17900	256	×4
#17901	256	×4
#17902	256	×4
#17903	256	×4
#17904	256	×4
#17910	256	×4
#17911	256	×4
#17912	256	×4
#17913	256	×4
#20597	256	×4
#20645	256	×4
#20699	256	×4
#20732	256	×4
#20733	256	×4
#20734	256	×4
#20735	256	×4
#20736	256	×4
#20737	256	×4
#20747	256	×4
#20843	256	×4
#20872	256	×4
#20908	256	×4
#20924	256	×4
#21032	256	×4
#21058	256	×4
#21113	256	×4
#21114	256	×4
#21115	256	×4
#21116	256	×4
#21117	256	×4
#21118	256	×4
#21119	256	×4
#21120	256	×4
#21137	256	×4
#21169	256	×4
#21257	256	×4
#21311	256	×4
#21358	256	×4
#21359	256	×4
#21360	256	×4
#21361	256	×4
#21362	256	×4
#21370	256	×4
#21382	256	×4
#21385	256	×4
#21386	256	×4
#21387	256	×4
#21388	256	×4
#21389	256	×4
#21390	256	×4
#21466	256	×4
#21517	256	×4
#21592	256	×4
#21627	256	×4
#60536	256	×4
#94885	512	×8
#94886	512	×8
#94887	512	×8
#94888	512	×8
#94889	512	×8
#94890	512	×8
#94891	512	×8
#94892	512	×8
#94904	512	×8
#94905	512	×8
#94906	512	×8
#94907	512	×8
#96688	512	×8
#96689	512	×8
#96690	512	×8
#96691	512	×8
#96692	512	×8
#96693	512	×8
#96694	512	×8
#96695	512	×8
#96700	512	×8
#96701	512	×8
#96702	512	×8
#96703	512	×8
#96716	512	×8
#96717	512	×8
#96718	512	×8
#96719	512	×8
#96896	512	×8
#96898	512	×8
#96899	512	×8
#96902	512	×8
#96903	512	×8
#96906	512	×8
#96907	512	×8
#105269	512	×8
#105270	512	×8
#105275	512	×8
#105276	512	×8
#105281	512	×8
#105286	512	×8
#105287	512	×8
#105292	512	×8
#105293	512	×8
#105346	512	×8
#105347	512	×8
#105350	512	×8
#105351	512	×8
#105354	512	×8
#105355	512	×8
#105358	512	×8
#105359	512	×8
#105362	512	×8
#105365	512	×8
#105368	512	×8
#105369	512	×8
#105372	512	×8
#105373	512	×8
#105668	512	×8
#105669	512	×8
#105672	512	×8
#105674	512	×8
#105675	512	×8
#105678	512	×8
#106220	512	×8
#106221	512	×8
#106224	512	×8
#106226	512	×8
#106227	512	×8
#106230	512	×8
#106232	512	×8
#106233	512	×8
#106236	512	×8
#108418	512	×8
#108419	512	×8
#108422	512	×8
#108424	512	×8
#108425	512	×8
#108428	512	×8
#109082	512	×8
#109083	512	×8
#109086	512	×8
#109088	512	×8
#109089	512	×8
#109092	512	×8
#109094	512	×8
#109095	512	×8
#109098	512	×8
#109478	512	×8
#109479	512	×8
#109482	512	×8
#109484	512	×8
#109485	512	×8
#109488	512	×8
#109546	512	×8
#109547	512	×8
#109550	512	×8
#109552	512	×8
#109553	512	×8
#109556	512	×8
#109558	512	×8
#109559	512	×8
#109562	512	×8
#110303	512	×8
#110304	512	×8
#110307	512	×8
#110309	512	×8
#110310	512	×8
#110313	512	×8
#123447	512	×8
#123448	512	×8
#123449	512	×8
#123450	512	×8
#123451	512	×8
#126565	512	×8
#126570	512	×8
#126580	512	×8
#126624	512	×8
#126634	512	×8
#126644	512	×8
#126670	512	×8
#126676	512	×8
#126678	512	×8
#126725	512	×8
#126727	512	×8
#126741	512	×8
#126743	512	×8
#126757	512	×8
#126759	512	×8
#126795	512	×8
#126797	512	×8
#126807	512	×8
#126809	512	×8
#126819	512	×8
#126821	512	×8
#128254	512	×8
#128266	512	×8
#128277	512	×8
#128287	512	×8
#128518	512	×8
#128520	512	×8
#128539	512	×8
#128541	512	×8
#128547	512	×8
#128549	512	×8
#128559	512	×8
#128561	512	×8
#128621	512	×8
#128623	512	×8
#128629	512	×8
#128631	512	×8
#128641	512	×8
#128643	512	×8
#128647	512	×8
#128649	512	×8
#128659	512	×8
#128661	512	×8
#128677	512	×8
#128679	512	×8
#128683	512	×8
#128685	512	×8

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.