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 ◆.

893 groups of the catalog are in this class; the 765 with an abelian direct factor are hidden.

group	order	× stem
#1655	128	×1	◆ stem
#1656	128	×1	◆ stem
#1657	128	×1	◆ stem
#1658	128	×1	◆ stem
#1659	128	×1	◆ stem
#1660	128	×1	◆ stem
#1661	128	×1	◆ stem
#1662	128	×1	◆ stem
#1663	128	×1	◆ stem
#1664	128	×1	◆ stem
#8504	256	×2
#8505	256	×2
#8506	256	×2
#8507	256	×2
#8508	256	×2
#8509	256	×2
#8910	256	×2
#8911	256	×2
#8912	256	×2
#8913	256	×2
#8914	256	×2
#8915	256	×2
#8916	256	×2
#8917	256	×2
#8918	256	×2
#8919	256	×2
#8997	256	×2
#8998	256	×2
#8999	256	×2
#9000	256	×2
#9001	256	×2
#9002	256	×2
#9003	256	×2
#9004	256	×2
#9005	256	×2
#9006	256	×2
#9007	256	×2
#9008	256	×2
#18984	256	×2
#18987	256	×2
#18990	256	×2
#18991	256	×2
#97000	512	×4
#97001	512	×4
#97002	512	×4
#97003	512	×4
#99325	512	×4
#99326	512	×4
#99327	512	×4
#99328	512	×4
#99329	512	×4
#99330	512	×4
#99535	512	×4
#99536	512	×4
#99537	512	×4
#99538	512	×4
#99539	512	×4
#99540	512	×4
#107352	512	×4
#107353	512	×4
#107354	512	×4
#107355	512	×4
#107356	512	×4
#107357	512	×4
#107358	512	×4
#107359	512	×4
#107360	512	×4
#107361	512	×4
#107362	512	×4
#107363	512	×4
#107364	512	×4
#107365	512	×4
#109999	512	×4
#110000	512	×4
#110001	512	×4
#110002	512	×4
#110003	512	×4
#110004	512	×4
#110005	512	×4
#110006	512	×4
#110007	512	×4
#110008	512	×4
#110009	512	×4
#110010	512	×4
#110011	512	×4
#110103	512	×4
#110104	512	×4
#110105	512	×4
#110106	512	×4
#110107	512	×4
#110108	512	×4
#110109	512	×4
#110110	512	×4
#110111	512	×4
#129656	512	×4
#129672	512	×4
#135858	512	×4
#135862	512	×4
#135869	512	×4
#135875	512	×4
#136747	512	×4
#136759	512	×4
#136770	512	×4
#136780	512	×4
#136790	512	×4
#136800	512	×4
#187578	512	×4
#187609	512	×4
#187611	512	×4
#193018	512	×4
#193021	512	×4
#193022	512	×4
#193023	512	×4
#193108	512	×4
#193148	512	×4
#194424	512	×4
#194474	512	×4
#194477	512	×4
#194478	512	×4
#194479	512	×4
#194480	512	×4
#194481	512	×4
#194610	512	×4
#210388	512	×4
#210389	512	×4
#210390	512	×4
#210391	512	×4
#6351371	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.