Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C22×C3×#686 |
| Fitting | C22×C3×C5×D4 ⋊ C2 |
| Hall | C3×C5 ⋊ C22×D8 |
| Sylow | C5 ⋊ C22×C3×D8 |
676 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 254 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10601001, C3×#10600965, C3×#10602406, … |
| maximal normal subgroup of | C3×#10601001, C3×#10600965, C3×#10602406, … |
| maximal quotient of | C22×C3×#3941, C22×C3×#3964, C22×C3×#3939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9998);