Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C2×C3×#4022 |
| Fitting | C2×C3×C42×C5 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×#126 |
| Sylow | C5 ⋊ C2×C3×#126 |
492 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10601578, C3×#10601622, #14281437, … |
| maximal normal subgroup of | C3×#10601578, C3×#10601622, #14281437, … |
| maximal quotient of | C2×C3×#65226, C2×C3×#65222, C2×C3×#65229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9684);