Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | D3×C22⋊#168 |
| Hall | C3×C5 ⋊ C2×C22⋊C8 |
| Sylow | C5 ⋊ D3×C22⋊C8 |
| Sylow | C3 ⋊ C2×C22⋊#168 |
404 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#64688, D3×#64745, D3×#64689, … |
| maximal normal subgroup of | D3×#64688, D3×#64745, D3×#64689, … |
| maximal quotient of | D3×#64745, D3×#64748, #14280824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2684);