Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | A4×#689 |
| unambiguous semidirect product | (C22×#689)⋊C3 |
| Hall | C22×#689 ⋊ C3 |
| Sylow | C5 ⋊ A4×Q16 |
146 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | S4×#689, #14513327, #14513328, … |
| maximal normal subgroup of | S4×#689, #14513327, #14513328, … |
| maximal quotient of | A4×#3939, A4×#3942, #10615432⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6385);