Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×D3×Q32 |
| Fitting | C3×C5×Q32 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×Q32 |
| Sylow | C3 ⋊ C2×C5×Q32 |
164 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×SD64, D3×#64741, C5×D3×Q64, … |
| maximal normal subgroup of | C5×D3×SD64, D3×#64741, C5×D3×Q64, … |
| maximal quotient of | C5×D3×#358, C5×D3×#366, C5×#69207, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4611);