Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C5×D3×M32 |
| Fitting | C3×C5×M32 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×M32 |
| Sylow | C3 ⋊ C2×C5×M32 |
180 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×#347, D3×#64732, C5×#69087, … |
| maximal normal subgroup of | C5×D3×#347, D3×#64732, C5×#69087, … |
| maximal quotient of | C5×D3×#346, C5×Dic3×M32, C5×#69071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4600);