Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×C3⋊D3×C22⋊D5 |
| Fitting | C23×C32×C5 ⋊ C22 |
| Hall | C32×C5 ⋊ C22×D4 |
| Sylow | C32 ⋊ C22×C22⋊D5 |
| Sylow | C5 ⋊ C2×D4×C3⋊D3 |
1416 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 1416 conjugacy classes of subgroups — too many to draw. Only its 240 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 360 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×D5×C3⋊D3, C3⋊D3×#4083, C3⋊D3×#4099, … |
| maximal normal subgroup of | C2×D4×D5×C3⋊D3, C3⋊D3×#4083, C3⋊D3×#4099, … |
| maximal quotient of | C3⋊D3×#4083, C3⋊D3×#4099, C2×C3⋊D3×C22⋊(C5⋊D5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5621);