Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×D4×C3⋊D15 |
| Fitting | C2×C32×C5×D4 ⋊ C2 |
| Hall | C32×C5 ⋊ C22×D4 |
| Sylow | C32 ⋊ C2×D4×D5 |
| Sylow | C5 ⋊ C2×D4×C3⋊D3 |
1416 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1416 conjugacy classes of subgroups — too many to draw. Only its 287 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 360 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×D5×C3⋊D3, #120×C3⋊D15, #72230223, … |
| maximal normal subgroup of | C2×D4×D5×C3⋊D3, #120×C3⋊D15, #72230223, … |
| maximal quotient of | #120×C3⋊D15, C2×D4×C3⋊(C3⋊(C5⋊D5)), #127×C3⋊D15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5824);