Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #41×D45 |
| Fitting | C5×C9×#41 ⋊ C2 |
| Hall | C5×C9 ⋊ C2×#41 |
| Sylow | C9 ⋊ D5×#41 |
| Sylow | C5 ⋊ #41×D9 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D45 |
| commutator, cosocle | C2×C5×C9 | C24 |
| Frattini | C2×C3 | C23×D15 |
| Fitting | C5×C9×#41 | C2 |
| socle | C2×C3×C5 | C23×D3 |
| hypercenter | #41 | D45 |
| hypocenter | C5×C9 | C2×#41 |
| LCS | G ▷ C2×C5×C9 ▷ C5×C9 | |
| UCS | C1 ◁ C4 ◁ #41 | |
492 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 155 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.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1671);