Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10623663 |
| Hall | C5×C9 ⋊ C2×#41 |
| Sylow | C9 ⋊ C2×#709 |
| Sylow | C5 ⋊ C2×#3697 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D5×D9 |
| commutator, cosocle | C2×C5×C9 | C24 |
| Frattini | C2×C3 | C22×D3×D5 |
| Fitting | C2×C4×C5×C9 | C22 |
| socle | C22×C3×C5 | C22×D3 |
| hypocenter | C5×C9 | C2×#41 |
| LCS | G ▷ C2×C5×C9 ▷ C5×C9 | |
| UCS | C1 ◁ C2×C4 | |
492 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1579);