Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#41×D9 |
| Fitting | C5×C9×#41 ⋊ C2 |
| Hall | C5×C9 ⋊ C2×#41 |
| Sylow | C9 ⋊ C2×C5×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | C22×D9 |
| commutator, cosocle | C2×C9 | C24×C5 |
| Frattini | C2×C3 | C23×C5×D3 |
| Fitting | C5×C9×#41 | C2 |
| socle | C2×C3×C5 | C23×D3 |
| hypercenter | C5×#41 | D9 |
| hypocenter | C9 | C2×C5×#41 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C4×C5 ◁ C5×#41 | |
492 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 360 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1656);