Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | #41×C3⋊D15 |
| Fitting | C32×C5×#41 ⋊ C2 |
| Hall | C32×C5 ⋊ C2×#41 |
| Sylow | C32 ⋊ D5×#41 |
| Sylow | C5 ⋊ #41×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×C3⋊D15 |
| commutator, socle, cosocle | C2×C32×C5 | C24 |
| Frattini | C2 | C23×C3⋊D15 |
| Fitting | C32×C5×#41 | C2 |
| hypercenter | #41 | C3⋊D15 |
| hypocenter | C32×C5 | C2×#41 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C4 ◁ #41 | |
984 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 257 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, 5830);