Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C8×D5×D9 |
| Fitting | C5×C8×C9 ⋊ C22 |
| derived, Hall | C5×C9 ⋊ C22×C8 |
| Sylow | C9 ⋊ C2×C8×D5 |
| Sylow | C5 ⋊ C2×C8×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D5×D9 |
| commutator, hypocenter | C5×C9 | C22×C8 |
| Frattini | C3×C4 | C2×D3×D5 |
| Fitting | C5×C8×C9 | C22 |
| socle | C2×C3×C5 | C2×C4×D3 |
| prime radical | C2×D5×D9 | C4 |
| cosocle | C4×C5×C9 | C23 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C8 | |
228 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 360 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 322);