Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×C4×D45 |
| Fitting | C22×C4×C5×C9 ⋊ C2 |
| derived, Hall | C5×C9 ⋊ C23×C4 |
| Sylow | C9 ⋊ C22×C4×D5 |
| Sylow | C5 ⋊ C22×C4×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D45 |
| commutator, hypocenter | C5×C9 | C23×C4 |
| Frattini | C2×C3 | C23×D15 |
| Fitting | C22×C4×C5×C9 | C2 |
| socle | C23×C3×C5 | C2×D3 |
| prime radical | C23×D45 | C2 |
| cosocle | C2×C5×C9 | C24 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C22×C4 | |
708 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 253 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1662);