Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of Dic90 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×#67099 |
| Fitting | C24×C5×C9 ⋊ C2 |
| Hall | C5×C9 ⋊ C22×D4 |
| Sylow | C9 ⋊ C22×C22⋊D5 |
| Sylow | C5 ⋊ C22×#611 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D45 |
| commutator, cosocle | C2×C5×C9 | C24 |
| Frattini | C2×C3 | C23×D15 |
| Fitting | C24×C5×C9 | C2 |
| socle | C23×C3×C5 | C2×D3 |
| hypercenter | C24 | D45 |
| hypocenter | C5×C9 | C22×D4 |
| LCS | G ▷ C2×C5×C9 ▷ C5×C9 | |
| UCS | C1 ◁ C23 ◁ C24 | |
708 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
372 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1675);