Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×Dic3×D15 |
| derived, Hall | C32×C5 ⋊ C2×C42 |
| Sylow | C32 ⋊ C42×D5 |
| Sylow | C5 ⋊ C4×D3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D3×D15 |
| commutator, hypocenter | C32×C5 | C2×C42 |
| Frattini | C22 | C2×D3×D15 |
| Fitting | C2×C32×C4×C5 | C22 |
| socle, cosocle | C22×C32×C5 | C23 |
| prime radical | C22×C3×D15 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C2×C4 | |
462 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3704);