Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C3⋊#672 |
| unambiguous semidirect product | (C2×C3)⋊(C3×#672) |
| derived | C3×C5 ⋊ C2×C3×C16 |
| Hall | C32×C5 ⋊ C2×C16 |
| Sylow | C32 ⋊ C2×#672 |
| Sylow | C5 ⋊ C2×C3×C3⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C8 | D15 |
| commutator, hypocenter | C3×C5 | C2×C3×C16 |
| Frattini | C8 | C2×C3×D15 |
| Fitting | C2×C32×C5×C8 | C2 |
| socle, prime radical | C22×C32×C5 | C8 |
| cosocle | C3×C5×C8 | C22×C3 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C3×C8 | |
134 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1329);