Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of A4×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×A4×D15 |
| unambiguous semidirect product | (C22×C4×D15)⋊C3 |
| Fitting | C22×C3×C4×C5 ⋊ C2×C3 |
| derived | C22×C3×C5 ⋊ C2×C3×C4 |
| Sylow | C5 ⋊ C4×D3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | A4×D15 |
| commutator, hypocenter | C22×C3×C5 | C2×C3×C4 |
| Frattini | C2 | C2×A4×D15 |
| Fitting | C22×C3×C4×C5 | C2×C3 |
| socle, cosocle | C23×C3×C5 | C22×C3 |
| prime radical | C2×A4×D15 | C2 |
| LCS | G ▷ C22×C3×C5 | |
| UCS | C1 ◁ C4 | |
276 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5429);