Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of A4×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C2 |
| direct product | A4×C3⋊#168 |
| unambiguous semidirect product | C3⋊(A4×#168) |
| unambiguous semidirect product | (C22×C3⋊#168)⋊C3 |
| derived | C22×C3×C5 ⋊ C3×C8 |
| Sylow | C5 ⋊ A4×C3⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | A4×D15 |
| commutator, hypocenter | C22×C3×C5 | C3×C8 |
| Fitting, cosocle | C22×C3×C4×C5 | C2×C3 |
| socle | C23×C3×C5 | C3×C4 |
| prime radical | C2×C3×C5×A4 | C4 |
| LCS | G ▷ C22×C3×C5 | |
| UCS | C1 ◁ C4 | |
116 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 360 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2554);