Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C2 |
| direct product | C3⋊C8×A5 |
| unambiguous semidirect product | C3⋊(C8×A5) |
| derived | C3×A5 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×A5 |
| commutator, hypocenter | C3×A5 | C8 |
| Fitting, cosocle | C3×C4 | C2×A5 |
| socle, prime radical | C2×C3×A5 | C4 |
| LCS | G ▷ C3×A5 | |
| UCS | C1 ◁ C4 | |
103 conjugacy classes of subgroups; only the 14 normal subgroups are shown.
This group has 103 conjugacy classes of subgroups — too many to draw. Only its 14 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1688);