Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×A5⋊Q8 |
| unambiguous semidirect product | A5⋊(C3×Q8) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C2×S5 |
| commutator, cosocle | C2×A5 | C22×C3 |
| Frattini | C2 | C2×C3×S5 |
| Fitting, hypercenter | C3×C4 | S5 |
| socle, prime radical | C2×C3×A5 | C22 |
| hypocenter | A5 | C3×Q8 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2×C3 ◁ C3×C4 | |
157 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 157 conjugacy classes of subgroups — too many to draw. Only its 18 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
57 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4619);