Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×S5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C2×D3×S5 |
| unambiguous semidirect product | (C3×S5)⋊C22 |
| unambiguous semidirect product | ΓL(2,𝔽4)⋊C22 |
| unambiguous semidirect product | (D3×A5)⋊C22 |
| Fitting | C2×C3 ⋊ C2×S5 |
| socle | C2×C3×A5 ⋊ C22 |
| derived | C3×A5 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×S5 |
| commutator, cosocle, hypocenter | C3×A5 | C23 |
| Frattini | C1 | G |
| Fitting | C2×C3 | C2×S5 |
| socle | C2×C3×A5 | C22 |
| LCS | G ▷ C3×A5 | |
| UCS | C1 ◁ C2 | |
471 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 471 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 30 |
42 conjugacy classes — view the full character table.
| maximal subgroup of | S52, C2×#72219548, D3×C22⋊S5, … |
| maximal normal subgroup of | D3×C22⋊S5, C22×D3×S5 |
| maximal quotient of | D3×C22⋊S5, D32×S5, C2×D3×#11757163⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5849);