Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C24 |
| direct product | C2×C5×D3×S4 |
| unambiguous semidirect product | (C3×S4)⋊(C22×C5) |
| unambiguous semidirect product | (C3⋊S4)⋊(C22×C5) |
| unambiguous semidirect product | (D3×A4)⋊(C22×C5) |
| Fitting, socle | C23×C3×C5 ⋊ C2×D3 |
| derived | C3×A4 ⋊ C23×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D3×S4 |
| commutator, cosocle, hypocenter | C3×A4 | C23×C5 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C5 | C2×D3 |
| LCS | G ▷ C3×A4 | |
| UCS | C1 ◁ C2×C5 | |
544 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 90 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#5935, C2×D3×D5×S4, D3×S4×AGL(1,𝔽11), … |
| maximal normal subgroup of | C2×D3×D5×S4 |
| maximal quotient of | D3×S4×AGL(1,𝔽11) |
| automorphism group of | C22×D3×C11, C3×C11×A4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5899);