Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210 |
| direct product | C23×C3×D3×D5 |
| unambiguous semidirect product | (C5×D3)⋊(C24×C3) |
| unambiguous semidirect product | (C3×D5)⋊(C24×C3) |
| unambiguous semidirect product | D15⋊(C24×C3) |
| Fitting, socle | C23×C32×C5 ⋊ C22 |
| derived | C3×C5 ⋊ C25×C3 |
| Hall | C32×C5 ⋊ C25 |
| Sylow | C32 ⋊ C24×D5 |
| Sylow | C5 ⋊ C24×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3 | D3×D5 |
| commutator, cosocle, hypocenter | C3×C5 | C25×C3 |
| Frattini | C1 | G |
| Fitting, socle | C23×C32×C5 | C22 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C23×C3 | |
3126 conjugacy classes of subgroups; only the 1048 normal subgroups are shown.
This group has 3126 conjugacy classes of subgroups — too many to draw. Only its 1048 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×D32×D5, C23×C3×D3×AGL(1,𝔽5), C23×D3×ΓL(1,𝔽16) |
| maximal normal subgroup of | C23×D32×D5, C23×C3×D3×AGL(1,𝔽5), C23×D3×ΓL(1,𝔽16) |
| maximal quotient of | C3×D5×#1004 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5946);