Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D32×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×D32×D5 |
| unambiguous semidirect product | (C3×D3×D5)⋊C23 |
| unambiguous semidirect product | (D5×C3⋊D3)⋊C23 |
| unambiguous semidirect product | (D3×D15)⋊C23 |
| Fitting, socle | C22×C32×C5 ⋊ C23 |
| derived, Hall | C32×C5 ⋊ C25 |
| Sylow | C32 ⋊ C24×D5 |
| Sylow | C5 ⋊ C23×D32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D32×D5 |
| commutator, cosocle, hypocenter | C32×C5 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C5 | C23 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
3126 conjugacy classes of subgroups; only the 628 normal subgroups are shown.
This group has 3126 conjugacy classes of subgroups — too many to draw. Only its 628 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D32×AGL(1,𝔽5), C2×D5×#3811, C2×#13088405, … |
| maximal normal subgroup of | C22×D32×AGL(1,𝔽5), C2×D5×#3811, C2×#13088405, … |
| maximal quotient of | C2×D5×#3811, D32×D4×D5, D5×#64330, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5924);