Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26 |
| direct product | C22×C5×GO+(4,𝔽2) |
| unambiguous semidirect product | #157⋊(C23×C5) |
| unambiguous semidirect product | D32⋊(C23×C5) |
| Fitting, socle | C22×C32×C5 ⋊ D4 |
| Hall | C32×C5 ⋊ C22×D4 |
| Sylow | C32 ⋊ C22×C5×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | GO+(4,𝔽2) |
| commutator, cosocle | C3⋊D3 | C24×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C5 | D4 |
| hypocenter | C32 | C22×C5×D4 |
| LCS | G ▷ C3⋊D3 ▷ C32 | |
| UCS | C1 ◁ C22×C5 | |
740 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C5×AΓL(1,𝔽9), C22×C3×C5×GO+(4,𝔽2) |
| maximal normal subgroup of | C22×C5×AΓL(1,𝔽9), C22×C3×C5×GO+(4,𝔽2) |
| maximal quotient of | C22×C3×C5×GO+(4,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5919);