Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D3×(C2×D3)⋊AGL(1,𝔽5) |
| Hall | C32×C5 ⋊ C2×C22⋊C4 |
| Sylow | C32 ⋊ C2×C22⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ D3×(C2×D3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D32×AGL(1,𝔽5) |
| commutator, Fitting, socle | C2×C32×C5 | C22×C4 |
| prime radical | C2×D32×D5 | C2 |
| cosocle | C2×C32×D5 | C23 |
| hypocenter | C32×C5 | C2×C22⋊C4 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 | |
562 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽5)×#67, D3×#67⋊AGL(1,𝔽5), #72230047, … |
| maximal normal subgroup of | D3×AGL(1,𝔽5)×#67, D3×#67⋊AGL(1,𝔽5), #72230047, … |
| maximal quotient of | #72269803, #72269807 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4721);