Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of ((C24⋊C5)⋊C2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×((C24⋊C5)⋊C2)⋊C3 |
| unambiguous semidirect product | ((C24⋊C5)⋊C2)⋊C32 |
| unambiguous semidirect product | AGL(1,𝔽16)⋊(C2×C3) |
| unambiguous semidirect product | (C3×(C24⋊C5)⋊C2)⋊C3 |
| Fitting, socle | C24×C3 ⋊ C3×D5 |
| derived | C24⋊C5 ⋊ C2×C32 |
| Hall | (C24⋊C5)⋊C2 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | ((C24⋊C5)⋊C2)⋊C3 |
| commutator, cosocle, hypocenter | C24⋊C5 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C24×C3 | C3×D5 |
| LCS | G ▷ C24⋊C5 | |
| UCS | C1 ◁ C3 | |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
42 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(2,𝔽4), C3×AΓL(1,𝔽16), #72241555, … |
| maximal normal subgroup of | C3×AΓL(1,𝔽16), #72241555, D3×((C24⋊C5)⋊C2)⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5862);