Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C3⋊((C24⋊C5)⋊C2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×C3⋊((C24⋊C5)⋊C2) |
| unambiguous semidirect product | C3⋊(C3×(C24⋊C5)⋊C2) |
| Fitting, socle | C24×C32 ⋊ D5 |
| derived | C3×C24⋊C5 ⋊ C2×C3 |
| Sylow | C32 ⋊ (C24⋊C5)⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊((C24⋊C5)⋊C2) |
| commutator, cosocle, hypocenter | C3×C24⋊C5 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C32 | D5 |
| LCS | G ▷ C3×C24⋊C5 | |
| UCS | C1 ◁ C3 | |
189 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5905);